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

BACKGROUND: 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. AIM: 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. METHODS: 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. RESULTS: 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. CONCLUSIONS: 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.