The “Square Cube Law”
In: Mathematics
Imagine you have a cube of something. It has side length one, and six faces of area one (total surface area 6), and volume of one.
Now, if you want to double the side length, you’ll have a 2x2x2 cube. Six faces of area 4 (total 24), and the volume is now 8. So the volume has gone up by the scale factor cubed (faster), and the surface area has gone up by the scale factor squared (slower than cubed).
Every type of shape scales this way. So when you make something bigger, you have to worry about how surface area-dependent properties interact with volume-dependent properties.
In living systems, volume affects things like weight and how many cells you need and how much blood you need to supply it. Surface area affects things like how much oxygen you can absorb through your lungs and how much heat you can exchange with the environment. Cross sectional area (also scales like area) affects things like how much weight your bones and muscles can support.
If any of the square things can’t keep up with the cube things, you have a scaling problem.
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