= Body surface area
{title2=BSA}
\b[Body surface area] is the total <surface area> of the body's external covering, usually expressed in square metres. It is an anatomical geometric quantity. An estimate calculated from height and <mass> is a measurement model for that quantity, rather than a direct measurement of every part of the skin surface.
For an idealized external surface $\Sigma$, its geometric definition is $S=\int_\Sigma dS$, a <surface integral>. Geometrically similar bodies enlarged by a length factor $\lambda$ have <surface areas> scaling as $\lambda^2$ and, at equal <density>, <masses> scaling as $\lambda^3$. Thus an area estimate based on <mass> alone has the similarity form $S\propto M^{2/3}$. Real bodies need not be geometrically similar, which motivates empirical models using more than one body dimension.
The calculation proposed in a 1987 primary letter is commonly written in the following unit-specific form:
$$
\widehat S=\sqrt{\frac{H_{\rm cm}M_{\rm kg}}{3600}}\;\mathrm{m^2}.
$$
Here $H_{\rm cm}$ and $M_{\rm kg}$ are the numerical values of height in centimetres and body <mass> in kilograms. The primary correspondence is by <R. D. Mosteller>.<Simplified calculation of body-surface area by R. D. Mosteller>[New England Journal of Medicine 317, 1098 (22 October 1987), DOI 10.1056/NEJM198710223171717]{ref} The VA implementation explicitly documents this formula and its required input units.<Formulas for Body Surface Area Calculator in the VA Clinical Reminders Manager's Manual>[July 2012 manual, printed p. 36, Mosteller formula]{ref}
At stipulated height 180 cm and <mass> 80 kg, the estimate is $\sqrt{180(80)/3600}=2.00\,\mathrm{m^2}$. Entering 1.80 while retaining the centimetre-based constant instead gives $0.20\,\mathrm{m^2}$, a tenfold error. The coefficient includes the unit convention; it is not a dimensionless universal law.
<Formula uncertainty versus surface-area model error> separates input precision from predictive adequacy. For independent small height and <mass> errors, this model gives $u(S)/S\simeq\tfrac12\sqrt{[u(H)/H]^2+[u(M)/M]^2}$. Relative input uncertainties of 1% and 2% therefore contribute about 1.12% to the calculated area. Residual error of the empirical body model is additional.
Dividing <cardiac output> or a ventricular volume by body surface area changes the reported quantity and units. It does not automatically remove every age, body-shape or population effect. Specify the formula and input units when comparing indexed physiological measurements.
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