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Original Article

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

Pages 170-184 | Received 03 Jun 2007, Accepted 09 Jan 2008, Published online: 09 Jul 2009
 

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 × massa × heightb, 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 = α(mass × height)1/2 + β(mass/height), where α and β are constants. For realistic values of mass and height the two equations are numerically equivalent. For individuals, β 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 α or β and the ratio height3/mass. Values of α, β, 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.

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