 Body surface area

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:Here $H_{\mathrm{cm}}$ and $M_{\mathrm{kg}}$ are the numerical values of height in centimetres and body mass in kilograms. The primary correspondence is by R. D. Mosteller.^[ref] The VA implementation explicitly documents this formula and its required input units.^[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 $u(S)/S\simeq \frac{1}{2}\sqrt{[u(H)/H{]}^2+[u(M)/M{]}^2}$. 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.