Using a melee weapon in one hand, which is obviously meant to be swung in both hands.
Say a character has a large sword. It may be anything from a regular two-handed sword, or it may be something utterly ludicrous in size. Clearly this thing requires both hands for any normal person to swing it. So anyone who swings around something so huge using only one hand is obviously not normal, and not someone to be trifled with. Often they'll be able to wield this huge weapon as effectively as a 'regular' single handed weapon. In fact, it will often seem as if the enormous slab of metal weighs next to nothing, allowing the character to pull off ridiculous(-ly awesome) feats that make even expert swordsmen look like amateurs. And if a guy is swinging a sword the size of a Buick around one-handed, what would happen if he used both hands?
The character is typically The Big Guy, The Brute, The Berserker, or a Badass Abnormal. Quite often they're the protagonist. Anyone doing this usually possesses some degree of Super Strength or Charles Atlas Superpower.
Very common in video games and manga/anime. Does not have to involve a BFS (though it often does), or even be a sword. Any normally two-handed melee weapon qualifies, though swords are by far the most common usage of this trope.
Obviously, trying to wield a large sword using one hand in reality is a good way to give yourself a hernia. The trope naming German Zweihänder for example, is sometimes cited as being over seven feet long, and named for the requirement that it be wielded with "two hands." Trying to swing something that large around with just one hand would be impossible to do with any degree of skill.
It is worth noting that real swords are in fact much lighter than one would think, and it may be quite possible to swing even a large sword using one hand, albeit with greatly reduced balance and with too low a speed to make it useful in a fight. The issue is less with force and weight as leverage and length—the only distance one hand has for applying torque is the hand's width, whereas two hands each have half the distance between each other. In fictionland, however, swords tend to be much larger and heavier than would be feasible in reality, so the audience reaction is "There is no way he could use that thing one-handed." It is not this trope if the sword or other weapon could be reasonably used one handed by a normal person.
Of course, some of the weapons used by practitioners of this trope are so huge that not even using both hands would do them any good.
Often comes with Implausible Fencing Powers. Sometimes taken to ridiculous levels when Dual Wielding is involved. For the Gun Counterpart, see Firing One Handed. Related to BFS. Subtrope of Improbable Use of a Weapon.
Examples:
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Anime and Manga
Kirito from Sword Art Online wields a huge black iron sword with one hand in ALO. The reasoning for this is that he is used to heavy swords from SAO.
Guts from Berserk is quite capable of wielding his freakishly large BFS, the Dragon Slayer, using just one hand. His other hand is mechanical, as he lost the original one during the Eclipse, and the only way he can wield the thing using that other hand is with a magnet inside of it.
In Bleach, Kenpachi Zaraki wields a very large sword, similar in design to a nodachi, in one hand, and uses a very reckless fighting style to boot. In the Hueco Mundo Arc, he encounters an enemy so powerful that he resorts to holding his sword properly, which has a marked effect on his power. Amusingly, he had to actually be taught that this works better when the head captain forced him to take formal swordsmanship lessons. He normally refuses to use the techniques he was taught, because he doesn't want his battles to be too easy.
And, again from Bleach, Nnoitra Gilga use several big-ass scythes in his One-Winged Angel form, all of them with one hand (he has six of them).
Protagonist Ichigo remarkably averts this: his Zangetsu in any pre-Bankai form is definitely a BFS (it's generally about as long as his wingspan — and he's both tall and somewhat long in the arm — and quite broad, its primary form resembling a chopping knife for most of the series) but he typically wields it two-handed. Though it's shown a couple of times that he can one-hand it.
The eponymous half-demon swordswomen of Claymore do this, often being able to Spam Attack with their huge swords. It's lampshaded in the first chapter and explained as a specific effect of their being made part-Yoma. The thin handles of the claymore swords also are a hint that the swords are made of Thunderbolt Iron. Which is why they can survive being used against Awakened Ones and do not break even when subjected to or used for Implausible Fencing Powers.
