Why is the body mass index calculated as mass/height2, not as mass/height3?

The body mass index or BMI, mass/height(2), is used to predict fatness and health. It is an approximation to the Benn index, mass/height(p), where p (typically 1.1-2.5 for adult populations) makes the index uncorrelated with height. Mass/height(3) is an index of body build that is independent of scale and statistics.

To explain why p varies and is less than three, show how statistical methods can distort perceptions of mass-height relationships, and clarify the nature of the BMI.

A hypothetical adult population is modelled statistically, with mass being approximately proportional to height(3) and with neither variable determining the other. Values of p are calculated both for the model and for real adults.

In both cases p increases with the correlation between mass and height. Both p and that correlation are usually lower for women than for men.

In adult populations mass must vary more nearly with height(3) than with height(2), although, for reasons explained, conventional statistical techniques suggest otherwise. Nevertheless the BMI is a valid predictor of fatness from mass and height in adults and is properly divisible into fat mass and fat-free mass indices. The validity of the latter three indices for children is questionable.