A modification of the Du Bois height-weight formula for surface areas of newborn infants

In 1916 Sawyer, Stone and Du Bois announced a series of measurements by which the surface area of adults and children could be estimated with an average error of 1.3 per cent. In a subsequent paper of the same series (1916) by Du Bois and Du Bois, a new formula based on height and weight alone was presented which was stated to have an error of $pL 5 per cent. This formula is as follows:

or

The constant C was found to be 71.84 (log 1.857).

It was not known whether the formula held for children under two years.

Since the first method is based on a separate estimation of the surfaces of the extremities, head and trunk there seems to be no reason why this method should not be applicable at any age. The height-weight formula should however apparently be checked for young infants.

In a series of 100 newborn babies, none over 12 days old, ranging in weight from 2,140 to 4,520 grams and in height from 45.2 to 56.9 cm., the surface area was measured by the Sawyer, Stone and Du Bois method and compared with the results obtained by the height-weight formula of Du Bois and Du Bois. Taking the former as the correct measure, we found that the latter showed a constant deviation below the former which averaged 191 sq. cm. or a mean error of −8.6 per cent. Correcting the constant, it was found that the surface area could be computed in these infants by the height-weight formula with an average error of ± 2.5 per cent.

For newborn infants the corrected formula is as follows:

or