= Formula uncertainty versus surface-area model error
\b[Formula uncertainty versus surface-area model error] separates precision in evaluating a body-size formula from adequacy of that formula for an individual's actual <body surface area>. Repeating height and <mass> measurements can reduce their sampling uncertainty without making the predicted anatomical surface exact.
The Mosteller formula, documented with centimetre and kilogram inputs in the VA manual, is $\widehat S=\sqrt{H_{\rm cm}M_{\rm kg}/3600}\,\mathrm{m^2}$.<Formulas for Body Surface Area Calculator in the VA Clinical Reminders Manager's Manual>[Printed p. 36, Mosteller formula and input units]{ref} An original measurement model can instead write $S_{\rm true}=f(H,M;\theta)+D$, where $\theta$ represents fitted coefficients and $D$ residual model discrepancy. Variation in body shape is not represented by improved arithmetic alone.
For small independent input errors with fixed coefficients,
$$
\left[\frac{u(f)}f\right]^2\simeq\frac14\left[\frac{u(H)}H\right]^2+\frac14\left[\frac{u(M)}M\right]^2.
$$
Coefficient uncertainties, correlations and model discrepancy are additional terms when significant. The GUM explicitly requires a measurement model to include relevant corrections and quantities reflecting incomplete knowledge.<Guide to the expression of uncertainty in measurement by JCGM>[§4.1.2]{ref}
For stipulated prediction $2.00\,\mathrm{m^2}$, input-related <standard uncertainty> $0.02\,\mathrm{m^2}$ and independent zero-mean discrepancy uncertainty $0.10\,\mathrm{m^2}$, the combined value is $\sqrt{0.02^2+0.10^2}\approx0.102\,\mathrm{m^2}$. Reducing only the input term tenfold gives approximately $0.100\,\mathrm{m^2}$, illustrating a <repeatability floor from surface-area model discrepancy>. These are constructed uncertainties, not published performance limits. A known nonzero model bias calls for correction; assigning a zero-mean random term does not remove it.
Normalization can transmit the discrepancy into another quantity. For fixed measured <cardiac output> $Q$, the ratio of $Q/\widehat S$ to $Q/S_{\rm true}$ is $S_{\rm true}/\widehat S$. A stipulated true area 2.0 and predicted area $1.8\,\mathrm{m^2}$ therefore increases the indexed result by about 11.1%. Extra displayed digits do not resolve the anatomical mismatch.
A validation experiment compares predictions with independently characterized surface measurements over the intended range of body shapes and sizes, retaining uncertainty in the reference method. Report input repeatability, coefficient estimation, average bias and residual spread separately rather than interpreting them all as one source of error.
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