A scientific principle often ignored in media:
- When an object undergoes a proportional increase in size, its new volume is proportional to the cube of the multiplier and its new surface area is proportional to the square of the multiplier.
For example, if you double the size (measured by edge length) of a cube, its surface area is quadrupled (2^2 = 4), and its volume is increased to eight times its original volume (2^3 = 8).
The point of this law is that with living beings, strength is (more or less) a function of area (the strength of a muscle or bone is proportional to the area of its cross-section, not to its total volume), but weight is a function of volume. And Newton's famous Second Law (the "force = mass × acceleration" one) means that if you double a critter's height while keeping it the same shape, you end up with four times the muscle power moving eight times the mass, so instead of having the same relative agility as the original, the double-sized creature actually has only half. The same goes for most machinery.
This applies to flyers as well: Double the size, and you get four times the wingpower attempting to keep eight times the weight airborne, so the creature's ability to fly has actually been cut by half. Helicopters are hit particularly hard by this law; the largest payload of a cargo helicopter is about 20 tons, versus the world's largest airplane, with a payload of 275 tons. Sorry, Hotelicopter.
Airships, on the other hand, benefit greatly from the square/cube law, as even small increases in size can quickly increase the volume of buoyant gas they can carry. Take the Graf Zeppelin and its successornote the Graf Zeppelin ll for example. The original Graf was 776 feet in length. The Graf ll was a mere 30 feet larger in any direction, but carried double the volume. Because these gains came at almost no increased structural weight, the returns went entirely into making the Graf ll an even more palatial flying cruise liner than her predecessor.
Buoyancy in general, whether it be in the air or in the water, is an easy way to minimize the limitations of the square-cube law when increasing size, because buoyancy is dependent on density, not mass. Good news for the whales, then.
This law is relevant when an object is shrunk down as well. Make something half its size and it will have roughly twice the proportional strength and endurance. This is why small animals, like ants, are able to carry things far heavier than themselves, part of how fleas can manage to jump so far relative to their size, and why cats can survive falls of effectively any height — get small enough and your terminal velocity will be a survivable speed. However, don't think this is all win for the Incredible Shrinking Man, who will likely not survive to enjoy his newfound strength. Since body heat production is at least partially proportionate to volume, while heat loss is dependent on surface area exposed to the air, a shrunk human will find they are dissipating heat faster than their body produces it. It won't be long until the shrunk human freezes to death, even during a summer day. (This, incidentally, is why shrews eat their body weight in food and hummingbirds live on sugary nectar — their little bodies need to produce a lot of heat and this requires high-energy diets.)
A full explanation for the biological aspect is a lot more complicated due to subtler factors (muscle/bone stress, required oxygen uptake, dissipating body heat, etc.), but the gist of it is the same in every case: You can't just scale something up (or down) to a different size and expect it to still work the same way as it used to.
Again, the law is not limited to living creatures, but applies to anything with mass (and, well, everything has mass): A skyscraper twice as wide and tall as another will have eight times the weight, and require a far stronger support structure — wood and brick just can't hold the weight (traditional wood, that is). This is why modern skyscrapers were impossible until steel could be mass-produced to build their frames. Likewise, the humanoid Humongous Mecha needs incredibly strong legs to hold its massive frame upright (probably some sort of Unobtainium), and that's not even considering how the ground beneath it also needs to be able to support that same amount of weight without caving in, or the fact that it needs some incredibly powerful motors just to get those powerful legs and arms moving (which is why we call them Impossibly Graceful Giants).
Knowing that audiences are becoming more savvy about this as compared to the days when Attack of the 50-Foot Whatever and the Incredible Shrinking Man were safe, standard plots, many creators who knowingly break the law will try to invent some Artistic License – Physics to justify or Hand Wave how their creation can get away with breaking it — say, the Applied Phlebotinum didn't just change their size, but also does something else to sustain their new size and counter the Law's negative effects upon them.
See Attack of the 50-Foot Whatever, Humongous Mecha, and Ridiculously Small Wings for examples of media ignoring the Square-Cube Law. Sometimes justified by the use of Required Secondary Powers. Compare Muscles Are Meaningless and Pintsized Powerhouse. Compare/Contrast Giant Equals Invincible, where the law can either debunk or justify the trope (as a giant creature super-strong and massively-durable enough to simply withstand its own weight and be able to move with any reasonable efficiency would logically be able to shrug off far more damage than something smaller). Do not confuse with Scaled Up — though the trope name may sound familiar, Scaled Up involves a serpentine transformation that usually completely ignores the laws of physics, anyway.
- 20th Century Boys:
- Lampshaded when Friend's cult tries to have a giant bipedal robot built, and the engineer they get shoots down most of their ideas as impossible. On the eve of the new millennium, they end up using a fake robot that was just two crawler tread "legs" supporting a zeppelin with a cover and metal frame over it.
- Towards the end of the series, that same engineer manages to pull it off. Though this version is at least slightly more plausible, as it's not humanoid, but rather something that looks like a cross between a frog and a chicken with the legs connected at the sides for better weight distribution. The robot is also primarily remote controlled, since, while it does have a cockpit inside, operating it manually is rendered nearly impossible due to severe motion sickness induced by its uneven gait.
- Lampshaded in Attack on Titan in a bit of Expo Speak concerning the Titans' Bizarre Alien Biology — they're actually much lighter than something that big has any right to be, yet still hit with the force of displacement you'd expect if their weight was proportional to their size. This is far from the only thing about them that makes no sense, and humans know it.
- Interestingly, the flagship Titan for the series (the Colossal Titan) follows the Law better than its smaller counterparts; since it is exceptionally massive even by other Titan's standards, its anatomy has changed in order to better support its massive frame. It has no skin and proportionally tiny arms and head to cut down on excess mass, while its torso and legs are extremely large and well muscled in order to support its frame. It is also almost never seen doing anything other than standing in one spot and kicking something, so it doesn't normally have to worry about the bodily stresses it would undergo by ambulating.
- A later Titan would show up to be even larger than the Colossal, and was incapable of even standing upright. Its arms were underdeveloped, while its head and body were massive. The best it could do was slowly drag itself along the ground.
- In Black Bullet, the monstrous Gastrea are explicitly described as inverting this principle: they are based on small animals, mostly insects, with their size drastically increased, but instead of being too weak to support their own weight, they are that many times 'stronger' proportional to their size than the original animals.
- Pow's One-Winged Angel form enlarges him greatly, until he becomes kaiju sized, and the first thing he does is to complain about his newfound massive weight.
- Averted by Gerard Valkyrie of the Wandenreich whose "The Miracle" ability increases his size, strength and speed accordingly so that it makes him gigantic while making him even faster.
- Justified in Cannon God Exaxxion, where the titular colossus has a gravity control device powered by Antimatter. It also addresses the problem of weight distribution on the feet by replacing them with invisible forcefields that distribute the machine's (still considerable, even when mitigated by gravity control) weight over a wider area, which has the unfortunate side-effect of flattening innocent bystanders who are dozens of feet away from the mech itself.
- Dragon Ball:
- The franchise has a few characters that can grow in size, or are already gigantic compared to normal people. A Saiyan can become a massive ape monster called an Oozaru if they have their tail and see a full moon. For these characters, they already have superhuman strength, and growing larger boosts that strength somehow, Oozaru multiplies Saiyan strength 10-fold, so they can survive their size. The issue of bulky muscles becomes a plot point in the Cell saga. The Saiyans develop a Super Saiyan form that is muscular to the point they look like oversized bodybuilders (do a Google image search for Super Saiyan Third Grade and you'll get an idea from the first few pictures). It grants major strength, but at the cost of mobility, making the form useless, not to mention that it is very inefficient at energy consumption and quickly wears out the user.
- Given that the characters by this point have enough physical strength to level mountains with a flick of the wrist, it seems odd that a slightly higher body mass would make such a huge difference. This, of course, is overcome when the Super Saiyan 2 form is reached, where strength and speed increase proportionally and with less drain on stamina.
- Franken Fran: Mentioned and briefly explained by Fran, when she witnesses the 50 foot sea monster that is terrorizing the city. Hand waved as Fran remembers her lost master talking about how dinosaur DNA is one of the most obscure scientific mysteries — and that she is renowned for making even more impossible creatures than herself.
- Full Metal Panic! hangs a lampshade on this fact; although it glosses over the existence of relatively small Humongous Mecha, an extremely huge example appears on the villains' side in one episode, and accordingly a character points out that it ought to collapse under its own weight. When the particular bit of Applied Phlebotinum which prevents this is destroyed, it indeed does so. Bonus points for the mecha not simply falling over; rather, its legs rupture and collapse outwards under the weight.
- On the subject of mecha anime, New Getter Robo hangs a lampshade in the final episode. When the final boss grows into a planet-sized form, Hayato and Benkei respond:
Benkei: Whoa, look at how big it's gotten!
Hayato: No way. At that size, it should be collapsing from the sheer pressure of its own weight!
- Giant Robo: Ginrei Special has one robot whose weight was 2/3 armor, and needed to use its Jet Pack just to stay standing up.
- Yoshiyuki Tomino originally wanted to avoid this in Mobile Suit Gundam, with all the battles taking place in space, but eventually broke down and had the middle third of the series set on Earth. His novelizations are almost entirely set in space, though. Likewise, supplementary material notes that half the reason for Zeon's massive arms race throughout the series was in part because the Zaku was well-suited for space combat, but ended up being plodding enough that infantry with anti-mobile suit missiles could easily take them on in a gravity-affected environment.
- Mobile Fighter G Gundam generally has issues with scaling weight up linearly from human to massive robot; with their given weight figures in that series, the average Gundam is made of material with the density of styrofoam.
- Later Gundam shows hand wave this trope. Starting in Mobile Suit Zeta Gundam, the mechs are built out of stronger, lighter materials. In addition, the Gundam Mk. II is built using Movable Frame technology that further lightens the weight by incorporating all the internal systems into, and all the armor* directly onto, the skeletal frame of the suit, allowing for more agile and more human-like movement. That technology becomes more common and, eventually, the standard. After Char's Counterattack, the technology is streamlined and miniaturized, resulting in mechs that are shorter, yet far more powerful than the earlier models. This, not coincidentally, made the new model kits smaller and cheaper to produce at the same scale.
- Zeta Gundam also had the absolutely gigantic Psyco Gundam, which really shouldn't have been able to walk on Earth. This is lampshaded the first time it shows up, with the characters wondering how in the hell that thing doesn't crush itself under its own weight. The Psyco Gundam in fact needs its own Minovsky Drive like the White Base to support it's own immense mass.
- Gyo obeys the law — while the walkers that carry fish up to the size of Great White Sharks can walk around on land just fine, a walker carrying a whale lumbers out of the ocean, only for its legs to immediately collapse under the weight of the whale, without any water to support it.
- Mentioned briefly by Koizumi in Haruhi Suzumiya when he's showing Kyon a Celestial/Shinjin/Avatar tearing up a section of Closed Space. He notes that the giant should be unable to support its own weight, but also that the laws of physics in general simply don't seem to apply to them.
- Discussed extensively in Heaven's Design Team when the team tries to deal with a rampaging creation by modifying a gorilla. First, they double its size, causing it to collapse of heat stroke since the internal body heat it generates get increased thanks to its much larger volume. Then, the team shaves its fur and gives it a cockscomb as a cooling element to resolve the heat issue, the creature collapses again because its leg broke.
Mars: Increasing the height by 2 increases the weight by 8 times, but only increases the bone thickness by 4 times. Its bones can't support its weight.
- Howl's Moving Castle is explicitly only able to stand up because of magic. When the magic was taken out of the "castle," it immediately collapsed under its own weight.
- In Kuromukuro, we have two ways to avoid this issue in regards to giant robots — one is that the most common used robots are Mini-Mecha not bigger than a tank. The other is that the actual Humongous Mecha utilize technology that allows them to manipulate gravity, which handwaves all the problems regarding the law.
- Another Humongous Mecha series that avoids this problem is Kenran Butousai, which takes place on a terraformed Mars that has been almost completely flooded. The mechs are more like giant diving suits.
- Mazinger Z: Go Nagai had this trope in mind when he created Mazinger-Z. When the anime was being made he insisted the cartoon-makers that Mazinger WAS heavy and HAD to look heavy, so they used shots low shots to make Mazinger seeming bigger and imposing, and it moved slowly and noisily. And even though Go Nagai had always intended that Mazinger-Z flew, he was afraid of making Mazinger seeming light if it flew from the start. So he held back the appearance of the Jet Scrander until that it was well established that Mazinger was heavy. Still it moves too quick to be so heavy.
- In Miss Kuroitsu from the Monster Development Department, when Wolf bête suggests increasing the size of their monster by 25x, Kuroitsu does the calculations about how much more mass and materials it would require, noting the square-cube law (working out that it would take 15,625x the material), then calculates the additional costs, and shows the final cost (over 100 billion yen). After seeing this. Wolf bete concedes the point, looking utterly humiliated.
- This trope is largely averted and ignored by Neon Genesis Evangelion; however, there is a notable justification in the form of the enormous Rei-Lillith hybrid that appears at the climax of The End of Evangelion, which appears to be made out of some sort of weird substance that is halfway between light and matter, the experience of passing through which causes one to go insane.
