Square-Cube Law/Sandbox



"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.

If, for example, the edge length of a cube is doubled, its surface area is increased four times and its volume (and mass) is increased by the factor 4.

An animal scaled up 10 times has 1,000 times the mass of its smaller version, while the cross section of muscles and bones would only increase 100 times. Bones and muscles would be stressed ten times more compared to the original. The oxygen uptake per kilogram would be 10 times lower. The change in the ratio of surface area and body volume would mess up the the ability to dissipate heat... In other words, you can't just scale something up (or down) and expect it to still work.

In case of flying animals the wing loading would be increased with increased size. Water-dwelling creatures would be less affected, since buoyancy depends on displaced water, which does go up as the cube of the size.

This is not limited to living creatures: A skyscraper requires much more structural support than a two-story house, and can't be made of the same materials because wood and brick can't support their own weight once you get the structure tall enough. Likewise, a Humongous Mecha a with humanoid shape would require incredibly strong legs (probably made of some sort of Unobtainium) to be able to support its huge frame, and it would need some really large feet so that it wouldn't sink up to its waist every time it took a step.

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.