# Dimensional analysis of the Body Surface Area

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?

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 $$\beta_h = 0.725$$.
To make everything explicit, using again the Du Bois, Du Bois formula: $$BSA = 0.007184 [m^2] \times \left(\frac{W}{1 [kg]}\right)^{0.425} \times \left(\frac{H}{1 [m]}\right)^{0.725}$$
• 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 $\text{meters}^{0.8273}$ – ja72 Nov 8 at 5:08