- Acknowledged/lampshaded in Patlabor: Humanoid-style labors tend to be made with very large feet and small torsos. This trope is mentioned to a certain extent early in the TV series when Kanuka puts a labor through a bunch of stock action movie moves (jumping, flipping, etc). Noa asks Asuma why he's wincing, and he explains that while the new police labor model (the Ingram AVS-98) is technically capable of performing any motion that a human body can (with regards to degrees of freedom), it can't really take much more punishment than standard walking without requiring pretty serious maintenance, and implies that Kanuka's short performance will mean days of work and hundreds (possibly thousands) of dollars in components to bring the labor back to 100% operating capacity.
- Rurouni Kenshin: Kenshin invokes this law during his match with Senkaku. While he's every bit the Lightning Bruiser, Senkaku is more than twice the size of Kenshin, and eventually, his body couldn't take the strain of having all that mass keep up with Kenshin's godlike speed.
- Superheroes like, say, Ant-Man, usually don't even bother giving this a wave. When shrinking, Ant-Man maintains the strength of a regular human despite his size, and when growing, his size is "Proportionate" (as strong as the writer needs it to be). Heck, all size-changing superheroes seem to be riddled with problems. Despite their fists often being nearly the size of a pinpoint, moving with the force of a superheroic punch, they always seem to hit like a wrecking ball instead of like a knife...
- However, there was at least one early story where Dr. Pym increased his size beyond a certain limit and collapsed, unable to move and needed The Wasp's help to shrink him back down to a reasonable size again.
- A note should be made about the new Ant-Man (Eric O'Grady): he does try to take advantage of his proportionate strength to punch out a guy (to impress a woman), but doesn't realize that his punch is more like a bullet than a hammer.
- Marvel Universe heroes use "Pym Particles" to grow and shrink, so there's an extra layer of Phlebotinum keeping it working. DC's The Atom, on the other hand, knows that shrinking is dangerous — it's even been made into a plot point and weapon, as seen in Justice League: The New Frontier (The Atom can alter his mass independently of his size, so it's less of an issue for him).
- In a Marvel What If? one-shot featuring a Soviet Fantastic Four, Pym (fighting for the USA) died from suffocation when Reed forced him to grow, rendering his lungs incapable of supplying enough oxygen to sustain him. Reed did this in an attempt to incapacitate him without considering the consequences, and afterward he was horrified by what he'd done.
- In Hank Pym's first appearance as Giant-Man, Marvel Comics played the Law quite accurately — after he's grown a few feet, he's no longer capable of standing and needs the Wasp's help just to get at a reversal pill. He pegs his maximum effective size as twelve feet or so, and sticks to it for a while. The limitation didn't last long, though — soon he was fighting giant monsters at Godzilla size!
- The Ultimates version of Hank Pym can grow to just under sixty feet, as according to his wife, 60ft is the point at which the human skeleton can no longer support its own mass (later generic Giant-Men manage to surpass this, with no mention as to how). His ability is reverse-engineered from Jan's ability to shrink, and she mentions that she can't shrink smaller than an inch because her body automatically knows what its limits are.
- It's eventually revealed that Pym Particles don't just work on size, they affect strength (this trope) and density as well. It turns out a few other superhumans have powers that apply Pym Particles in this manner.
- Given a nod in the original Guardians of the Galaxy. Yellowjacket — whom we've only seen shrink up until then — grows to fight Blockade. She wins the fight, but the exertion puts enough strain on her heart that she loses consciousness.
- The movie version of Ant-Man is at least vaguely aware of this trope. Whilst our hero uses 'Pym Particles' to break this law with impunity, the villain's attempts to recreate the effect on test subjects/victims fail. Messily.
- When Ant-Man and Squirrel Girl team up this trope is not only discussed but utilized against the main villain (an obscure villain from Marvel’s past named Enigmo whose power is the ability to split himself at the cost of his mass) because, while Ant-Man’s Pym Particles allow him to bypass the square cube law, Enigmo does not have any Phlebotinum to help him out in that situation so when all the little Enigmos are tricked into recombining into one giant Enigmo, the first step they take results in them breaking their leg and falling.
- The writers occasionally lampshade this, and there has been at least one Retcon that Spidey is actually stronger than the proportionate strength of a spider — or even simply possessing a spider's strength-to-weight ratio, which is likely what the creators originally meant.
- He has a villain called the Walrus who claims to possess the same strength-to-weight ratio as a walrus. Superdickery pointed out that this would make him weaker than an ordinary human. (The laws of physics were nonetheless basically told to go fuck themselves, as The Walrus indeed turned out to have Super Strength).
- Discussed in Avenging Spider-Man 10 when he uses his physics knowledge to discover that Robyn Hood is going to explode.
- The Incredible Hulk: The Hulk is known to get stronger and larger as he gets angrier (maximum height is roughly twelve feet); this might be justified, though, as his relative muscle (and presumably bone) mass increases as well as his height. Furthermore, Hulk is generally not depicted as merely scaling up; in most depictions, the cross-sections of his arms and legs increase out of proportion, which would balance things out some.
- It's been implied that he draws his strength from outside of his own body, and therefore muscle mass would be irrelevant.
- The size changing as he gets angrier and stronger thing is depending on the writer and the artist; some have his height stay consistent once he transforms, though this itself can be an informed ability as an artist will alter his height between panels for various reasons. Officially the Hulk's transformed height is just under eight feet tall. He'll often be shown as over ten, but that's usually stylistic or for dramatic effect.
- Where Hulk comics fail to justify or avert is in that we frequently see him standing on floors that should not be able to support what his weight must be. Hard wood would splinter under him, for example, as he probably weighs about as much as a four-door car. Floors would take an even greater beating when you realize that all that weight is being concentrated on two relatively small areas.
- The opening Superman vs. the Amazing Spider-Man has a rare aversion. After realizing that the giant robot he's fighting is emitting a special gravity beam, Superman pushes down on it from above, applying enough pressure to negate the beam's effects. The robot quickly collapses into the ground, unable to support its own weight without the assistance of the gravity device.
- Atomic Robo:
- Lampshaded in the comic, where the presence of giant ants has pretty much everyone pointing out that they should be crushed by their own weight, and the only one that doesn't say it's impossible is the guy that thinks it's covered by "imaginary physics" and "imaginary radiation", which would give them laser eyes.
Robo: This is just... there can't be giant insects. They'd crush themselves.
Jenkins: But do THEY know that?
Robo: Probably not, no.
- A giant monster attack in Volume 4 has Robo ask "Why do we even have the Square Cube Law!?"
- Lampshaded in the comic, where the presence of giant ants has pretty much everyone pointing out that they should be crushed by their own weight, and the only one that doesn't say it's impossible is the guy that thinks it's covered by "imaginary physics" and "imaginary radiation", which would give them laser eyes.
- An interesting inversion appears with the superheroine "Micro-Might". Her power is, specifically, to take advantage of the Square-Cube Law — shrinking herself down to half height, but keeping the same mass — to become stronger and tougher. (Okay, so it plays a bit fast-and-loose with the actual equations, but it's still nice to see someone USE the law instead of just ignoring it.)
- When she's forced into Phlebotinum Overload, she becomes so dense that she can't move and can barely speak.
- Likewise, one of the Power Pack kids (whichever one has that power this week) can expand but becomes less dense, eventually turning into a vapor cloud, or can contract into a super-dense mini-tank.
- Fantastic Four:
- A plot point in one story; Reed Richards encounters an alien able to absorb energy to grow to gigantic size and notices that its footprints aren't getting any deeper, so its weight isn't increasing, therefore its mass isn't, either. It's just puffing up like a balloon. So he manages to "overinflate" the alien by feeding it too much energy. Note that the footprints should have actually become shallower if his feet grew and the mass (and thus weight) did not increase, so we will have to assume Reed Richards deemed this bit too trivial to mention (for him to not realize this would be out of character).
- In another story, the Four found themselves on an enormous alien environment with human giants that were many miles tall. Reed Richards thought that what they were seeing was not real, as the human body would be unable to support its own mass if it grew to that height.
- When Gladiator lifted the Baxter Building, Richards theorized that his powers weren't merely physical strength, as there's no way the building could survive being lifted and supported by one of its corners.
- In Ultimate Fantastic Four, Warren Ellis justified Ben Grimm's "Thing" appearance in this way. For Ben to be as strong and durable as he is, his size and weight were correspondingly scaled up to around nine feet tall and eight tons, with super-dense skin and hyper-efficient organs (handy, as Ben sinks like a stone in open water). His mass and strength are so great that the mere act of walking around measures on the Richter Scale, leading Reed to develop a body suit lined with a new type of shock absorber to act as a Power Limiter for Ben. Otherwise, Ben taking a stroll through Times Square could result in the destruction of New York City itself.
- The Official Handbook of the Marvel Universe tried to be scientifically accurate, so it constantly faced this problem, handwaving them away with references to anti-gravitons or similar technobabble that at least suggests that some writer is aware that there's a scientific problem.
- In one issue of Nodwick, this law is specifically addressed by a potion intended to grow people to giant size; specifically, it doesn't increase mass, and as such the 'inability to support own weight' point is moot. Of course, some other problems, like how a fifty-foot tall being weighing one hundred pounds reacts when being exposed to an ambient breeze, immediately present themselves.
- Mentioned in an issue of Planetary dealing with a secret government project that used '50s super-science to turn "undesirables" into, basically, the monsters of '50s horror movies. One guy got the Amazing Colossal Man treatment; he was in pain for the rest of his short existence.
- Discussed in great detail in The Science of Superheroes, with regards to superheroes that are able to make themselves larger or smaller.
- Discussed in the pre-New 52 Jaime Reyes run of Blue Beetle. Since you can't scientifically increase somebody's size past a certain threshold without them falling apart into a pile of bones and blood, magic is always behind giant humans.
- Invoked in the Wonder Woman Vol 1 story arc Judgment In Infinity: When the Adjudicator appears standing beside the Washington Monument—which he's taller than—a woman who was visiting the monument wonders, "But—a man that huge—It's supposed to be scientifically impossible, isn't it?"
- This is the ultimate fate of the Human Flame in Final Crisis Aftermath: Run! - he grows so tall that he literally cannot move, allowing Green Lantern John Stewart to easily take him away.
- Discussed by Shinji in Reconciliation:
Shinji: But seriously, they violate the Square Cube Law to such a ridiculous degree. They literally stand due to being badassery on a gigantic scale, a through no other force but badassery do they do not sink into the ground.
- Discussed in the Deva Series, where it is noted that the Seed can't get much bigger without magical assistance if they want to maintain their power. And since one of their key gimmicks is Anti-Magic protection...
- Lampshaded and handwaved in Nobody Dies; it's quoted in dialog between two subordinate scientists that they can never get Yui to explain why the Evas don't sink into the ground due to their weight, and the current dominant theory is that the ground is too scared of them to let them in.
- In Harmony Theory, due to the reduced amount of ambient magic to support their bodies, dragons have to maintain a reasonable size to survive. Max Cash goads a young and inexperienced dragon named Boomer into giving into greed. This causes him to grow gigantic and powerful, but then his body starts to collapse on itself.
- Children of an Elder God: In the prologue, a scientist finds an arthropod-like, gigantic Eldritch Abomination and wonders how it can support its own weight:
"How... How can that thing support its own weight?"
- Equestria Girls: Friendship Souls: As Ember puts it to Adagio, "mass is mass". A larger Adjuchas might not be anything special in terms of spiritual power, but its larger mass means that its blows can still send a Hollow of greater strength but smaller size flying. Similarly, Soul Reapers, Quincies, and Arrancars only weigh as much as a normal human, so if caught off-guard even an ordinary human can knock them down.
- It's explicitly stated in the series bible for RainbowDoubleDash's Lunaverse that pegasus wings are too small to allow them to fly without their magic.
- For a series that usually is very good about thinking through how even magic has to follow the rules of physics and common sense, the Triptych Continuum really falls down on this one in Scootalift. It's explicitly stated that Snowflake's ability to fly despite the horrible injuries to his wings from a capless birth comes not from pegaus magic, but from his massive muscular development.
- And ultimately, it turns out be both a Subverted Trope and a plot point. Snowflake's flight is directly powered by his talent: he gets in the air because he's determined to fly. (It's the same kind of Surge which allows newborn foals to take off, only under his direct control.) Believing it's been strength all along was a self-imposed delusion.
- Mentioned in A Discordant Note with Velka, a magically created crow the size of an elephant. Harry notes that if not for the magic he used when she was still an egg, it would be impossible for her to fly.
- Kaiju Revolution: According to a Q&A, the Kaiju are able to bypass this thanks to their ability to metabolize radiation which makes them so efficient on a cellular and subatomic level that they exist partially outside of reality.
- Izuku in the first chapter of Quantity of Quirks is five and a half meters tall and built like All-Might. As a result, the boy is so heavy that his footsteps cause tremors and make Mineta bounce in the air. Thankfully, his strength is even more immense, such as throwing his "baseball" (which is the size of a medicine ball) 174 kilometers away.
- Momo in The Emerald Phoenix stands at her canon height of 5'8, very tall for a fifteen-year-old Japanese girl and weighs in at triple of what someone her age and body type should (Her canon weight is never given). This is because her violation of the law is her Required Secondary Power so that her mass can act as fuel to create objects that weigh much more than she should. Luckily for her, it comes with a tertiary power in that she's stronger than she looks, able to lift adult sized robots with one arm.
- Bee Movie famously opens by hanging a great big lampshade on this.
