Square-Cube Law

The smaller cube will be three times as agile as the larger cube. (Assuming they are capable of movement.)

The bigger they are, the harder they fall.

—Joe Walcott

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, and its volume is increased by eight times.

The point of this law is that with living beings, strength is (more or less) a function of area,[1] 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 size, 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.

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.

On the other hand, the buoyancy of aquatic swimmers is completely unaffected by the law because it's a function of density—weight divided by volume, both of which change at a cubic rate. Good news for whales.

A full explanation is a lot more complicated due to subtler biological factors (muscle/bone stress, required oxygen uptake, dissipating body heat, etc.), 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.

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. 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 Art Major 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 and Humongous Mecha for examples of media ignoring the Square-Cube Law. Sometimes justified by the use of Required Secondary Powers. Compare Muscles Are Meaningless and Pint-Sized Powerhouse.

Examples of Square-Cube Law include:

Anime and Manga

  • The Dragon Ball 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 Ultra Super Saiyan 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.
    • Lampshaded in Trunks and Cell's fight; the more Trunks powers up, the more he bulks up, but he loses speed and agility.
    • This, of course, is overcome when Super Saiyan 2 form is reached, where strength and speed seemingly increase proportionally.
  • 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.
  • 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.
    • 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 the skeletal frame of the suit. 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.
    • Mobile Suit Zeta Gundam also had the absolutely gigantic Psycho 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.
  • 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.
  • 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.
  • 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.
  • 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!

  • Lampshaded in 20th Century Boys, 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.
  • 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.
  • 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 he is renowned for making even more impossible creatures than herself.
  • Gyo obeys the law—a zombified whale that rises onto the land immediately collapses under its own weight.
  • 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 maintenence, and implies that Kanuka's short perfomance will mean days of work and hundreds (possibly thousands) of dollars in components to bring the labor back to 100% operating capacity.


Comic Books

  • 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...
    • 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.
    • Lampshaded in an issue of Blue Beetle. When Giganta attacks El Paso, Peacemaker talks about how her growth has to be magical to avoid breaking the Square Cube Law, and drops hints about a science-induced growth experiment that... didn't go well.
    • Marvel Comics 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 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, 60 ft 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.
    • 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 Official Handbook of the Marvel Universe (usually the best authority on how superpowers in Marvel work, though that isn't saying much) often claims that characters who shapeshift or change size do so by "drawing mass from another, possibly extradimensional source", although they never attempt to explain the nature of this other dimension.
  • Spider-Man 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. Super Dickery 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).
  • 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.
  • Lampshaded in Atomic Robo, 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.
    • A giant monster attack in Volume 4 has Robo ask "Why do we even have the Square Cube Law!?"
  • An interesting inversion appears in PS238 with the superheroine "Micro-Might". Her power is, specifically, to take advantage of the Square-Cube Law - shrinking herself down to half height, 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 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.
  • A plot point in one Fantastic Four 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).
  • 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.

Fan Works

  • 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.
  • An issue of scientific scrutiny in The Teraverse in the wake of assorted giant monsters (such as a multi-hundred-foot-tall tarantula) that by all rights should not be able to support their own weight.

Film

  • Actually hand waved in Monsters Versus 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.
  • Avatar may have gotten away with ten-foot tall humanoids thanks to a few throw-away lines from the Colonel. For one, they handily let us know that Pandora has lower gravity than Earth, where long, lanky creatures are expected to be more prevalent. Secondly, the native Na'vi have bones reinforced with naturally occurring carbon fiber, which makes any structural strength issues null and void. Additionally, the Na'vi aren't all that much taller than humans (a factor of two at most), but are significantly skinnier, meaning their mass wouldn't increase as a direct cube law compared to humans. The lower gravity of Pandora also allows Humongous Mecha.
    • Said Humongous Mecha were designed for use on Earth - Pandora's lower gravity is what makes them viable in hand-to-hand combat with the natives.
  • Subtle aversion in Transformers: Revenge of the Fallen. Devastator, a large, gorilla-like robot made from construction equipment, 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 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.
  • 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.
  • 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, or collapses the decking beneath her weight. Could potentially be handwaved by her goddess powers or something, but it's never explicitly addressed either way.
  • 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).


Literature

  • 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.
  • 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.
  • 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-Cubed 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.
  • There was a short story which played with this concept; among other things, a supervillain unleashes an army of giant ants on a city. The ants are all killed, but someone realizes that in order for the creatures to support their own weight, their legs would have to made of some incredible super-strong wonder-substance. They harvest the substance and are able to reproduce it. It turns out this was villain's Evil Plan all along, as it causes the global steel industry to collapse overnight. The villain ends up ruling the world. Of course, if the ant attack actually worked, he wouldn't have complained. Either way he'd win.
  • Pointed out in Everworld when the characters encounter a wolf bigger than an elephant. Of course, since the wolf is Fenrir, a godlike being from Norse Mythology, normal laws of physics probably 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.
  • 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 Honorverse series. The warships, with their original lengths, had a density exceeded by that of smoke. The Great Resizing fixed that problem.
  • In Orson Scott Card'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.
  • 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 Stanislaw 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.
  • In 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 desgin looks like it allows for a greater distribution of weight.
  • 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.
  • 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 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 impenetrable barrier.
  • Immanuel Volikovsky 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 simple 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 Volikovsky 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. The book then goes on to have Jupiter eject a planet the size of Venus which causes ... well, the science was bad and the writing not much better.
  • 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.


Live Action TV

  • Actually played straight in Super Sentai and by extension Power Rangers, where the Humongous Mecha move like hulking slow behemoths as they should.
  • 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.
  • Once on MythBusters, 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.

