We know how complex cells evolved.

The square cube law impacts the structure and mechanics of organisms in many ways.

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.


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!


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

"The Square Cube Law Impacts Biomechanics" is tagged with: Evolution

Vote Fact or Myth: "The Square Cube Law Impacts Biomechanics"

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Stewart Macpherson on
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.


Thomas DeMichele on

Really interesting argument, but I am lost on the idea that gravity doesn’t have an effect in water? Maybe you are dumbing down what you mean?

Stewart Macpherson on

A whale is suspended in its own peculiar medium- water. Astronauts train in deep tanks of water because this simulates weightlessness. A whale experiences weightlessness (does not feel the effects of gravity), even although it experiences hydrostatic pressure, which is a force in ALL directions simultaneously, unlike gravity which is uni-directional.

Therefore, since the whale ‘floats’ in its own medium (water) it would have no need for such massive bones. Whale bones are indeed very large compared to most land (air medium) animals, but according to the square/cube law they should have no need for such large bones because there is no force of gravity in their medium.

That being the case, if the square/cube law were fact (which it most definitely is NOT), the whale would have no need for such massive bones, it would be more like the jelly fish.

The reason the square/cube law causes so much confusion is that it states that it is the sole purpose of the load-bearing capacity of the skeleton of living things to support its body mass. This is only partially true. It is, in fact, the combined (reciprocal) action of tendon AND bone. The bone resists bending allowing the muscle and tendon to facilitate movement, for nature has designed us to MOVE, rather than stand motionless, like a post and lintel, innert structure.

Stewart Macpherson on

Hi Thomas,
I notice you have stopped responding to my comments on ‘Square cube law impacts biomechanics’. Could this be that you cannot establish, whether or not, this centuries old assumption is indeed in question, or whether you are not able to find anyone willing to stick there neck out and challenge me?

You see, it matters not to me either way as I have no ‘position’ to lose- I am not even an academic. But that does not mean I do not know what I’m talking about, I assure you. My own privateer study into structural engineering has unequivocally demonstrated to me, in the form of proof-of-concept models (whose dimensions are independent of scale), that Galileo’s mathematical insights have been wrongly interpreted from the start, not least, by Galileo himself!?

You might think this cannot be so. Once again, I assure you, EVERYONE has falsely misrepresented the importance of the ‘cross-sectional-area’ (csa) to the size (and therefore the load) on animal bone as proof that large animals cannot exist. As I am at pains to point out, this is not actually how bone reacts to load, which means it is independent of csa, and entirely dependent on its stiffness- a ‘hyper-elastic’ reaction.

Stewart Macpherson on

I am going to reply to myself, since nobody seems to want to talk (ironically enough, this is exactly what Galileo did in his Two Sciences).

Let’s look at his claim that the Cube (volume and therefore mass) of an object/mammal grows faster than the Area (surface). In pure mathematics this is an inescapable, nonetheless abstract, truth. However, this fact is then justified by reference to physical things like mammals. In particular the area of the cross-sectional dimensions, and by implication the load-bearing capacity of bone, are further assumed to behave according to this ratio; in the process implying that a section will have the same properties as a surface- a section will (similarly) increase ‘slower’ than a volume.

Unfortunately, when one cares to test this logic by doing the obvious (putting some numbers in) one finds that the Cube (volume/mass) does NOT ‘outstrip’ the Area (section). In fact what the simple arithmetic quite clearly shows is that section and volume scale proportionally, that is to say, ‘in step’ with each other, and coefficient of proportionality is the ‘six-ness’ of a surface.

This result is not as an observation of physical ‘things’ such as an elephant, it is an inescapable abstract mathematical certainty- maths does not lie, only humans are capable of misrepresenting it’s consequences and outcomes…

When all this is said and done we further find that between Newton and Galileo the resultant gibberish around structural properties are just as baffling, and the real truth is that they made wildly fictitious and problematic assumptions based on invention and intuition alone. There now, have I said enough… (gulp!)