The Square Cube Law Impacts Biomechanics fact

We know how complex cells evolved.

Why Do Large Animals and Small Animals Seem to Be Built Differently? It’s Allometry My Dear Watson.

The square cube law says that volume increases faster than surface area when an object increases proportionally in size. This impacts biomechanics (the way organisms are built and function).[1][2][3]

Here is what that means and some interesting implications in bullet-point form:

  • Isometric scaling happens when proportional relationships are preserved as size changes (for example in an organism, during growth within a life cycle or over time due to evolution).
  • Isometric scaling is governed by the square-cube law (when size doubles “isometrically” surface area squares, and volume and mass cube).
  • If an organism doubles in length isometrically then the surface area available to it will increase fourfold (square), while its volume and mass will increase by a factor of eight (cube).
  • In animals, skin is on the surface layer. Meanwhile, the volume and mass of animals is comprised of cells, skeleton, and muscle.
  • Allometric scaling is any change that deviates from isometry.
  • Larger and smaller animals don’t tend to look alike, because builds and mechanics that work well with smaller size animals don’t tend to work as well with larger sizes. Further, what works well in one environment doesn’t necessarily work well in another. Thus, nature does more allometric scaling than isometric scaling in both life cycles and in evolution.
  • Smaller animals have an on-paper problem of lacking the surface area ideal for releasing the heat created from their cells. Larger animals have the on-paper problem of having too little surface area on paper (they also have the problem of needing very sturdy bones to prop up their massive bodies; see Galileo in his Dialogues Concerning Two New Sciences).
  • Due to the square cube law, larger animals should need exponentially more surface area than they have on-paper. Nature solves this problem by “making” the metabolic rate of the cells of larger animals lower (their cells work less, thus produce less heat, thus the larger animal can have less surface area to volume than the smaller animal and still not overheat).
  • Smaller animals have the opposite problem, they have a lot of surface area, but they lack space for cells. Thus, smaller animals have cells that work overtime (they don’t have more room, and have a lot of surface area, so their cells work faster to account for this). This is why smaller animals tend to have shorter lives and need to eat more frequently (as food is converted into energy, AKA metabolized, which allows cells to work).
  • One way to say this is that smaller animals tend to have a faster “speed of life” than larger animals in general (this isn’t always true, as nature has some pretty interesting builds).

The takeaway: The square cube law impacts many aspects of why specific size organisms and specific types of environments are built the way they are built and grow the way they grow. Its really a matter of efficiency.

Anything not clear from the above should become clear by watching the videos below.

What Happens If We Throw an Elephant From a Skyscraper? Life & Size 1.

How to Make an Elephant Explode with Science – The Size of Life 2.

Article Citations
  1. Square–cube law: Biomechanics
  2. Allometry
  3. Biomechanics

The square cube law impacts the structure and mechanics of organisms in so many interesting ways that fitting them all into a catchy title is rather elusive. The concept is super interesting though. If you didn’t fully get it, check out those videos again. They are worth watching!

Author: Thomas DeMichele

Thomas DeMichele is the content creator behind,,, and other and Massive Dog properties. He also contributes to MakerDAO and other cryptocurrency-based projects. Tom's focus in all...

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Stewart Macpherson Doesn't beleive this myth.

I have never heard so much nonsense in all my life. Firstly, whilst three dimensional mass may seem ‘intuitive’ it does not really exist, in the same sense that there is no such thing as ‘a force due to gravity’. In other words Things are never truly solid. They merely comprise myriad surfaces- like 3D fractals. Secondly, an animal, whether it be man, mouse or elephant does not support itself through having the requisite cross-sectional area of bone, alone. It does, however, move by mutual interaction of muscle and tendon attached to bone. The bone provides the mechanism of locomotion by being stiff enough to provide energy for motion (which comes from our food) by mutual exchange with our tendon. Don’t believe me?

Always be suspicious of the exception to the rule. The exception to the square/cube law is the whale. Which does not interact with the air. It is suspended in its own medium; water. Therefore it does not feel the effects of ‘gravity’. Ask yourself this question, if that’s the case, why is the cross-sectional area of its bone so large. Indeed, it is the largest mammal on earth? Surely, if the square/cube law was correct, by that definition, a whale would have no need for bone at all. It would be more like a giant jelly-fish. No, No, No. this kind of reasoning is fantasy.

A mammal primarily supports itself by the mutual interplay between its nervous system, which triggers the command, to its muscle which contracts, pulling on its tendon, which is, in turn, resisted by the stiffness of the bone. That, is the true property of bone. It has very little to do with load-bearing capacity. In deed load-bearing capacity is simply a happy coincidence.