There also are Asuna's Pactio artifact, both of Setsuna's swords — her regular nodachi and her second Pactio artifact (which can grow to enormous size), Yue's Ariadne sword, and (briefly) Fate's stone sword, all of which are positively BFSes and are usually wielded one-handed.
Lancer in Fate/Zero dual wields lances, as you might expect. In a nod to reality, it's very tiring even for a mythical hero to do so, leading him to ditch one of them in midfight so as to not exhaust himself.
Actually Lancer "ditches" his 2nd spear to set up a trap for Saber.
In Ranma ½, Ryoga's umbrella turns out to be so incredibly heavy that Akane (who, remember, is a highly trained martial artist and in excellent shape) can barely lift it. Yet, as she observes, Ryoga wields it in one hand like a normal person with a normal umbrella, tipping her off to his monstrous natural strength.
In Naruto, Zabuza Momochi and Kisame Hoshigaki both wield their massive swords (Decapitating Carving Knife and Samehada, respectively) one-handed; both are very heavily built. At later points in the series, Suigetsu and Kakashi both use Zabuza's sword; Suigetsu alternates between both arms and one (sometimes using ninjutsu to make it larger and stronger) but Kakashi has only been shown using it one-handed.
Bui from YuYu Hakusho wields an axe so large and heavy that it causes his footsteps to crack solid stone floors, and with a single hand he can swing it faster than most humans can percieve. The axe is by far his weakest form of attack.
In Gamaran the most (and perhaps only) blatant example can be found in KibeRyuho, the Silver Demon: his gargantuan iron club "Black Claw Comb" is made to be used with both hands. However, thanks to the ludicrous Super Strength obtained with the Juugan drug he eventually manages to swing the whole damned thing with a single hand.
In A Song of Ice and Fire, the 8-foot-tall and freakishly strong Gregor Clegane can wield a greatsword with one hand as easily as shorter knights use one-handed swords.
In With Sword and Fire, Longinus Podbipięta uses a massive bastard sword called Zerwikaptur (Hood-Ripper), often one-handed, while the other characters have difficulty even holding it up.
In Codex Alera, the superhumanly strong Knights Terra use greatswords and giant mauls in one hand to devastating effect.
In the Book of Five Rings, Musashi encourage the reader to use the tachi (a long katana) with one hand in order to use Dual Wielding. While it's not an impressive feat, as a katana isn't that heavy, still most swordsmen used it with both hands to deliver faster and stronger hits.
Belgariad: Garion, Torak, and 'Zakath all do this one occasion. Likely justified, as the swords in question are magic.
In the case of Garion, the sword in question is powered by a Cosmic Keystone that explicitly makes the sword lighter than it would normally be. When the stone is removed, he can barely lift or carry the sword at all, much less in one hand (he once removed the stone while forgetting the sword is slung in the scabbard at his back. It brought him to his knees). Torak, by contrast, is a god, and would not be expected to have difficulty handling any sword.
Tabletop Games
There's a feat in 3rd ed. Dungeons & Dragons called Monkey Grip that allows a character to use two handed weapons as one handed weapons. As the system is one of the bigger cases of Shields Are Useless, and there is an inherent damage boost to two handed weapon use and even with the feat you suffer a penalty, it's common to see comments on how bad it is.
Of course, that feat has other, Crazy Awesome uses. Like dual-wielding greatswords and using greataxes made for minotaurs.
Additionally, it is possible to enchant greatswords/claymores to be wielded like shortswords, so even the squishy thief can swing around a blade longer than her arm span.
In Advanced Dungeons & Dragons second edition, a magical sword known as the "sun blade" is classed as a bastard sword with regards to appearance, damage dealt, and overall size, but is regarded as a short sword in terms of encumbrance and weight, and can be wielded by people with proficiency in using either a bastard or a short sword.
The Sun Blade also shows up in Pathfinder' as well. In addition to the aforementioned qualities, it gains substantial bonuses versus undead, basically turning it into a budget-version of the Holy Avenger for Paladins.