"According to all known laws of aviation, there is no way a bee should be able to fly. Its wings are too small to get its fat little body off the ground. The bee, of course, flies anyway because bees don't care what humans think is impossible."
- In Epic (2013), the tiny scale the Leafmen and Boggans live at reverses the Square/Cube Law, making them Pintsize Powerhouses able to jump crazy far and shrug off falls from cliffs. Of course they don't explain this to the audience at all. For those familiar with the law it's a refreshing accuracy, but one wonders how many kids, who don't even know what a cube is, were left wondered why they good guys seemed so indifferent about throwing people off of birds to their apparent-death all the time.
- Actually hand waved in Monsters vs. Aliens, the 49 foot 11 inch woman is mentioned to have gained Super Strength from the alien meteorite she was hit by. Not that that explains how the roadways can support her weight. Or those cars she used as skates.
- In My Little Pony: A New Generation, it turns out that pegasi can't fly without magic because their wings are presumably too small compared to the rest of their bodies, though they can still glide.
- Tends to handwave away the issues with a human shrinking to ant size, or even to subatomic size, with "Pym particles", though the suit needs to be closed when shrinking to avoid becoming a blob of undifferentiated tissue. Shrunken characters also retain their original strength, but it's inconsistent as to whether their mass is changed.
- Ants can be grown to human-size without ill effects, or even a containment suit, and retain their proportional strength.
- In Captain America: Civil War Scott grows to over 60 feet tall, though he mentions that he passed out the last time he tried that. Scott's arms also move slowly when he attacks in this form, which is true to the square-cube law; every body part of a giant would accelerate slower than the corresponding part of a normal sized human, and simply swatting away a human wouldn't involve moving his arm far enough to reach its maximum potential speed. He also seems noticeably slower mentally, as if he's drunken or light-headed. And in Ant-Man and the Wasp he claims he slept for three days after that scene, after becoming "Giant-Man" in that film he has trouble breathing within a few minutes and collapses, in the middle of a bay. However he has no problems when he's twelve feet tall (aside from ceilings).
- In Avengers: Endgame, Scott becomes Giant Man to save Hulk, War Machine, and Rocket from drowning in the flooded subbasement of the remains of the Avengers HQ, breaking through the bulk of the ruin and joining the final battle in that form. He must have been eating his Wheaties, because he spends at least half the fight at max size, punching Leviathans out of the sky and crushing enemy forces underfoot, and isn't even winded when he reverts to normal size to take care of a special task.
- Arachnid actually discusses the Square-Cube Law, though its brief and hasty explanation of why the titular giant spiders aren't subject to it is unconvincing (something to do with the spiders being of extraterrestrial origin).
- Discussed in the 90's HBO remake of Attack of the 50-Foot Woman — the doctor treating Nancy remarks that at her new size her heart is under tremendous strain due to the change in her mass, and that any undue stress may cause it to give out.
- Invoked in Chappie. The Scout model droids, which the eponymous protagonist is based on, is a human-sized robot which can move and respond faster than the truck-sized Moose which the Big Bad of the film is unsuccessfully trying to press into police service — Scouts are far more suited to close quarter actions and law enforcement. Also, in the finale, Chappie is not only able to outmaneuver the Moose, but outlast it, as the Moose, despite its appearance as an unstoppable juggernaut, is actually lightly armoured for its size due to weight concerns — one of the Scout robots Chappie is based on took an anti-tank rocket to the chest at close range and wasn't getting back up afterwards but only needed some repairs to get working again, while the Moose was severely damaged by smaller anti-personnel grenades and ultimately blown apart by a grenade strapped to a combat knife.
- It's never explained how any of the kaiju in Godzilla films can move, never mind in some cases fly, (though Ghidorah has some Gravity Master powers, so he might get a handwave). The 2014 film does give Godzilla larger and thicker legs to help support his weight, and he moves with an extremely slow gait when he's outside of water.
- Lampshaded in Shin Godzilla when the government initially believes the larval Godzilla will be unable to support its own weight on dry land, only for it to do just that because it's a Metamorphosis Monster.
- On other hand, this also explain why Godzilla and (most of) other Kaijus are extremely durable they're impervious to conventional weaponry. The Kaijus need to be insanely strong to even support their own weight.
- Likewise, The Incredible Shrinking Man film may have averted this, by having Scott slowly shrink giving his body a chance to adapt.
- In Iron Man 2, we see North Korea's attempt at making an Iron Man suit, which appears to be 20-foot-tall machine covered in guns... which immediately falls over because of how thin its legs are to the top-heavy body.
- Kamen Rider J: In a rare case of the law being acknowledged during a piece of Toku media, when J assumes his Jumbo Formation, he gains significantly more strength at the cost of his speed. At the same time, his increased weight per square foot means the ground can visibly be seen cracking and collapsing under his feet when he materialises, and does so for a second time when he jumps into the air to take out Fog Mother's giant form with his Jumbo Rider Kick. Of course, his increased weight probably means he shouldn't be able to jump at all, but that wouldn't satisfy the Rule of Cool.
- Kong: Skull Island: As with most Kaiju-type creatures, a one-hundred foot tall gorilla would be incapable of doing anything besides lying there with his skeleton being crushed by the weight of his musculature, and the flying creatures would be incapable of doing so.
- Giant cockroach movie Mimic hand waves the Square-Cube Law during an autopsy scene, where the entomologist discovers that the Judas Breed has evolved lungs. This explains how they can breathe, but not how a six-foot cockroach with six-foot wings can fly while carrying an adult woman. The issue is simply skipped in the Donald Wollheim story the film was based on: the mimic, a giant moth, is never seen flying and in fact may not be able to fly. Its newly-hatched offspring, the size of very large moths, fly just fine.
- In Pirates of the Caribbean: At World's End, Calypso grows to gigantic size on board the Pearl, yet neither tips the ship over (again), sinks it, nor collapses the decking beneath her weight. Could potentially be handwaved by her goddess powers or something, but it's never explicitly addressed either way.
- Seeing as she bursts into a bunch of crabs a few seconds later, it's safe to say that the laws of physics don't apply to her.
- Likewise, there is no explanation to where all that extra mass would come from, so the total mass of the ship and its contents remain the same (perhaps her density decreases as she grows?)
- Pacific Rim:
- Guillermo del Toro and the effects artists admit that huge beings, robots or monsters alike, would move slowly, but the Kaiju and Jaegers move quickly to make for fun scenes. They do nod to the trope, as the blueprinted robots have different body proportions compared to a humanoid: very large feet, supermodel-like legs, less mass in the upper body.
- Gipsy Danger using a civilian oil tanker as an Improvised Weapon is flatly impossible; it would have buckled under its own weight the minute they dragged it out of the water, let alone started swinging it around like a bat. Of course it looked great, though.
- The Star Wars movies: The Jedi Starfighter seen in Attack of the Clones is very fast and maneuverable, able to evade a homing missile through an asteroid ring. In the original trilogy, the Imperial Star Destroyer has the same basic triangular shape but is a thousand times its size and weight. It moves at a slower rate and is much harder to course-correct (as Han Solo demonstrated in The Empire Strikes Back).
- Transformers: Revenge of The Fallen: Subtle aversion: Devastator, a large, gorilla-like robot made from nine smaller robots combining, is so massive that he cannot stand up straight without risking his legs caving in on themselves. It was for that very reason that the folks at Hasbro and ILM opted to go with the gorilla-walk.
- This even contributes to his death - a single blast from a railgun is enough to damage his leg and knock him off balance, and his weight means that the resulting fall tears him to pieces.
- The same aversion is seen with the other robots in both films. Smaller guys like Bumblebee or Barricade are pretty agile, while the medium-size bots like Ironhide can move, but they aren't that swift. Moving up to Optimus Prime and Megatron, they're clearly focused on power brawling, although Optimus is a Lightning Bruiser.
- In the live-action movie, in truck mode, Optimus became a conventional tractor (one with a hood) instead of his original cab-over design, to give him enough extra mass to get to 30 feet tall when in robot mode, rather than 25 feet like the other Autobots.
- Transformers: Revenge of The Fallen: Subtle aversion: Devastator, a large, gorilla-like robot made from nine smaller robots combining, is so massive that he cannot stand up straight without risking his legs caving in on themselves. It was for that very reason that the folks at Hasbro and ILM opted to go with the gorilla-walk.
- The dragon species created in Duumvirate has wings in its juvenile stage, but loses its ability to fly as it grows up.
- Mentioned in Feet of Clay by Terry Pratchett, regarding how different sizes of animal would end up after a given fall of about two stories — a spider wouldn't notice it, a mouse would walk away, etc.
- In Guards! Guards! almost all the characters realize right away that the dragon can't possibly fly under its own power... unless it's fueling itself with magic. The descriptions specifically point out that its flight looks completely unrealistic compared to a bird's, because it's actually magically levitating itself.
- Discworld's gnomes are also terrifyingly strong, despite being six inches tall, and able to knock a man out and break bones with a headbutt or otherwise — because they have the strength of a grown man, concentrated in a very small area. Said gnomes also possess all of a grown man's bad temper concentrated into that same space, which makes the above acts of violence not only possible but also fairly probable.
- The Nac Mac Feegle seem considerably stronger than an average man, given that they steal cows by picking them up and carrying them off, one Feegle to a hoof. For an average-sized cow, that means they're each lifting in the vicinity of 400 pounds, and carrying it at a dead run.
- They're actually mostly shown stealing sheep, and even a large full grown sheep would be about 350 pounds — about 87 pounds. Still a lot to carry at a run, but slightly less fantastic.
- Surprisingly averted in the Diadem series by John Peel. There are only two flying mythological creatures seen: a sphinx and a dragon. The sphinx is rather small and has enormous wings. In series genius Pixel realizes the large dragon breaks the square/cube law and surmises it flies some other way. They then discover the dragon flies under the same principle as a hot air balloon. Pixel puts the flames out and the dragon crashes.
- Star Trek novels:
- Justified in the Star Trek: Voyager novel Ragnarok, where Chakotay explicitly notes that the creatures in question must have evolved in a low-gravity environment.
- In the Star Trek: The Next Generation novel Metamorphosis, Data at one point encounters something flying on wings that couldn't possibly hold it. This bothers him only briefly before he decides, after all the impossible things he's seen in the rest of this mission, why not?
- Made a plot point in the City of Heroes book "The Web of Arachnos". The massive army of robots are defeated when they're unable to do things the smaller bots were able to do due to their size, which leads one of the two creators to yell at the other for forgetting the Square-Cube law and going for Rule of Cool/Intimidating over practical.
- Noted in The BFG: a cook scales up a meal to the giant's scale based on his height, rather than his mass. The giant is not impressed.
- Discussed in Perdido Street Station — the Construct Council is a Humongous Mecha, but cannot actually stand up. Presumably it's just done to look impressive.
- Pointed out in Everworld when the characters encounter a wolf bigger than an elephant. Since the wolf is Fenrir, a godlike being from Norse Mythology, normal laws of physics don't apply to it.
- Jalil also point out (while watching a dragon fly) that the it can't possibly be capable of flight. He's quite put out that physics isn't working the way it's supposed to, and later forms a working theory that the gods edited the physical laws when they left our universe and created the Everworld universe, forming a personal goal to take a look at the 'source code.'
- Animorphs: when the Animorphs run into the Helmacrons Shrink Ray, they find themselves able to toss around pebbles as big as themselves, while Tobias (to them, now a hawk the size of a human) notes that he can flap faster and climb proportionally higher, and might even be able to carry one of them. Evidently the shrink ray also reduces mass along with size.
- In Gene Wolfe's Book of the New Sun, giants eventually get large enough that they have to live in the water, where they grow to truly immense sizes. The narrator is quite shocked to find out that the giant he meets (on land) is nowhere near full grown.
- In Stan Lee's Riftworld!, the giants are supported by a telekinetic field, which has the side benefit of making them Immune to Bullets.
- A plot point in Danny Dunn And The Smallifying Machine. In learning to walk at 1/4 inch high, the accidentally-shrunken characters have difficulty adjusting to their reduced weight; falling, they hit the (much closer) ground almost before they've realized they've tripped, but suffer no injuries due to lack of mass. Difficulty coping with the surface tension of water is also addressed.
- This trope originally bit David Weber on the butt, with the Honor Harrington series. The warships, with their original lengths, had a density exceeded by that of smoke.
- In Orson Scott Card's Ender's Shadow series, Bean has a genetic disorder that causes his brain to continue growing as an infant's does, giving him extreme intelligence, at the cost of causing his body to continue growing as well, leading to a projected lifespan of about eighteen years. Since the problem is caused by gravity, he eventually leaves in a relativistic spacecraft with controllable gravity, so that he can possibly survive until a cure is found. Said cure is found for his children, but not in time for Bean, who Died Standing Up after having to lie down for five years due to his now four-and-a-half-meters-tall body.
- In one of the I Was a Sixth Grade Alien books the characters are shrunk to about seven inches and quickly discover that this has not affected their strength or mass after trying to get off a desk they attempt jumping down onto a open drawer and snap right through it.
- In Stanisław Lem's Fiasco, humongous mechas obey the laws of physics. Inertia, for example, is applied realistically: to stop or turn around with a giant mecha, you need a lot of space, just like with a battleship. Sudden movements would lead to great structural damage to itself, so the controls are designed in a way to limit the maximum acceleration of actuators depending on the load the appendages have to bear.