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"?

    • 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.
    • 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.
  • Subverted in the Buffy the Vampire Slayer episode "Life Serial". In order to distract Buffy, Jonathan transforms himself into a much larger demon (that seemed to be modeled on the South Park Satan) except that as the demon he "actually had the proportional strength of, uh...me."
  • 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.


Professional Wrestling

  • 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.


Tabletop Games

  • 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 notes that a creature who has his all dimensions doubled weighs eight times as much, but avoids the rest via A Wizard Did It.
    • And yet, while getting it right there, completely fails to grasp it in the monster sections. Numerous monsters in the books are given proportions that indicate the world is being overrun by very scrawny ogres made of balsa wood.
    • Also played somewhat straight in that a creatures lifting capacity does not typically scale directly with the creature's mass. For an 8x mass increase for an extra size category, a creature typically receives a 6x increase in carrying capacity. It gets worse when A Wizard Did It, as spells such as enlarge person increase the creatures weight by the usual eight times, but only increases their carry 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 creatures shape, it more or less points out that it has to be scientifically plausible or the creature will die because of an unsound anatomy.
  • 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.
  • Warhammer 40,000, thanks to Rule of Cool-powered physics, it looks like cumbersome size can always be counterbalanced by slapping more guns and/or spikes on the thing.
    • Humongous Mecha - Imperial Titans, Gargants… Stompas at least have wide feet.
    • Land Battleships - Baneblade and its derivatives (13.5m long and 8.4m wide, it's bigger than Maus - see below)
    • Giant monsters - Squiggoths, Hive Tyrants… 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 (or at very least sink butt-deep into the ground) from it's own weight is anyone's guess.
  • 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.


Video Games

  • The giant that appears in Touhou 12.3: Hisoutensoku is repeatedly pointed out to be impossible due to this law. Sanae even draws comparisons to Humongous Mecha from anime. Of course, since this takes place in Gensokyo, the fact that it's impossible is a perfect justification for it showing up...
  • 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.
  • In 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.
  • Liir from Sword of the Stars 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.
  • 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.


Web Original

  • 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.


Web Comics

  • 8-Bit Theater - lampshaded in this 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.
  • Similarly, in Order of the Stick #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.
  • 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.
  • In this strip of El Goonish Shive, 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.
  • Used in this Bob the Angry Flower strip, if not stated outright.
  • Schlock Mercenary has some huge critters on Eina-Afa. Analysis shows they are laced with metal glasses, especially muscle and skeletal tissues, and generally contain enough metal compounds to be highly poisonous for more conventional organic lifeforms ("depending on how you like your aluminium").


Western Animation

  • Lampshaded on The Venture Brothers 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.
    • The same character states the "proportional strength of an ant" idea to likewise be nonsense.
  • On Chipand 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.)
    • Of course, given how fatal falling seems to be in Disneyverse, perhaps they are right to fear it.


Real Life

  • 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. Similarly, leaner people tend to have fewer health issues than overweight or very muscular people, because they have less weight to carry around.
  • Robert Wadlow, who stood 8'11",[2] 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.
  • A sad example... 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.
  • The Nazis were getting hammered in the tank battles on the Eastern Front, so they decided to build a scaled-up tank, with armour 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 a 1,000 tonne, 25 metre long Landkreutzer with a 12" main gun, infirmary and toilet facility, and its big brother, the 1,500 tonne, 42 metre long "Monster" Landkreutzer with a 32" inch main gun. Those Wacky Nazis, indeed!
      • Interestingly, due to advancements and progresses in engineering technique and equipment (like the engines and how much power one can get out of them), the first two are likely. A handful of coal mining vehicles have definitely the weight and shape of the 1000tonner and the Maus. The only thing keeping them out of play is actually the new world's reliance on air power and mobility, fast strikes, and light compact squads and battalions. If it were still 'conventional arms only' then sure, they would almost be viable now. The actual maximum dimensions of military vehicles tends to be limited by the size of the train tunnels, highways and cargo planes that get them into the battle, while industrial vehicles like those enormous dump trucks are assembled in the place where they will work.
    • Another Nazi failure was the planned demolition of Berlin to build, among other things, the Volkshalle. 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.
    • Which is especially weird, because Germans themselves learned that big, heavily armored, but slow vehicles are most vulnerable to air support, after they met KV-2 (which was built to be used against fortifications, after all).
  • 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 push the envelope on size-there were dragonflies with 3 foot wingspans, for example. Nowadays, the same insects would suffocate.
    • Nowadays, as always, the insects grow to whatever size the local atmosphere supports, so all it takes for monster dragonflies and mosquitoes to return is a bit more oxygen.
  • Elephants often break bones just from tripping and falling over.
  • 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. 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 and a poisonous saliva like a Komodo Dragon's) that may have lessened the need to to run, thus the risk of falls.
    • It is now discovered that the 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.
      • More like specialist kill-hijackers, same as male lions prefer to be.
    • Imagine how slow sauropods would have been due to their gigantic sizes.
      • They couldn't have been too slow, or they would have depleted forests of their leaves faster than they could move to new areas.
    • Early paleontologists believed that large dinosaurs lived in swamps, because they approach being too large to move under their own power without the bouyancy of water. 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 - The Other Wiki has more on the various estimates of its length and mass, but it would have been every bit a "terrestrial blue whale".
  • 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.
  • 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.
  1. ↑ (the strength of a muscle or bone is proportional to the area of its cross-section, not to its total volume)
  2. ↑ about 272 cm
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