In Exalted, you can wield a two-handed weapon in only one hand if you have three times the minimum strength to wield it the normal way. This is somewhat uncommon, since it's hard to have a strength score higher than five dots within a human lifetime without artifacts or charms to provide bonuses. As a result, it's best to avoid offending a Solar wielding a grand daiklave in one hand, since he is easily strong enough to pull a fully laden wagon.
The basic daiklave itself is the size of a mundane two-handed weapon (its inherent magic allows wielders to lift it in one), and Solars and Lunars can learn Charms to allow them to wield even grand daiklaves and other two-handed Artifact weapons in the one.
Video Games
The image for this trope used to be War, from Darksiders. His BFS, Chaoseater, is at least eight feet long and two feet wide. War swings it around in his right hand like it weighs next to nothing. His other hand is a Power Fist. Even a de-powered Horseman of the Apocalypse gives Cloud a run for his money.
Siegfried (the guy who used to beNightmare) also uses one arm to wield hisBFS in certain stances.
Cloud Strife certainly counts, whether armed with the Buster Sword in Final Fantasy VII, or the First Tsurugi in Final Fantasy VII: Advent Children. It also should be noted that in his battle stance, he's wielding it with two hands.
Sephiroth does this as well, and his sword already is a BFS by all standards, having a length of about three meters, which dwarfs Cloud's Buster Sword in length.
Angeal and Zack, the first and second wielders of the Buster Sword, are also capable of using it one handed; though that's probably due to their SOLDIER enhancements.
Orochi of Warriors Orochi wields his massive scythe with a single hand.
In the sequel Kiyomori Taira wields an absurdly large set of rosary beads with one hand.
In Ultima VII, there is a character, Dupre, that comes with a Two Handed Sword (which is one of the best weapons in the game, magical or not) in just ONE hand, and a shield in the other. It's a bug, since moving the sword to his backpack and then back to his hand makes him to use in both hands, but is awesome nevertheless.
In some of the One Piece video games, the resident BadassMaster Swordsman Mihawk will swing his gigantic sword with one hand. Recently, the New Fishman pirate Dosun is shown using a colossal maul with only one hand.
Ragna the Bloodedge of BlazBlue does this with a sword described as "a massive slab of metal." He also tends to use it in Reverse Grip, making it even more implausible.
In Mount & Blade, a character on horseback will always wield their weapons one-handed (reasonably enough, as using both hands would be unbalanced and very impractical) and yes, this goes all the way up to six-foot greatswords and longaxes. Any two-handed weapon (except polearms) used this way suffers a 25% damage and skill penalty, though.
Barbarians in Diablo II can wield two-handed weapons like this, allowing for either a shield or another weapon (even another two-handed weapon) to be used in the other hand, though they take a damage penalty for one-handed use. For barbarians using a Frenzy build, however, nothing tops it.
World of Warcraft: Warriors can do this with the Titan's Grip talent. Not only that, Titan's Grip allows the Warrior to dual-wield normally two-handed weapons.
The infamous Thunderfury, Blessed Blade Of The Windseaker, which is particularly notable for being a one-handed sword that is, in fact, bigger than some two-handed swords.''
In Bujingai: Swordmaster, one of Lao's swords is large and has a two-handed grip, but he still uses it with one hand.
You can learn the ability to do this in the Final Fantasy Tactics games—called "Monkey Grip" in some games—so you can equip a shield on your free hand.
In the Tactics games as well as some other Final Fantasy games you can invert this by using the opposite ability—Doublehand—to wield one handed weapons with both arms for extra power.
The Qunari Arishok in Dragon Age II wields a claymore and a two-handed battle axe in each hand, which is not surprising considering his enormous body height and clearly Super Strength. On a related note, the in-game model of Arishok belongs to the Rogue class (rather than the burly Warrior you'd expect) and his weapons are technically daggers, since the game's engine limits dual-wielding to this class and weapon exclusively.
