How strength scales with height

Generally, the smaller the creature, the greater its strength in proportion to its weight. The reason lies in the square cube law.

When something increases proportionally in size, say by doubling all its dimensions by r, its surface area increases by a factor of r², while its volume increases by r³.

Since a number cubed increases faster than one raised to the power of two, an object’s volume also increases faster than its surface area.

This has numerous consequences for the respiratory system, the size of animals, heat dissipation, and so much more in the physical world.

The force exerted is proportional to the cross-sectional area of a muscle.

But the weight of that muscle, which it has to support primarily, increases faster than its area, since it is proportional to the volume.

This means that a smaller muscle is almost always stronger gram for gram than a larger one.

This is most evident with insects, which can carry many times their weight (also assisted by the exoskeleton that acts as a support), while a gorilla can lift at “most” a few times its own body weight.

The same thing happens, even though to a lesser extent, with people.

Taller people have more strength in an absolute sense, while shorter people are stronger proportionally.