Why does BMI have units of kg/m^2 when we are three dimensional? Wouldn’t kg/m^3 or g/cm^3 be more accurate?
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Density isn’t really a good measure of how overweight you are, since being heavier doesn’t necessarily mean you are denser.
Others have pointed out that it’s a consequence of an arbitrary formula which has been shown to work. But it’s also worth asking _why_ it works.
From dimensional analysis, it’s a loose proxy for (the inverse of) your surface area to volume ratio by taking a proxy for your volume (your mass) against a proxy for your surface area (the square of your “characteristic length”). A shape that approximates a sphere will tend to have very low surface area to volume, and more convoluted / “branchy” shapes will have higher surface area to volume. It follows that the more volume you have for a given surface area, the rounder you are!
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