# Siri Equation

Many body composition equations derive their measure of percent body fat from first determining body density. Once body density is determined, percent bodyfat (%BF) can be calculated using the Siri equation below :

% Body Fat = (495 / Body Density) - 450.

## Derivation

The Siri Equation is based on the two compartment model, that is the body is made up of essentially two components: fat mass (the total fat of an individual) and fat-free mass (everything else: bone, water, lean tissue etc). Studies have determined that the densities of these two components are:

fat mass = 0.9 grams per cc
fat-free mass = 1.10 grams per cc.

As density = mass / volume, and the mass of a human is made up of the total of fat mass and fat-free mass, therefore density = (fat mass + fat-free mass) / volume. Following this through and substituting mass/density for volume, and using the values for density above, eventually you get to the Siri Equation as listed.

## Similar Equations

Here are a few other equations that similarly convert body density to percent body fat. Various equations are required to best fit different populations, age groups and gender.

Brozek Percent Fat Equation:
%fat = (457 / Body Density) – 414.2

Schutte Percent Fat Equation (for African American males):
%fat = (437.4 / Body Density) – 392.8

Wagner Percent Fat Equation (for African American males)
%fat = (486 / Body Density) – 439

Ortiz Percent Fat Equation (for African American females)
%fat = (483.2 / Body Density) - 436.9

## References

• Siri, W. E. (1961). Body composition from fluid space and density. In J. Brozek & A. Hanschel (Eds.), Techniques for measuring body composition (pp. 223-244). Washington, DC: National Academy of Science.
• Brozek, J., Grande, F., Anderson, J. T., & Keys, A. (1963). Densitometric analysis of body composition: Revision of some quantitative assumptions. Annals of the New York Academy of Sciences, 110, 113-140.

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