- And again in Peace on Earth, where the main character, Ijon Tichy, explores the surface of the Moon with the help of remote-controlled robots, the largest of which give him an impression of being merged in some thick liquid.
- The short story giANTS actively weaponized the law to deal with mutant South American army ants (specifically, stuck in the nomadic phase and heading north). Genetic Engineering Is the New Nuke indeed.
- Dragonriders of Pern:
- Dragon bones are specifically mentioned as a very different and much stronger material than Terran animals' bones, and larger dragons don't move much when they don't need to. Then again, they are alien enough to generate lots of concentrated phosphine without any harm.
- Likewise, The Dragonlover's Guide To Pern shows that the skeletal structure of a dragon is very different from any Terran animal's. The design looks like it allows for a greater distribution of weight.
- Of course, this trope suggests that their skeletal structure (and other anatomy) should also be very different from that of their native fire lizard cousins...
- Then to go along with the telepathy and teleportation powers of the dragons it was revealed that they have telekinesis as well, so at least part of their flight is likely a result of self-directed telekinesis to augment their wings.
- It was implied that there were once natural dragons on Pern, and that the fire lizards are either descendants of them or have a common ancestor, so it makes sense they would keep an unnecessarily complex body structure despite their smaller size (see the human appendix and whale leg bones).
- Deliberately used in The Dresden Files novel Small Favor, where Harry is fighting a twenty-foot-tall fairie hitman with a car-sized sword, battle armor, and hefty anti-magic defenses. He manages to get said hitman chasing him over a patch of waxed floor and changes direction, causing the faerie to fall over and mangle himself in the impact. He's not overwhelmingly injured (being a faerie and thus very resistant) but it smarts like hell.
- Addressed in the Harry Potter books with Rubeus Hagrid — he is a half-giant, quoted to be two times as tall as a regular man and nearly five times as wide, having the weight of 1,000 to 1,500 pounds. If you try to be as large as a Kodiak bear raised on the hind legs, having the body structure (and presumably the muscular strength) of a Kodiak bear helps a lot. Even better when your 7 days a week job is mostly physical labor around Hogwarts lands. In the movies, however, they aimed for a height of 8'6" (about 259 cm), of course towering over any human, but certainly not "twice as high." They do, however, give him an appropriate girth for his new scaled-down height (Robbie Coltrane's real proportions).
- In There Is No Darkness, the protagonist is an enhanced human — well over two meters, 180 kilograms — and when in a fight against an enhanced bear that outmasses him by a ridiculous margin, realizes square-cubes applies.
- In his novella The Forgotten Planet, Murray Leinster plays this very straight in his presentation of a world in which insects have grown to enormous sizes, such as ants two feet long and spiders with yard-long legs, based on fossil records of actually giant insects, and are at the outer limit of what cube-square effects allow. But other insects, such as water striders, are no larger than normal, as gigantism would destroy them.
It's also explicitly said the gigantic size of the insects was due to a specific combination of factors which had to match exactly for them to evolve: atmosphere very humid and very rich in oxygen, thick clouds keeping constant warmth via greenhouse effect, huge quantities of nutrients available due to gigantic sizes attained by fungi. The key of the heroes survival is simply climbing to a plateau with temperate climate — the mere coolness of a temperate night renders the giant insects motionless and vulnerable.
- The short story Surface Tension, by James Blish, deals with a race of microscopic humanoids, and does a good job of showing physics on such a scale — for example, the surface of the pond they live in is an (almost) impenetrable barrier, and they can actually "sled" on the thermocline (the dividing line between warm surface water and deeper, cooler water) in some seasons.
- Immanuel Velikovsky studied ancient legends and concluded that other planets were responsible for global catastrophes here on Earth. Among other notions, Venus was once a comet ejected from Jupiter responsible for the Biblical plagues of Egypt, and Earth once orbited Saturn and the Biblical flood was caused by Saturn going nova and also ejecting Earth to its current orbit. Scientists everywhere rolled their eyes and dismissed him entirely because everything he suggested violated every understanding of planetary physics, as well as conservation of energy and angular momentum. However, he did influence a portion of the American public, some of whom latched onto the notion that the only reason dinosaurs could exist was because of lessened gravity on Earth's surface due to the presence of Saturn in the sky. One author inspired by Velikovsky correctly stated that a human of saurian dimensions would collapse under his own weight and die, then incorrectly reasoning that dinosaurs couldn't possibly have survived.
- In Cruel Zinc Melodies, the Big Creepy-Crawlies that were created from normal insects keep running into problems with their magically-increased size, as when a giant beetle tries to take flight from a rooftop and winds up splattered on the pavement.
- In S. Andrew Swann's Dragons of the Cuyahoga, there is a bubble of magic over Cleveland thanks to a semi-permanent magic portal open in the city, allowing dragons, elves, magic spells and other "fuzzy gnome" phenomena to flourish. The novel opens with one of said dragons fooled into flying out of the bubble and into our world where the square/cube law rules supreme. The results are... messy. Murder via reality.
- The book Gulliver's Travels nods to this law; the Lilliputans realise that since Gulliver is proportioned the same as they are but is 12 times the height, he is therefore 1,728 times the bulk and thus needs that much more food. However, it also ignores the fact that if the Lilliputans were really human-proportioned but 6 inches tall, they would rapidly freeze to death. The book also ignores the fact that the Brobdingnagians could not possibly exist because they should collapse under their own weight, despite the narration pointing out that they are as large compared to Gulliver as he is to the Lilliputians.
- In The Name of the Wind, Kvothe and Denna discuss this as they figure out a way to stop the Draccus; Kvothe mentions that it would probably take only a fall of about ten feet to kill the thing.
- The premise of H. G. Wells' The Food of the Gods is that growth goes in fits and spurts because of certain factors in the bloodstream of growing animals, or the sap of plants, which are depleted and have to be replenished before the next spurt of growth occurs. When two protagonists synthesise a Food containing the missing factors (which are the same for all species), the result is giant animals and plants (humans given the Food grow to typically forty feet high) which however suffer no loss of agility or other consequences of their giant size.
- The Dromi in Mikhail Akhmanov's Arrivals from the Dark series are a race of Lizard/Fish People (they're more amphibian than lizard) who continue growing in size and mass as they age. The clans are ruled by Adipose Rex-like elders who eventually are eventually crushed by the weight of their own bodies. Curiously, none of them tries to survive by living on a spaceship with the Artificial Gravity turned down/off.
- A Song of Ice and Fire
- It obeys the law with its roughly-12-to-14-foot giants, who have a body shape that is compared to bears; disproportionately large feet on the ends of short, thick legs, and wider hips than chests, bringing their centre of gravity right down.
- The series averts this trope with the dragons, which can grow to enormous sizes and are still able to fly perfectly well. However, there has been shown to be some connection between live dragons and the magical powers in the world, so it's possible the dragons get some magic-fueled exemption from this law. Also, really large dragons do obey the law, to an extent. The largest known dragon, Balerion the Black Dread, grew into such an gargantuan size that he had difficulty keeping himself afloat; his last rider, King Viserys I Targaryen, was only able to ride him to circle King's Landing before the dragon had to rest.
- It's also averted with The Wall, a man-made border which separates the Seven Kingdoms with the uncharted northern lands. It's 213 meters (700 feet) high, and built entirely on ice. While making the TV show, the author recognized that such a huge ice structure would simply be impossible to maintain itself. Once again, however, it can be argued that it was built with the help of magic (keep in mind there is supposed to be a horn that, when played, will make the structure collapse).
- The Stormlight Archive: Greatshells are a variety of arthropod that can reach the size of small islands. It's justified both by the planet's lower gravity and by a symbiosis with mandras, Nature Spirits that manipulate gravity to offset the greatshell's weight.
- Vin in Mistborn: The Original Trilogy takes advantage of this effect. Burning pewter grants her Super Strength but does not physically alter her 5-foot-nothing body. This allows her to jump several times her own height using nothing but her super-strong legs.
- In the same work, the koloss start out at the size of a human and keep growing their entire life. They are hyper violent and thus tend not to live a particularly long time, but the rare ones who survive long enough to grow to ten or twelve feet tall eventually die from heart failure.
- In Mercedes Lackey's Valdemar books, it is stated that Gryphons can only fly because of magic — their wings are too small to lift a body with their mass. They were designed with special organs to gather and channel ambient magical energy, and in an area with little or no such, they can't fly.
- Invoked in the Cordwainer Smith story 'Golden the Ship Was — Oh! Oh! Oh!'. The golden ships are 90 million miles long and move enormously fast. In reality, they are just giant bubbles, with sensor-fooling equipment to make them look solid.
- Invoked in Shadow of Doubt as Salli and Ali watch their culture's version of a Kaiju movie. Salli complains that such a creature shouldn't be able to move, and Ali responds that the aliens who made it, "... laugh at the Square-Cube Law!"
- Applied in Jarosław Grzędowicz's Pan Lodowego Ogrodu (Lord of the Ice Garden): the protagonist stumbles upon artificially created dragons that, due to the square/cube law being in effect, cannot move effectively and starve to death; then he finds an entire boneyard of dragon bones. The creator of said dragons later goes around the issue by making the dragons lighter than air.
- In Tom Sawyer Abroad the chapter "Tom Respects the Flea" assumes all parameters of a flea: strength, speed, intellect — will scale linearly with size.
S’pose you could cultivate a flea up to the size of a man, and keep his natural smartness a-growing and a-growing right along up, bigger and bigger, and keener and keener, in the same proportion—where’d the human race be, do you reckon? That flea would be President of the United States, and you couldn’t any more prevent it than you can prevent lightning.
- In the Old Kingdom volume Abhorsen, Lirael can make a Charter skin, a kind of physical spell, that enables her to turn into an owl. When she and her companions need to travel a long distance quickly, Sam proposes that she tweak the spell a little to become a really big owl, and carry everyone else in her claws. Whether this counts as a violation of the square-cube law is debatable; in theory a bird that big shouldn't be able to fly, but there is magic involved.
- In The Sun Eater, the alloy adamantine is has proven impervious to even mono-molecular high matter blades and normally requires anti-matter or energy weapons hotter than a star to destroy. But when the massive dreadnought Tamerlane is forced to go planetside, its weight is so immense that the adamantine plates shear along their weakest bonds as the Tamerlane is trapped in the planet's gravity well.
- Temeraire: This is Hand Waved with the historical in-universe discovery that dragons have internal sacs of lighter-than-air gas, which, in the largest breeds, negate over 80% of their weight. When Kulingile goes through a growth spurt where his sacs outpace the rest of him, he needs to be tethered down at night.
- Addressed in InCryptid when some of the characters find themselves in Another Dimension with Big Creepy-Crawlies (as in, millipedes the size of a train, and spiders so big that a small one is the size of a large horse). They note that the gravity doesn't feel different, and the giant arthropods must have lungs rather than tracheae to get enough oxygen to their organs (magic may have something to do with it as well, but the author doesn't just handwave it with A Wizard Did It).
- The Philip José Farmer short story "After King Kong Fell" uses this In-Universe by Tim Howller to speculate on the size of Kong's penis proportionately to his body.
- Animal Planet: Animal Olympics played with the law. While they ignored the fact a human sized insect would be crushed by its own weight, they did note that small animals have much more proportional strength. So, a dung beetle the size of a human could lift many metric tons, while an elephant the size of a human could barely lift a fourth of its now much smaller weight. The only reason why the insects didn't win all the events is because they often were either too good at their events (such as a flea that cleared the entire stadium completely) or too stupid to complete the event.
- Of particular note is Beakman's World's explanation of the law. Which famous dead guy did they get to help?... they didn't. They got a 3-inch-tall Lemuel Gulliver.
- Discussed on The Big Bang Theory, comparing the viability of giant ants vs. giant rabbits and mice. Notably, the production blog for the show cited this very page in explaining the problems with enlarging arthropods and mammals.
- Subverted in the Buffy the Vampire Slayer episode "Life Serial". In order to distract Buffy, Jonathan transforms himself into a much larger demon (that seems to be modeled on the South Park Satan), except that as the demon, he "actually had the proportional strength of, uh... me."
- Doctor Who:
- Actually played realistically with the Master's weapon in the 20th-century show and then again during the Chris Chibnall era, the Tissue Compression Eliminator, which shrinks people down to a couple of inches tall and causes them to die painfully from square-cube law effects.
- But ignored as usual in several other stories, most glaringly with the Giant Robot in "Robot", and all the regulars in "Planet of Giants" (in which the twist is that it's Earth, and they've been shrunk).
- Rory's jokes aside, ignored again with the Teselecta's miniature crew in "Let's Kill Hitler".
- In "Arachnids in the UK", a mutant Giant Spider grows so large that it can no longer breathe efficiently and starts to suffocate.
- Equally lampshaded and played straight in an episode of Farscape. Most of the crew are shrunk and one complains that it shouldn't be possible. Another tells her that it's better to think of a solution than to complain that what just happened isn't possible.
- Game of Thrones:
- The law is followed with the giants. They are twice the height of a regular humans, and to compensate for the increase in weight, their legs are disproportionately long and thick, and they appear to move slowly. This effect was realized by a combination of tall actors outfitted with prosthetics and overcranking.
- This trope is the reason for why all of the actors who've played Gregor Clegane (an 8-foot tall behemoth known as the "Mountain That Rides") have been no taller than seven feet (the shortest being 6'9"). While there certainly are 8-foot tall men in the world, a man of that height with Gregor's proportions is literally impossible. The loyal Stark servant Hodor is supposed to be almost a foot shorter at just over seven feet (the actor being 6'10"); luckily they two never interact so it isn't quite so obvious.
