= Mosteller formula
{c}
{title2=$\mathrm{BSA}=\sqrt{h_{\rm cm}m_{\rm kg}/3600}$}
The \b[Mosteller formula] estimates <body surface area> from height and body <mass> using a single square root:
$$
\widehat S=\sqrt{\frac{h_{\rm cm}m_{\rm kg}}{3600}}\;\mathrm{m^2}.
$$
Here $h_{\rm cm}$ and $m_{\rm kg}$ are numerical values in centimetres and kilograms. <R. D. Mosteller>'s primary correspondence appeared in 1987; the VA calculator documentation explicitly states this equation and the required units.<Simplified calculation of body-surface area by R. D. Mosteller>[New England Journal of Medicine 317, 1098, DOI 10.1056/NEJM198710223171717]{ref}<Formulas for Body Surface Area Calculator in the VA Clinical Reminders Manager's Manual>[Printed p. 36, Mosteller equation]{ref}
For stipulated height 180 cm and <mass> 80 kg, $\widehat S=2.00\,\mathrm{m^2}$. An equivalent metres-and-kilograms expression uses the divisor 36 rather than 3600: $\widehat S=\sqrt{h_{\rm m}m_{\rm kg}/36}\,\mathrm{m^2}$. Changing the height unit without changing the constant gives a tenfold area error. The constant belongs to the empirical formula and unit convention; the expression does not calculate an anatomical surface from first principles.
The <equal-product ambiguity in height-mass surface estimates> is instructive. Height 160 cm and <mass> 90 kg also give product 14,400 and the same predicted area. These two input pairs do not specify the same body shape or prove equal actual skin area. Additional anatomical information has been deliberately compressed into a two-input predictor.
Small relative changes obey $d\widehat S/\widehat S\simeq\tfrac12(dh/h+dm/m)$. A 2% <mass> increase at fixed height therefore changes the predicted area by about 1%; the exact factor is $\sqrt{1.02}$. This sensitivity concerns the calculated prediction, not the accuracy of the empirical body model. <Formula uncertainty versus surface-area model error> separates those questions.
If a stipulated <cardiac output> of 5 L/min is divided by predicted area $2\,\mathrm{m^2}$, the indexed value is $2.5\,\mathrm{L\,min^{-1}\,m^{-2}}$. Normalization changes the quantity and its units. It does not independently validate the area estimate or make the indexed quantity a complete description of cardiovascular function. Record the exact formula and measured input units whenever such normalized results are compared.
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