In the first game, one-handed swords were a little large for humans but start to look more like two-handed swords for elves and dwarves (a one-handed sword is about as long as this distance between the ground and an elf's chin). Enter the Rogue talent that lets you dual-wield one-handed weapons instead of requiring a dagger in your off-hand...
Many classes in Fire Emblem swing around huge weapons one handed. Ike wields all of his swords in Path of Radiance and Radiant Dawn (including his iconicRagnell) in this manner and is explicitly pointed out to be doing so in Super Smash Bros. Brawl by Solid Snake on Snake's level.
The Black Knight also does this with his Alondite, the twin of Ragnell. Ashnard, the Big Bad of Path of Radiance, also wields his lance-esque sword Gurgant with one hand.
Even more ridiculously, the legendary hero Altina dual-wielded Ragnell and Alondite, but that was ages ago.
In Fate/stay night, Berserker one-hands a giant sword that is more a seven foot slab of rock, so fast that even his missed attacks cause a Razor Wind.
On the other hand, Berserker's humongous size makes said sword look small by comparison.
Played straight when Shirou traces Berserker's sword and fights with it.
Auron uses large, Western swords (which are labelled as katanas). Although he can clearly lift and use them with no effort, most of his attacks (Overdrives included) actually have him use both hands. In Kingdom Hearts II, however, he keeps his left hand tucked away under his robes, playing this trope straight.
In the Dynasty Warriors franchise, Lu Bu does this with a halberd.
Pang De and DW7 Zhang Liao Dual Wields two large Pole axes.
In Dark Souls, it's possible to use many very large weapons one-handed, including an actual zweihander. You can also invert it by holding a small dagger with both hands.
Silent Hill gives us Pyramid Head, who swings and drags his Great Knife in one hand (though his slow movements suggest it isn't easy). While the player can aquire this weapon, James Sunderland wields it with two hands and swings it even slower.
Baldur's Gate: In the first game, Sarevok wields a big sword one-handed. In Shadows of Amn, you can get this sword as an actual item — and only then will you see it was a two-handed sword, by the rules simply impossible for your characters to wield in one hand. (However, in Throne of Bhaal, this rule applies to Sarevok as well.)
RuneScape has an interesting inversion. The Dominion Sword looks for all intents and purposes like a normal, one handed longsword. However, you can only wield it two-handed. (as in, you aren't allowed to equip a shield, even though the sword is obviously small enough for you to do so.)
Played straight with the Slayer master Vannaka, who wields both a steel two-handed sword and Dragon square shield at the same time although not even players with maxed Strength can wield two-handed swords with a shield.
In Dwarf Fortress, each weapon has a minimum size to be used at all and a minimum size to be used one-handed without penalty; units above the second size won't even try to wield the weapon with two hands available. Because they were meant to let at least some dwarves wield any weapon one-handed, the size standards for this are rather unrealistically small. Even slightly above average humans are big enough to wield things like pikes, two-handed swords, halberds, mauls, and great axes one-handed without issue. For reference, the in-game weight of an iron maul or great axe (the two largest weapons) is over 10 kilograms.
Justified, considering that they are easily eight or nine feet tall. Jygallag and Umaril do this in their respective expansions, too.
In Baldur's Gate: Dark Alliance 2, Dorn the barbarian can learn a high-level skill (it costs 15 skill points) that allows him to wield two-handed swords, axes and hammers in one hand, and even dual wield them should he wish.
All the types of spears in Titan Quest are used with one hand, no matter how large or heavy they look.
In Dungeons, the Zombie King wields a very large sword with one hand.
In the Kingdom Hearts Saix wields an in name only "Claymore" in one hand with a Reverse Grip. Terra also wields some of the largest Keyblades in the series one handed.
Web Comics
Marty of Dubious Company combines this with Dual Wielding great axes. Predictably, he spends most of his time trying to keep his balance after each swing, that Tiren is able to bodyslam him out of Walter's way and Elly is able to avoid getting hit just by fretting.