- Not entirely impossible: there have been non-pathological (ie, those without gigantism) giants of Gregor's size throughout history, though certainly not common.
- The prequel series House of the Dragon shows that not even the magic dragons are immune to this — while dragons never stop growing, they aren't immune to the effects of age, with Vhaegar, the oldest dragon and oldest living creature in Westeros (she's been around since House Targaeryan first conquered the continent), is now massive, but has gotten slower and more worn down with age. Word of God indicates that dragons actually die when they get too big precisely because of this law.
- Played for laughs (naturally) in comedy series The Goodies, episode "Kitten Kong", in which (as the title implies) the three ply a kitten with a miracle growth-promoting food. In the end they manage to get it back to normal size, but then discover that they have a problem with mice — giant ones...
- Once on the show, Adam was attempting to use a toy as a scale model human to test parachutes. He calculated its weight as a proportion of height and got an unreasonably large number. He later realized his mistake and calculated as a ratio of volume. The irony is that this approach still doesn't work, because a parachute's effectiveness is based on its area.
Adam: I'm roughly 6 feet at 180 pounds. Proportionately, that's 72 inches to 180 pounds. 10 inches tall... 25 pounds. I just did the math. I need him to weigh 25 pounds.
Jamie: So what you're saying is, he needs to be made of depleted uranium.
Adam: Uh, do you have any? [looks at labeled shelves behind him] Is it under "D" or "U"?
- Later used correctly in the Lead Balloon myth. Adam and Jamie's small-scale lead-foil balloon didn't float up specifically because it was too small (as they explained on the show). When they scaled the balloon up to a much larger size, the ratio of volume to surface area became large enough for the balloon to float—in fact, they actually needed to mix air with the helium to keep the foil from ripping from too much buoyancy.
- Once on the show, Adam was attempting to use a toy as a scale model human to test parachutes. He calculated its weight as a proportion of height and got an unreasonably large number. He later realized his mistake and calculated as a ratio of volume. The irony is that this approach still doesn't work, because a parachute's effectiveness is based on its area.
- Star Trek: The Next Generation and its spinoffs justify their sometimes impractically-large spaceships with the structural integrity field, a sci-fi gizmo and occasional Plot Device that allows ships to endure more stress than their structure alone could withstand.
- Actually played straight in Super Sentai and by extension Power Rangers, where the Humongous Mecha move like hulking slow behemoths as they should. At least, that's the way it was done when it was People in Rubber Suits. The franchise has gradually adopted CGI to portray the mecha, which allows them to be a lot more flexible. Although Power Rangers is a weird situation: according to some tech specs from the box, the original Megazord weighed 172,000 pounds-86 tons — and was 333 feet tall, whereas it's Super Sentai counterpart Daizyujin was 41 meters tall, not even half the Megazord's height, and weighed 570 tons. Since succeeding Zords are likely of comparable stats, the world of Power Rangers must have access to unbelievably strong materials.
- Bonus points for one Sentai series where instead of growing, the monsters used mechs of their own in their likeness. They matched the original monster exactly from the waist up, but they all used a common set of very large and bulky robotic legs, seemingly acknowledging that moving the extra tonnage would require something much stronger than a scaled-up version of the monster's original legs.
- The backglass for Shaq Attaq shows Shaquille O'Neal as 30 times larger than the other players, effortlessly crossing the court in two strides while holding a minuscule basketball between his thumb and forefinger. Needless to say, the Square/Cube Law doesn't even get a passing glance.
- André the Giant was so huge due to acromegaly, a disorder of the pituitary gland which essentially causes your body to try to violate the square-cube law. He spent the later part of his life in constant pain due to the strain on his muscles and circulatory system, and died at 47.
- Quiet, Please (1947): In "Tanglefoot", the narrator's buddy breeds a housefly that is two feet long. The housefly is perfectly healthy, and capable of causing appalling damage to humans.
- GURPS details the stats needed for monsters of various impossible sizes with an eye toward the Square Cube Law (how the creatures can be so big is left up to the GM).
- Dungeons & Dragons:
- It is mentioned that creature who has his all dimensions doubled weighs eight times as much, but avoids the rest via A Wizard Did It. Notably with the spells Reduce Person and Enlarge Person, for which there is an equal increase/decrease in Strength and Dexterity, respectively, but only minor ones considered the shift in mass (mainly for balance reasons).
- Somewhat ignored in that a creature's lifting capacity does not typically scale directly with the creature's mass. For an 8 times mass increase for an extra size category, a creature typically receives a 6 times increase in carrying capacity. It gets worse when A Wizard Did It, as spells such as Enlarge Person increase the creature's weight by the usual eight times, but only increases their carrying capacity by approximately 2.6 times.
- There is an artifact in the Book of Vile Darkness called the Despoiler of Flesh that gives you very flexible control over a creature's shape, but more or less points out that it has to be scientifically plausible or the creature will die because of an unsound anatomy.
- In editions where flight maneuverability is mentioned, it's noted that the largest dragons become far less agile as they grow bigger. In 3.5, for instance, Small or Tiny dragons have Average maneuverability, Medium, Large, and Huge dragons have Poor maneuverability, and Gargantuan or Colossal dragons have Clumsy maneuverability — basically, the largest dragons will bank like cruise liners in flight, and are completely unable to pull off things like hovering or flying backward. And while they do get faster, it's nowhere near proportionate to their size; a dragon the size of a sperm whale travels only twice as fast as one the size of a border collie. Of course, the fact that said dragon is able to get off the ground at all is violating this trope pretty hard. One sourcebook explains that dragons get off the ground through a mix of ridiculously strong wing muscles, surprisingly lightweight bodies, and the fact that dragons are partly elemental (hence the Breath Weapon), which gives them a lot of energy to spare.
- Older game supplements often gave the existence of massive creatures like giants, rocs, and Big Creepy-Crawlies a handwave by stating that such creatures were connected to the innate magic field of the planet that helped sustain them beyond the limits of what bone and muscle alone could accomplish even if the being had no other magical abilities. It was suggested that were they were to find themselves transported to a world that lacked any innate magic (which was much stronger than what the Anti-Magic effects in the game), they'd instantly perish.
- When RoleAids released Giants, a vintage third-party D&D supplement, they took this trope into account, rationalizing giants' physiology with honeycomb-framework bones, radically different leg musculature, and super-tough hide to contain their extremely high blood pressure. Oh, and a heaping dose of A Wizard Did It (or rather The Gods Did It) for titans.
- Star Wars d6: The Executor class command ship is roughly 12 times the length of the Imperial Star Destroyer in each dimension, or roughly 1728 times its total mass and volume, and roughly 144 times its total surface area, but only accommodates roughly eight times its total crew complement (including stormtroopers and TIE fighter pilots) and 12 times as much weapons payload.
- In Savage Worlds third-party setting Toy Troopers where you play as the plastic Army Men, the author points out that while you are 50 times smaller than a human, it wouldn't be fun if you were 50 times weaker - and realistically you'd be over 100000 times weaker. While most threats are scaled to your size, falling damage is only doubled (that is, a human falling 3 yards gets 1d6 damage, a small toy soldier gets 2d6, despite this chasm being 450ft deep for him).
- Warhammer 40,000:
- The Imperial Titans and Baneblades, and Gargants, and Squiggoths, and Hive Tyrants... thanks to 40k's Rule of Cool-powered physics, it's likely cumbersome size can always be counterbalanced by the number of guns bolted to it.
- Taken to hilarious extremes with the Hierophant Biotitan who, despite being as large as a warhound, is supported by 4 relatively tiny stalks it calls legs. How it doesn't explode from its own weight is anyone's guess. note . Unsurprisingly its model is one of the most fragile non-dark eldar ones in the whole line.
- Averted in a few places, though. Space Marines are about 8 feet tall and almost 8 feet WIDE, with numerous extra organs, and a giant suit of power armor to help take the strain of their larger proportions. Of all the factions to get this right, the ORKS versions of Titans (called Gargants) seem reasonable. Either they have very widely spread out feet, or tank treads to move about, and it appears most of the weight is concentrated towards the ground. Also, if anyone has the right to ignore the square cube law, it would be the Orks, since their technology relies heavily on their innate Psychic Powers to work in the first place.
- The Square Cube Law is actually referenced by Imperial Biologists, who are astounded that creatures the size of a Squiggoth can exist (in their own words, it should collapse under its own weight and be completely incapable of movement, though such knowledge is likely cold comfort to troops staring down one charging at their lines). The only other faction to field super-huge creatures is the Tyranids, though both groups have in-universe explanations (the Tyranids make use of genetic engineering and Bizarre Alien Biology; the Orks just get to fall back on their usual excuse of "thinking it's real makes it real", which explains why Squiggoths only show up in large Ork warbands).
- The Tau initially only fielded relatively tiny Mini-mechas in the form of Battlesuits; one-pilot mechas roughly 10-12 feet tall to carry heavy weapons on an infantry scale. They scoffed at the idea of Imperial Titans, whom they thought that the huge amount of resources and manpower to keep one of those things running proportional to just, say, bring a massively huge gunship or artillery is just ludicrous and chalked it up to Imperial Propaganda. One Damocles Gulf War later they realized the humans were crazy enough to make titans and despite the impracticality of it, their effectiveness were unparalleled. This led to the development of the Riptide, Stormsurge, and titan-esque Ta'unar Supremecy Armors
- Werewolf: The Apocalypse fails to take this trope into account with the Garou and other shapeshifting races. A Garou's crinos form height is 150% that of their homid form height, with significantly more mass. Ironically, a Garou's dexterity increases in crinos form, when it should logically decrease. It's because they're part-spirit, probably.
- It's a bit of a standing joke among BattleTech fans who have done the math that despite usually weighing anywhere from twenty to a hundred tons, given their physical dimensions BattleMechs must be less dense than water and should therefore logically float, especially since they're also by default environmentally sealed so they can operate in vacuum and other hostile environments. The rules, of course, still have them wading through any water deep enough to be worth depicting on the map. The square cube law exists In-Universe, but its magnitude is reduced, with the upper scale of feasible battlemech tonnage capped at 100 tons; you can build them larger ("superheavy"), but then they are barely able to sustain their own weight and move at a snail's pace even with an enormous reactor. Only three superheavy designs exist, and only two of those were functional designs — the 110 ton Matar's design team was executed for "treasonous incompetence" as the mech could barely move under its own power.
- The impossibility of Humongous Mecha is repeatedly pointed out in Touhou Hisoutensoku ~ Choudokyuu Ginyoru no Nazo o Oe. The fantasy-absorbing nature of Gensoukyou would actually allow for one to exist inside of it, and Sanae becomes convinced that the giant shadow she saw is one. The truth is less glamourous and closer to respecting the laws of physics.
- Evil Eye Sigma should not be able to fly if it's actually a tank on wings as it's often described. It can be assumed that magic, more than its sinister bat wings are what keep it airborne.
- Played with in the Mega Man franchise. Large Robot Masters and their counterparts from the spinoff titles can jump much higher than your character and pull off some moves, even if they aren't equipped for flight. However, large bosses in the later portions have size and power, and can manage limited movement, but they can't maneuver for crap, sticking them in basic movement patterns most of the time.
- In the Mega Man X series the bosses of the opening stage are generally titanic Mechaniloids with the maneuverability of a brick and are much weaker than their size would dictate. The few exceptions are Gigantic Mechaniloid CF-0 from X2, which could jump extremely high and hit pretty hard; Egregion from X4, a huge dragon Mechaniloid that could fly very fast; and Mega Scorpio from X7, a centaur-like scorpion Mechaniloid who could turn and charge fairly quickly.
- Mario & Luigi: Bowser's Inside Story has Bowser grow to a lot more than twice his size. During the Giant Battles, he's probably closer to being 8-10 times bigger than normal. This trope is played surprisingly straight, as Bowser's normal ability to "dodge" attacks is completely removed. This being Bowser, he doesn't waste time dodging and opts to punch the foe over and over until someone falls. The one time the weight issue is brought up is in the Fawful Express battle, as Bowser will fall through a wooden bridge and lose if he takes too long.
- Whenever he shrinks again after the fight, he realistically shrinks towards his centre of mass — resulting in him falling several feet to the ground that is now far below him.
- In other Mario games, Bowser's size changes virtually every second or third game. One time the issue of the floor breaking beneath was during the final battle of Mario Party 5 during story mode. Bowser uses a potion to grow twice as large, then instantly crashes through the floor beneath him. The rest of the "fight" plays out with him stuck in the floor.
- One other thing to note is that Bowser is shown to float or levitate whilst giant, suggesting that he may at least be aware of the impracticalities of this trope.
- Giant Battles return in Mario & Luigi: Dream Team. However, they take place in the Dream World, which doesn't have to conform to the physics of the real world.
- Dwarf Fortress:
- Huge monsters made of metal like bronze or steel are strong enough to support their own weight (which is suitably high because it is calculated by the game based on their size and material) and are extremely durable, but that same weight also makes them relatively vulnerable to damage from falls. Very large grazing animals that have been domesticated are also almost impossible to keep because they need so much grass to eat.
