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Looking at the Body Surface Area in Wikipedia, the units used in the formula are:

BSA is in m2, W is mass in kg, and H is the height in cm

How is it possible to get the BSA in m2 from just the weight and the height?

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I can't access the original papers, but usually, these formulas were obtained by something like a linear regression in a log-log scale, i.e., the logarithm of the body surface area $b = \log_{10} BSA$ is obtained as a linear function of the logarithm of weight $w = \log_{10} W$ and the logarithm of height $h = \log_{10} H$.

So, they have obtained the coefficients of an expression like: $$ b = \beta_0 + \beta_w w + \beta_h h $$ such that $\beta_0$, $\beta_w$ and $\beta_h$ are chosen to optimize the fit, i.e., the observed points (each value of $b_j$ for individual $j$) are as close as possible to the result of the formula (for $w_j$ and $h_j$ for the same individual $j$).

For instance, the Du Bois, Du Bois formula obtained $\beta_0 = \log_{10} (0.007184)$, $\beta_w = 0.425$ and $\beta_h = 0.725$.

In particular, this means that the coefficients have dimensions that are needed for everything to make sense.

To make everything explicit, using again the Du Bois, Du Bois formula: $$BSA = 0.007184 [m^2] \times \left(\frac{W}{1 [kg]}\right)^{0.425} \times \left(\frac{H}{1 [m]}\right)^{0.725}$$

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  • $\begingroup$ Thank you. I cringe when I see people do log-log curve fitting with dimensional quantities. It is always important to make them dimensionless before any curve fitting to be done. Otherwise, you end up with units like $\text{meters}^{0.8273}$ $\endgroup$ Nov 8 '19 at 5:08

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