Estimating body surface area from mass and height: theory and the formula of Du Bois and Du Bois

Abstract

Background: Body surface areas are usually estimated by means of a formula due in its general form to Du Bois and Du Bois (1916), i.e. area = C x mass(a) x height(b), where C, a and b are empirical constants. Its physical basis is unknown.

Aim: The present study aimed to explain this formula, correct some errors in the associated literature and provide a clear basis for future developments.

Subjects and methods: Use is made of published data, but arguments are largely based on mathematics and modelling.

Results: A more fundamental formula is as follows: area = alpha(mass x height)(1/2) + beta(mass/height), where alpha and beta are constants. For realistic values of mass and height the two equations are numerically equivalent. For individuals, beta cannot be negative and b cannot exceed a, but, as regression parameters, these conditions may not be satisfied. This could be due to systematic or statistical relationships between individual values of alpha or beta and the ratio height(3)/mass. Values of alpha, beta, C, a and b are calculated for some published data.

Conclusions: The original type of formula suffices for practical purposes, but the new one is better in analytical contexts when other terms, e.g. for body shape, are to be incorporated.