- In V 0.34.11, tame elephants will literally starve to death while eating. (this was fixed in 0.40 though they require a very large pasture). Predatory animals (such as grizzly bears or giant grizzly bears) are exempt from the feeding requirement though. And then there's the giant desert scorpion and giant cave spider, both approximately the size of a (regular) bear... As well as various giant insects, giant slugs, snails, etc. Dwarf Fortress sometimes laughs in the face of the Square Cube Law. The rest of the time, it brings it down on these same creatures with a vengeance, as with the Bronze Colossus.
- Sword of the Stars:
- Liir are technically immortal and never stop growing, resulting in their Great Elders being very large. Eventually, they grow too big and die due to gravity. Suul'ka are Liir Great Elders who say "Forget this gravity junk" and teleport into space to continue their existence.
- The Black, the leader of the Black Swimmers (Liir Space Navy), is also this, as he was originally sent to kill the Suul'ka.
- Broken and lampshaded in Worlds of Ultima: The Savage Empire with the Myrmidex, a race of intelligent giant ants. As the manual says:
As such, they make hash of prevailing theory about he square-cubed laws, but they do exist, and are a formidable and savage race... much like the ants to which they appear to be related.
- Broken severely in Batman: Arkham Asylum with Killer Croc. His dossier says he is 11 feet tall and 580 pounds (9 feet tall and 320 pounds in the sequel). He should realistically weigh 3 or 4 times that. They seem to have realized this when putting him into the game proper, however. Croc moves extremely heavily, and a very powerful freight elevator struggles to slowly grind upwards with him in it. Without him, it moves much faster. Taken a step further in the Arkham Knight DLC "Seasons of Infamy". Croc's condition has mutated even further, and he's now roughly the size of a small Kaiju. However, he can barely move, and has to resort to all fours in order to get anything resembling speed.
- Duke Nukem: Manhattan Project has, as the end-of-stage boss of Stage 4, a cockroach about 24 feet tall and with corresponding other proportions; a real cockroach even a tenth that size would suffocate. (It also has breasts, despite being an insect rather than a mammal, but that's another trope entirely.)
- Mass effect fields in Mass Effect allow one to alter the mass of an object, getting around this problem. However, it still would take too much energy to let a capital ship land on a planet, so they don't. Except for Sovereign and the other Reapers. Despite being the largest ships in the setting, they have such a massive amount of power at their disposal they can easily land on a planet, walk around, and pop back into space. They are pretty slow and wobbly on the ground though, due to having to deal with the gravity. Additional details mention that their shields are a fraction of what they can maintain in space (which can take the firepower of an entire fleet without a scratch), due to the incredible drain by their mass effect cores.
- Guild Wars and its sequel has the 9 feet tall Norn. Furthermore their figure seems to be bulkier than the average human. That would mean, that they weigh at least 650 pounds (300 kg). To maintain that body weight, a similarly-built 6-feet man must be able to lift at least 330 pounds (150 kg).
- Pokémon is extremely inconsistent about height and weight proportions of their and often ignore square-cube law. Onix is a 28 ft. long snake made of boulders, but its weight of 463 pounds makes it seem like it's made of Papier-mâché.
- Pokémon Ruby and Sapphire introduces Wailord, the largest Pokémon ever at 14.5 meters (47 ft. 7 in.) long. It weighs only 398 kg (877.4 pounds). For comparison, a male sperm whale averages 16 meters (52 feet) long and weighs 40 tonnes (45 short tons). In fact, doing the math shows that Wailord is lighter than helium. Float Whale Pokémon, indeed. Though that would explain how they can participate in land battles without collapsing under their own weight.
- The remakes, Pokémon Omega Ruby and Alpha Sapphire, introduce the Primal form of Groudon (the heaviest Pokémon to date), which weighs just 300 grams short of a whole ton, while only being 5 meters high.
- Also in Pokémon Omega Ruby and Alpha Sapphire is Mega Steelix. While neither form is as heavy as a steel snake of its size should be, Steelix's mega evolution is only 14% larger (9.2m to 10.5m) but 70% heavier (400kg to 740kg).
- Pokémon Sun and Moon introduces Mudsdale, a 2.5 meter (8 ft. 2 in.) tall Clydesdale horse that weighs 920. kg (2028.3 pounds). This is ridiculously heavy by Pokémon standards, but that's the actual size and weight of a real Clydesdale.
- Designing a Humongous Mecha in Garry's Mod presents the many issues that real walkers would have — balance, and not collapsing under their own weight. Amusing, if one tries to build a BattleTech mech mentioned above, it'll have about the same density of styrofoam (or less) which will cause the Havok physics engine to freak out.
- An archaeology project in World of Warcraft mentions that an ogre once thought to use rylaks as mounts. While it managed to make a comfortable saddle, ogres are so large (about 15 feet tall and very fat) that it'd take a mount the size of a small mountain to remain airborne while carrying one, to say nothing of the question of how a creature of that size would manage to stay airborne in the first place.
- Subverted with the rest of the flying mounts, who tend toward tiny wings even for fantasy settings.
- The Dark CPUs in Megadimension Neptunia VII blatantly disregard the law, being EVA-sized monstrosities with humanoid proportions, but since they appear and disappear on a whim and destroy the fabric of reality when they attack, this is the least strange thing about them. It's given a nod nonetheless when Arfoire takes direct control of one — the protagonists note they've got plenty of time before she catches up, since Afoire has no idea of her new body's physics and keeps tripping over.
- When realistic physics engines started to come into vogue, a lot of game designers (most of whom had an artistic rather than engineering background) had to call in architects to assist in designing their in-game environments as their buildings and constructs would literally collapse as soon as the physics were activated as they were unable to support their own weight.
- Xenoblade Chronicles X has a lot of very large animals wandering the surface of Mira. Most of the enormous creatures are shown to have very large organic gasbags keeping them aloft, like living blimps, but the Millesaurs and Coronids are just plain gigantic four-legged dinosaurs. The in-game fluff explains the Millesaurs as having a surprising amount of their bulk consisting of an internal buoyant gas sac, which means they are a lot lighter than they look.
- Goliath-class machine lifeforms in NieR: Automata such as Engels or Grun are massive in scale (with the former being the size of a building and the latter being 1000m tall kaiju-sized monstrosity,) but they move like they're drowning in molasses and their melee attacks are slow and exceedingly easy to dodge (unfortunately, the thing that makes Grun so dangerous isn't his size, but the massive EMP blasts he emits.) At one point you fight two Engels at once in the City Ruins and the battle, combined with the Engels' sheer weight, eventually creates a massive sinkhole in the center of the map. However, this is subverted with Hegel, a giant flying centipede-like machine, though it's possibly justified with a throwaway line elsewhere in the game about the machine lifeforms utilizing anti-gravity devices. Hegel is also a weaker version of the cloned Emils, who are also capable of flight, though in this case the justification is that Emil and his copies are all magical in nature.
- All the Colossi in Shadow of the Colossus are unlikely to have existed, let alone walk, due to their bizarre shapes and sizes. One example is Phaedra, where its multi-ton weight is supported by ridiculously thin points at the end of its legs. A creature that size shouldn't be able to get up with those spindly legs or even use them as a stamping weapon. It's explained by A Wizard Did It reasons, since their world has obvious supernatural elements incorporated into it.
- Fate/Grand Order:
- Ivan the Terrible is roughly 17 feet tall. While he's really strong, his body is so heavy that he can barely walk. He usually gets around by teleporting or riding his elephant.
- Kingprotea has the ability to infinitely grow and her default mode easily beats everyone else in height, including the aforementioned Ivan. She also primarily teleports to the enemy to attack them. It's explained that the digital world of SE.RA.PH lets her circumvent this law and she can just keep growing without consequence, but it takes effect when summoned in the real world. She has to activate her Reality Marble in order to use her bulk in the real world.
- In Babylonia this is Zig-Zagged with one of the Seven Beasts, Tiamat, once she grows giant. Roman notes after scanning her that her legs aren't powerful enough to hold up her weight on land, which is part of the reason why she needs to use the Chaos Tide to flood the plains before her to keep going and what motivates the heroes' attempts to buy time for Uruk by burning away the Chaos Tide to slow her down. However, not only can Tiamat replenish it as fast as they can destroy it, but she then surprises everyone by growing a massive pair of wings from her back and beginning to take off into the sky, with everyone incredulous something so big could do that. In this case, the being in question is so mind-boggling powerful it basically gives the middle finger to physics in the first place on top of being a Reality Warper who literally can't die unless she's the last living thing in the world, meaning she can ignore such technicalities.
- Surprisingly played realistically in Lungfishopolis in Psychonauts, even though it's a Mental World where physics need not apply. Raz dwarfs the city, and due to his immense weight, he moves slower, jumps lower, can't use Levitation, and can only bounce off water two times instead of the usual three.
- One of the trials in Final Fantasy XIV has your party fighting a dragon that is as large as a settlement. Because of its huge bulk, it moves very slowly as it advances towards Ishgard and its attack animations also have a bit of a wind up. If you mistime shooting the dragonkillers (huge harpoons) at it, the dragon will jump several feet in the air to dodge it despite its size. Certain battles can also affect the player's size, which has them moving a little faster when shrunk and a bit slower when made bigger. The trope is also zig zagged with the player character races; the dwarf sized Lalafell race have faster movement animations while larger races like the Hrothgar have a slower gait to their movement. All races control and feel exactly the same to keep things consistent and even among all players.
- An NPC in The Legend of Zelda: Breath of the Wild expresses confusion at how the Rito Bird People are able to fly, since by his measurements wings their size shouldn’t be strong enough to carry them (adult Rito are on average a few feet taller than humans, with the same proportions.)
- In the Naval Ops series, not only are smaller vessels far more maneuverable and faster than the massive battleships, smaller ships also need to spend less tonnage on armouring themselves and have a greater amount of surface area covered by armor. However, Giant Equals Invincible also shows up here too. While Battleships and whatnot aren't as well covered by armor, they can also take far more damage than a smaller ship and the damage taken mostly strikes the bulkhead rather than any important system.
- Discussed in Kurzgesagt's"The Size of Life", which explains how growing or shrinking an organism would affect them realistically. Included in the explanation is a demonstration of sizing up using a fleshy cube.
- In RWBY, the Atlesian engineers do respect this law, as the resident Humongous Mecha, the Colossus, consists mostly of two giant, thick, vaguely conical in shape armored "boots" supporting a relativly small rotating cockpit with arms attached at its sides.
- Mentioned by name in Human B Gone's very first episode, where Professor Gregorsa (the narrator and also a giant cockroach) states that the setting's giant bugs "conquered the square-cube law".
- Lampshaded in this 8-Bit Theater issue. Red Mage attempts to defeat a giant by pointing out all the reasons a creature of its size simply could not exist, thereby making it vanish in a Puff of Logic. Said giant then proceeds to crush Red Mage with his club.
- See also the many lampshades hung in Atomic Robo, by the same author, and also published on the web.
- PvP: Scratch Fury has much better luck than Red Mage, but then, Scratch took the time to write out the equation.
- The Order of the Stick:
- Similarly, in #585, Vaarsuvius attempted to use his Common Sense and knowledge of the Square-Cube Law to aid in a Banishment spell, with equally futile results.
- Also invoked in #326, though not in as many words. Roy uses this law to make a hydra pass out, as its blood supply couldn't keep up with the number of heads it was growing.
- And played with in #754, when the "Empress of Blood" (a morbidly obese red dragon the size of a small house) is able to fly, despite her wings being maybe 1% of the size of her body. How can she do it? Because D&D rules don't have any rules for not being able to fly because you weigh too heavy.
Tarquin: Quite a stumper, isn't it?
Vaarsuvius: I should avoid casting any spells tonight, if only to give the laws of physics time to cry alone in the corner.
- Addressed with a technobabbly Hand Wave in this installment of The Inexplicable Adventures of Bob!.
- Addressed and mentioned by name in Muertitos here.
- Manly Guys Doing Manly Things addresses this in one of its extras. Poor uncharacteristically adorable scorpion.◊
- El Goonish Shive:
- In this strip, Raven mentions the law by name (he's a teacher), with the implication that the magic involved compensates for the violation of normal reality. This is explained in The Rant of the subsequent comic.
- Melissa invokes this trope when meeting a dragon. She even mentions The Flight of Dragons not applying here.
- A recurring theme in size magic, especially Tedd's experiments, is the difference between half scale and half size. The former means what you'd expect, you're shrunk to half your original height. The latter means that you're shrunk to half your original volume, and is a very different experience.
- Used in this◊ Bob the Angry Flower strip, if not stated outright.
- Archipelago: Alice Pintur is a Sizeshifter who can only change to smaller sizes than her normal (and she's not that tall to begin with). At first the villains laugh at this — until it turns out that she keeps her mass, making her stronger and tougher the smaller she gets. The first thing she does upon showing her power for the first time and becoming the size of a small child is to crush a sword blade with one hand.
- L's Empire features a penguin called Snowball with the ability to change his size. However his mass remains the same, resulting in a large — yet, ultimately very light — penguin.
- Played for Laughs in this Saturday Morning Breakfast Cereal comic, with a Kaiju that does have to deal with the law.
- In Ilivais X the Ilivais units are basically 80s super robots, and as such standing under their own weight would be impossible without assistance. This developed into "make them focused on flight" which then developed into "don't even bother giving them feet". As such, most of them have blade legs that end in a point, meaning that if they lose flight capability, they're utterly incapable of movement.
- In the Whateley Universe story "Boston Brawl", there's an Author Tract explaining how size-warping 'giants' really work, since the Square-Cube Law and some other laws of basis physics would seem to make it impossible. The giant Matterhorn only appears to be a 40-foot giant because everyone else interfaces with his warp displacement field instead of him.
- The Workshop at Whateley contains a Humongous Mecha that devisor students occasionally work on. The best it's done is take three steps before the knee came apart.
- Played dead straight on occasion, too — Jimmy T's antics on Hallowe'en come to mind, as do any Shifter (as opposed to Warper) size-changers.
- Discussed extensively in Small Problem.
- The Salvation War averts this to a degree. On the one hand, most of the "lesser demons" are only about 8 feet tall, basically are made of muscles on top of more muscles, and while they all have wings only two subspecies (harpies and gorgons) can actually fly, it is stated that their bodies must produce lighter-than-air gasses to even manage that. On the other hand, there are many much larger demons, such as Satan, that well reach over 20 feet tall, although they tend to stay on the backs of great beasts or in their throne rooms. All Angels can fly, but they also are stated to have the gas producing organs. Yahweh is stated to be HUGE, but never moves from sitting on the Eternal Throne. When Heaven is conquered, the great gates to the Eternal City are so giant they cannot be moved, so must be blasted down.
- Seanbaby discusses this in the article How MMA Proved That The Bigger Guy Usually Loses Horribly. More or less, while standard heavyweights are indeed some of the strongest professional fighters out there, superheavyweights (those over 265 pounds) tend to quickly run into the issues of their immense size and weight. This results in fighters who are immensely strong and fairly durable in the body region, but trade off with awful agility and stamina, typically pathetic skill, and a general weakness to getting hit in the head. "Big man" fighters who can actually win matches are a rare sight.
- On Chip 'n Dale Rescue Rangers, the main cast — two chipmunks, two mice, and a fly — are, encounters with size-changing rays aside, roughly the same size as their real-world counterparts, yet exhibit the same fear of falling a human should, given the same heights... often a distance that would likely only daze them for a few seconds. (This being Disney, however, something always lessens the threat to our heroes and their friends anyway, so whether their fears are founded or not is never shown.) A simpler example from the same show would be the cast frequently using large (for them) human-made tools with relative ease.
- Lampshaded on The Venture Bros. with Humonguloid, a giant with a heart condition and other severe problems. Of course, VB's science of choice being superscience, he later gets shrunk to the size of an ant and survives for decades with no major health problems and, indeed, no medical care (Although he ends up being accidentally crushed to death by a rocking chair in the season 5 finale). The same character states the "proportional strength of an ant" idea to likewise be nonsense.
- In Wakfu, this is how Sallygrove defeats Rubilax. Where every time Rubilax is hit, he grows in size and mass. However, them being in the middle of a desert, after getting too big he starts to sink into the ground. He chooses to return being trapped in a sword rather than dying suffocated in sand.
- In Adventure Time, the Eldritch Abomination known as Orgalorg could move around freely — in outer space. When it was transported to Earth, gravity compacted and condensed its size so much, the creature took on a smaller form: a penguin.
- Galileo Galilei's Dialogues Concerning Two New Sciences contains discussions on the subject. Possibly the Ur-Example.
- One of the classic explications of this idea, although never actually mentioning the term "square/cube law", is J.B.S. Haldane's "On Being the Right Size".
- Some breeds of dogs which have been bred for size are easily susceptible to numerous health issues that smaller dogs do not, from joint pain to heart problems, while smaller dogs live longer on average. Similarly, leaner people tend to have fewer health issues than overweight or very muscular people, because they have less weight to carry around. In general, larger species live longer, as it takes more time for them to grow, but smaller individuals of a species are able to support themselves better, as they have less mass to support.
- Robert Wadlow, who stood 8'11"note , provides a good example of what happens when people try to get that big. Namely, serious physical problems requiring him to get leg braces and walk with a cane, having little feeling in his lower body, and dying at age 22. His cause of death was closely tied to his size: a poorly sitting brace irritated the skin on his foot, causing a blister. Due to his lack of feeling he did not notice this, and it got infected which led to his death. The tallest man alive, Sultan Kösen, who is eight inches shorter, has undergone gamma-knife therapy to stop growing, and still walks with crutches.
- Similarly, André the Giant was in constant pain for most of his life because of his gigantism and the strain it placed on his body. It eventually killed him, though he still lived more than twice as long as Wadlow.
- Major League Baseball did a full examination of the heights of every player since 1880 and their age at death and discovered that every INCH taller a person is has a significant negative impact on life expectancy. The difference between 5'7" (170 cm) and 6'0" (183 cm) is almost 8 years.
- Averted in the case of Angus MacAskill, the tallest non-pathological giant recorded. Despite being even larger than the aforementioned Andre, he reportedly had no problems with his size and was renowned for his incredible feats of strength. This was because his size wasn't due to any gland abnormalities (hence being considered the tallest non-pathological giant). People born with gigantism typically have bodies that grow disproportionately which leads to additional strain and contributes to their health problems.
- Rather depressingly, beached whales die because their own body weight on land, without any support from water, crushes their lungs, causing compressive asphyxia (i.e. they cannot breathe under their own weight). Some cases of stranding have had the animals die due to drowning — their stomachs were crushed, and the animals vomited their food.
- This can also happen to the larger varieties of sharks, who are not only massive but have flexible skeletons made almost completely out of cartilage. Their bodies are simply not capable of supporting their own weight out of the water.
- On a slightly lighter note, weight is the reason why the largest whales gain nutrition by a less energy consuming method by filtering plankton into their mouths while swimming around. If they had to actively and aggressively hunt down food the same way their smaller cousins like orcas and dolphins do there is no way they would gain more energy from it than they had to spend moving their massive bodies around when chasing their prey. Sperm whales are the obvious exception, actively hunting their prey including enormous squid at extreme depths, despite being enormous themselves. Not as enormous as baleen whales, but still quite large.
- The Nazis were getting hammered in the tank battles on the Eastern Front, so they decided to build a scaled-up tank, with armor thick enough to shrug off enemy tank shells, and guns big enough to one-shot enemy tanks. The "Maus", as it was ironically called, weighed 200 tonnes, was 10 metres long and 3.71 metres tall. The tracks were 1.1 metres wide — more than half its 3.63 metre width — in order to try to spread the load, but it still tended to sink if the ground wasn't completely firm. The designers had a difficult job designing (and then redesigning) a suspension system strong enough to support the weight, and finding an engine big enough to drive the whole thing — in the end, more than half of the Maus was occupied by powerplant and transmission, and it still wouldn't go over 13 kph. Crossing bridges with that weight was out of the question, so it was designed to be able to ford rivers, completely submerged if necessary. It was to have a 150mm main cannon. Unfortunately, they were unable to do anything about it destroying roads and damaging nearby structures simply by its weight and vibration. In the end, only two prototypes were built. That's not all, though. Plans were on the drawing board for the 1,000 tonnes, 35 metre long Landkreuzer P.1000 Ratte, with a 12" main gun, infirmary and toilet facility, and its big brother, the 1,500 tonnes, 42 metre long Landkreuzer P. 1500 Monster, with a 32" inch main gun.note Those Wacky Nazis, indeed!
- The principle holds even for more practical tanks. T-34 and the Sherman were only marginally larger than the Panzer IV, yet they weighed nearly 10 tons heavier. The Panther was yet again somewhat larger than the T-34 and the Sherman, but heavier still by more than 10 tons. Many German generals thought the advantages of the larger Panther were not worth the penalty imposed by the heavier weight. Guderian in particular believed that the long-cannon Panzer IV was the best tank Germany produced during the World War II; despite the fact that it was more or less an even match for the Shermans and T-34s, it was an absolute workhorse in the German Army and was much more reliable and versatile than the Panther or the Tiger. The debate continues as Russians kept on producing smaller, lighter, cramped, cheaper but still fairly powerful (for their size and cost) tanks compared to their Western counterparts.
- Another Nazi failure was the planned demolition of Berlin to build, among other things, the Volkshalle, to be the center of "World Capital Germania". Meant to contain 180,000 people, it was basically a scaled-up version of Hadrian's Pantheon, which Hitler greatly admired. However, it was so big that the water vapor exhaled by its occupants would have created clouds and rain — assuming the entire building hadn't already sunk into the swampy ground. In Berlin, there remain a few gigantic concrete test cylinders the Nazis cast to see if the soil could support the Volkshalle's weight. Proving real life has a sense of dramatic irony, these cylinders have been steadily (albeit slowly) sinking for sixty years.
- Josef Stalin had several projects of similar magnitude. The most famous of these is the Palace of the Soviets, which would have been the tallest manmade free-standing structure in the world at the time, had it been completed. It was to be built on a place of former Church of Christ the Saviour, which was demolished to free the space for the Palace. The top of the Palace would feature a 30-meter statue of Lenin. It was cancelled when the architects finally got over their fear of Stalin to tell him that the building would simply sink into the ground (there are underground streams in Moscow). The designs were instead used to build five scaled-down structures. The place instead was made into a very nice giant open-air swimming pool with free admittance; until finally in 1990s the pool was demolished, and the original structure occupying the spot was reconstructed – namely, the lush and astronomically expensive Church of Christ the Saviour, with a giant underground conference hall, parking lot and other amenities for heads of rich Russian Orthodox Church.
- Millions of years ago, bigger creatures were able to walk the Earth thanks in part to the greater concentration of oxygen in the air. Insects in particular have an inefficient way to carry oxygen to their cells. Back when there was more oxygen, they were able to push the envelope on size — there were dragonflies with 3 foot wingspans, for example. Today the same insects would suffocate. Nowadays, as always, the insects grow to whatever size the local atmosphere supports, so all it takes for Big Creepy-Crawlies to return is a bit more oxygen.
- There is a theory which states that at the time of the dinosaurs Earth had lower gravity (for whatever reasons), but it doesn't get a lot of recognition.
- Elephants often break bones just from tripping and falling over.
- Large-sized skydivers are advised to rather perform the parachute landing roll instead of attempting to land on their feet if the landing appears to be rough or downwind. The square/cube law means the larger you are, the harder you fall and more probably sprain your ankles on rough landings.
- Square Cube law was often cited by proponents of the Tyrannosaurus rex being a scavenger and not a predator, many people assess that should the T. rex trip (as often happens to predators in real life), it would sustain crippling or lethal injuries. However, many Tyrannosaur fossils show crippling to fatal injuries that healed, indicating that falling wasn't an automatic death sentence. Others point that the Tyrannosaurus, while fast enough to catch up to larger prey, would not have been nearly as fast as smaller predators (like raptors), which could have lessened the damage in a fall. It may have also employed strategies (like ambushes) that may have lessened the need to to run, thus the risk of falls. However, it is now discovered that tyrannosaurs were a lot more lightly built than previously thought, increasing their speed and efficiency as a predator. Also, it is believed that their diet changed dramatically through their lifetime. At old age they may well have been scavengers or more like specialist kill-hijackers, like male lions. It is also believed that Tyrannosaurus and other large dinosaurs were perfectly capable of getting upright again should they have fallen down, most likely by shifting their centre of gravity to get back on their feet similarly to how resting birds stand upright.
- Imagine how slow sauropods would have been due to their gigantic sizes. The Walking with Dinosaurs animators found that Diplodocus would have to keep three feet on the ground at all times or they would trip over while designing early models.
- Early paleontologists believed that large dinosaurs lived in swamps, because they approach being too large to move under their own power without the buoyancy of water, hence the depiction of Brontosaurus in King Kong emerging from a lake to attack the human party before chasing them on land. But Science Marches On, and discoveries of new fossils or rethinking existing ones led to new schools of thought about dinosaur lifestyles, muscular and skeletal makeup, and even posture. Note that no land-dwelling dinosaurs were ever as large as certain sea creatures, though (except the near-legendary Amphicoelias fragilimus).
- There is one problem with the square-cube law that shows some imperfection when it comes to very large animals, especially in simulations. Simulations of large sauropods like Argentinasaurus are unable to even move, despite them clearly being able to walk in real life.
- It is now known that sauropods have hollow yet strong bones and air sacs just like theropods (particularly birds), which enabled them to grow such a huge size without getting too heavy.
- Dwarf species of deer and antelope, such as the muntjac or duikers, tend to have legs so skinny it's hard to believe they can stand upright, let alone run. Even species weighing over a hundred pounds can leave footprints the size of a kitten's. Compare that to the soup-dish feet of a moose or giant sable antelope. This is also visible in dogs: the legs and feet of a Chihuahua are far more skinny than a moderately sized dog like a Beagle.
- Ants and other insects are a classic example. While actually weak compared to say humans under a strict application of the Square Cube Law, they easily trump a linear interpretation of size to strength. Ants can lift/drag as much as 50 times their weight. Fleas can jump 200 times their height. A strict application of the law would have ants lifting thousands of times their weight. This difference is attributed to the fact that evolution forces larger things to have a higher percentage of muscle, and the different scaling rates of the anatomy such as the digestive system and neurology, etc. etc.
- It's not even necessary to adjust for scale. In absolute numbers, a cricket can jump much higher than an elephant, because this law works so much in its favor.
- Female Australian Wood Moths are so large (for a moth—wingspan up to 25cm/9.8", weight of 30g/1oz) that flying is difficult. They have no mouths and live off fat stored from the larval stage. Rather than fight the square cube law and waste limited energy, females tend to seek elevated spaces, waiting for mates to find them.
- Oblong objects suffer drastically from heat transfer over the area versus length. Therefore the largest snakes, such as anaconda and pythons, are pretty much confined to tropics where the temperature is high and constant throughout the year. The square/cube law is also the reason, why reports or 30 m or 100 ft or whatever long anacondas are hoaxes: 9 m is pretty much the maximal thermodynamic length of a snake living in current atmosphere and climate. The reason why there has been larger ophidians, such as Titanoboa is that the climate was much warmer then and able to sustain such bodies.
- There is another scaling effect. The resistance in a vascular system is inversely related to the fourth power of its radius.
- 9/11 Conspiracy Theorist Richard Gage once had a demonstration as to why the Twin Towers would not collapse. He took two boxes representing the "top block" of the Towers and the bottom block. He then dropped the upper block on the bottom, to simulate the building failing in the impact zone due to fire and impact, and the top portion falling on the lower, collapsing it. Since his model did not collapse, he asserts, it meant the Towers would not have collapsed. Some "debunkers" calculated that the model he used, being a few feet tall, would be something like thousands of times proportionately stronger than the 1000+ ft. Towers, especially once you take into account that the model was made of cardboard. Curiously enough, Gage and his organizations largely act like the video doesn't exist. He resurrected the argument in the wake of the blacksmith rebuttal clip that made the rounds in 2016, though.
- The Body Mass Index formula bases your healthy weight on the square of your height instead of the cube. This is not an accurate representation of human mass vs. height at all. The formula was made for the average man, and it fails when it comes to dealing with women, children, and outliers such as very short or very tall people. BMI does not distinguish muscle weight from fat weight, so some bodybuilders and athletes qualify as "obese" despite having lower body fat percentages.
- A mathematician noticed this and posted a letter pointing it out. It turns out that even the inventor of the Body Mass Index knew that his formula wasn't very accurate. Squaring works best for children, cubing works best for babies, and an exponent of 2.5 works best for adults. These values are generally related to the composition of body mass over the human lifespan up until physical maturity.
- Some BMI calculators do have allowances for large or small boned people, but even these consolations should be taken with a grain of salt. Often these are just flat percentages.
- A newer standard called BVI (body volume indicator) uses a 3D scanner to measure one's dimensions. Unlike BMI, it takes one's volume and distribution into account, providing a more accurate measure of obesity.
- By also taking into account the size of a person's waist (more than 40in for a man or 34.6in for a woman) most of these problems are removed.
- You see this all the time with young children, compared to adults. Notice how often young kids run around at full speed, fall down... and bounce right up and take off again. Or the number of times toddlers fall when learning to walk. They thump themselves, and, yes, occasionally draw some blood or get some quite impressive bruises, but their injuries are far less severe than what an adult would suffer going through a similar motion. With their low mass due to this trope, they just can't impact the ground with enough energy to cause more than minor damage (admittedly, being low to the ground and having less time for gravity to accelerate them downward is a factor as well). Small children are also likely to be able to do exercises like pull-ups without any training or effort, as the strength-to-mass ratio is much more favorable than for adults fully grown.
- Whilst the size of yachts is announced by their overall length (LOA), expressed as ft or m, their prices tend to rise exponentially rather than linearly in relation to their length. The reason is the square/cube law: the yacht price is relative to her displacement rather than her LOA, and increases in cube of the LOA.
- Ships of various types can often get larger and larger over time due to this. The main reason: A ship's drag comes from waves and water drag, water drag increases as the square of the length. However, the amount of stuff a ship can carry increases as the cube of the length. This means the proportion of space needed for engines, fuel, and such to push it through the water gets smaller as the ship size increases, leaving more room for other things, and saving costs. As a result:
- The first ocean going steamship was deliberately made larger than usual at the time, partly to avoid the need to refuel as a result of this effect.
- Container ships today are known to get bigger and bigger, limited only by available port infrastructure and by the size of canals, if the ship must travel through them.
- Exploitation of the cube squared law was the driving factor of the race to build the largest luxury liners that dominated ship building from the late 1800s to the 1930s. As a liner's size increases, the amount of free space to devote to more rooms (and thus more paying passengers) increases much faster than need to expand both common rooms and machinery necessary to propel the ship. However this was also a driving factor behind the Titanic Disaster. Laws at the time required lifeboats based off of tonnage rather than total number of people the ship carried. The proportions specified in the law were calculated assuming much smaller vessels, which meant far less efficient use of tonnage. When super ships like the Titanic rolled around, the law's requirements for lifeboats were horribly behind actual passenger capacity.
- This is also the reason why racing yachts tend to be long and sleek. The wet area of the yacht is relative to her waterline length and her beam, and the narrower the beam, the smaller the wet area and the drag it causes. Conversely, the longer the waterline, the greater the hull speed. This comes with a price, though: racing yachts are extremely spartan and cramped and uncomfortable to live in. Leisure yachts tend to have broader beam and dramatically more spacious living quarters.
- Replace cubes and squares with cylinders and circles and you have the driving factor behind the dreadnought race in the prelude to WWI. The difference between a twelve inch gun and a fourteen inch gun doesn't sound like that much but it equates to a much larger, heavier shell. The heavier the shell, the more explosives it holds, and the more armor it can punch through. So every time one nation came out with a battleship that could tote guns even half an inch bigger than the previous ship, all the other nations had to make a ship with the armor to withstand that firepower armed with equally large guns. This process was so vicious and rapid that many battleships were considered obsolete before they were launched. This eventually led to the Battlecruiser concept, skipping the extra armor in exchange for speed but keeping the size and big guns; the idea was popular but in the actual war they proved to be too much of a Glass Cannon to fulfill a Battleship's combat role.
- As engine design improved, battleship performance improved as well, leading to the Fast Battleships that would dominate World War II. These ships were bigger, more heavily armed, and faster than the Dreadnoughts and Super Dreadnoughts of the First World War, which ironically made them ideal escorts for the aircraft carriers, thanks to their mix of speed, range, durability, and room to mount lots and lots of anti-aircraft guns.
- This is also why supercarriers exist. Despite people constantly criticizing the concept and saying it would be more efficient to use many smaller aircraft carriers. While it would divide the eggs over a greater number of baskets so to speak, it would far more expensive and there is no way the many light carriers would ever be as versatile. As expensive as a super carrier is, building and maintaining one big ship is always more efficient than many smaller ones. Never mind that a supercarrier can launch very large aircraft when needed for odd jobs and a light carrier just can’t.
- Huge machinery (as in the 1000-tonne tank example above) are limited in size and agility by environment far more than by engine power.
- While giant, thousand-tonne mining excavators had been built for decades, motors made to drive them and track surface wide enough to avoid sinking into the ground or even leave tracks on the ground, they still have the inertia of their gigantic mass. This is why they are limited to a snail's pace: decelerating their mass by striking a rock, for example, would bend steel like cardboard, turning in place from a reasonable speed would throw a track. They are "movable", yet never truly "mobile".
- This is why, until a certain point in time, horses couldn't survive a broken leg — there was simply no casting material strong enough to carry around that much weight until the bone fully healed.note This improved somewhat with technology, in that it raised the chances of survival from "somewhere below absolute zero" to "possible, if the horse is very very lucky and the circumstances are right".
- It is believed that much of the notorious fragility of horses comes from this: the first domesticated horses were considerably smaller and stockier, but millennia of breeding for speed and size to better carry riders has stretched the limits of its anatomy.
- This trope can have interesting effects on ship and aircraft design. Samuel Pierpont Langely was one of the contenders for the first heavier-than-air controlled manned flight. He built a series of unmanned Aerodrome scale models which were successfully launched from a water-based platform (he decided to design the landing gear once he had the actual flying figured out). He scaled the design up and installed a more powerful engine for the first manned version, which upon launch promptly crashed into the water along with the test pilot, Charles Manly. Nine days after his second failed attempt, the Wright Brothers had their first successful flight at Kitty Hawk, North Carolina. However, the Aerodrome was later successfully flown, in 1914.
- A very significant example in real life would be the Sun itself. Amazingly, the incredible pressures and temperatures in the sun's core are barely enough to ignite any hydrogen fusion at all (relatively speaking). Taking the total power output of the sun and dividing it by its total volume gives a ridiculously low specific power output of 0.28 watts per cubic metre. As 99% of the sun's power is produced in the inner 10% that forms the core, the peak power production due to nuclear fusion is just 276 watts per cubic metre which is about the same as... that of a compost heap. Yes, the sheer power output of the sun is actually due to its tremendous size; its sheer mass means even insanely low percentages of hydrogen burnt still turns out to be 600 billion tons of hydrogen burnt every second. The surface luminance however is another story as it depends only on the surface area. Despite its low power density, the sun is an incredibly luminous object (~2 billion cd/sq.m at the surface, a laptop screen is just around 200-300) because of the square cube rule. A quick calculation shows that a brisk runner by comparison generates around 10000 W / cu.m of body volume, therefore a sprinter scaled to sun-size would in theory generate 50000 times more energy than the sun and become one of the most powerful stars in the entire galaxy. However, the body heat generated by all the cells of a sun sized runner at normal biological rates would cause his body surface temperature to reach an incredible 74000 K, hotter than even the most luminous star!
- This also creates problems for nuclear fusion in the laboratory, that not having the benefit of immense masses of plasma or gravity, artificially created plasmas need to achieve 10 to 100x the temperatures in the sun's core to achieve any reasonable power output at all.
- For that matter, even the most luminous star ever known still radiates at a measly 53 Watts / cu.m (over its TOTAL volume) and it's still 7.4 million times more luminous than the sun.
- Evolved stars show also very well the effect of the square-cube law. In red giant and red supergiant stars, evolved medium and (not very) high-mass stars, while the Stefan-Boltzmann law ensures they emit quite less energy per surface area than in their less bloated past a much larger area more than compensates for that being up to thousands of times more luminous. However, except for the diminutive core that must be really dense and hot in order to maintain nuclear reactions beyond standard hydrogen fusion, their masses are spreaded over such a huge volume that their mean densities are very low, pretty much similar to a vacuum. Conversely, white dwarfs and neutron stars, corpses of low/medium and high mass stars with the sizes of a planet and an asteroid respectively, pack in such a volume the mass of an entire star meaning extremely high densities, and have so little area that they're very faint despite having, when formed, much higher surface temperatures than any typical star (see the Stefan-Boltzmann law before).
- If smaller astronomical objects are your thing, an enhanced version of this law also applies to planets. There's a reason the moon, Mercury, and Mars are geologically dead, while Earth and probably Venus are still active. Geological activity is created by heat leaving a planet, the area through which the heat can leave is proportional to the square of a planet's radius, but all common sources of heat are proportional to greater than the cube of the radius: Radioactive heating is proportional to mass, which increases slightly faster than the cube of the radius (due to gravitational compression, a heavier body squeezes itself). Accretionary heating increases as mass squared, tidal heating goes as radius to the fifth. More heat per surface area means more geologic activity, and longer lasting activity, than a smaller planet made from the same materials in the same orbit and location.
- It's observed in powerlifting that the lighter weight classes will lift more weight as a percentage of their actual body weight than heavier weight classes. While the 300+ lbs super heavyweights can squat 1000 lbs, 150 lbs and under weight lifters can approach squat weights nearly five times their own bodyweight. This is probably because the lighter lifters are generally much shorter, and their short bones cause the weights being lifted to act across a shorter lever arm, making it easier to lift.
- Architecture, of course, deals with this. The invention of the arch in Rome enabled them to build some massive projects, including bridges and aqueducts. One of the biggest issues in medieval England was that their cathedrals kept collapsing. The flying buttress solved that problem.
- It's even observable with toys. Given the same material and proportions, a smaller doll or action figure will generally hold an awkward pose — one which puts frictional stress on the joints, such as standing with knees bent◊ — much better than a large one. This trope is also one of the worries involved in large and expensive figures, such as Hot Toys collectibles or Masterpiece Transformers — they're so heavy that something like falling off the shelf, which wouldn't even scratch a small toy, could seriously damage a large one. Bandai's luxury divisions, such as S.H. MonsterArts, managed to bypass this problem by adding additional attachable transparent support parts and stands to provide some extra stabilisation where required.
- A famous British advert for a Tonka dump truck toy showed a real dump truck being destroyed by a fall from a cliff while the Tonka truck survived.
- This law can be clearly seen in astronomy, where the larger the lens of a telescope the better the resolution and the more light it can catch (and the more expensive it is due to how difficult is to manufacture a large lens, a stronger mount to take care of extra weight, etc). For example, the price hike from a 4-inch refractor (lens) telescope to a 4.7-inch one is not much, but it is much higher from the latter to a 5.9-inch, just to have 50% extra light and 25% more resolution, and prices go astronomical for larger lenses. Mirrors in reflector telescopes are easier to manufacture thus not as subject to this.
- It's been observed that very large animals, such as elephants and whales, don't get cancer that reaches a stage where it's lethal. Instead, because cancer is a constantly mutating organism, some of it eventually mutates into a competitive cancer, prioritizing conquering the original cancer before trying to take over the body. The theory is that because large animals have so much more mass than say a human or a mouse, the cancer grows offshoots that compete against it before it has a chance to take over enough mass to become lethal.
- This is believed to be part of why big dog breeds have shorter lifespans than small ones. All the extra weight puts a lot more wear and tear on their muscles, bones, and organs, which are proportionally a lot weaker than smaller dog's.