Hydrostatic weighing

Hydrostatic weighing, also referred to as "underwater weighing," "hydrostatic body composition analysis," and "hydrodensitometry," is a technique for measuring the mass per unit volume of a patient's body.

Method
The following method has the advantage of needing no volume information of the body (see the note about the residual volume below). The procedure is based on Archimedes' principle, using the following three measurable values: The weight of the body outside the water, the weight of the completely immersed body (a weight that may be negative if the body in question is less dense than water) and the density of the water:
 * $$ \frac { \mbox{density of body}} { \mbox {density of water} } = \frac { \mbox{weight of body}} { \mbox{weight of body} - \mbox{weight of immersed body}}\,$$

Multiplying by the density of water gives
 * $$ \mbox{density of body} = \mbox {density of water} \frac { \mbox{weight of body}} { \mbox{weight of body} - \mbox{weight of immersed body}}\,$$.

Correcting for the residual volume of air in the lungs upon maximal exhalation, and the approximately 100 cc of air trapped in the intestines gives:
 * $$ \mbox{density of body} = \frac { \mbox {density of water} * \mbox{weight of body}} {( \mbox{weight of body} - \mbox{weight of immersed body}) -  \mbox {density of water} * ( \mbox{residual lung volume} + \mbox{100 cc})}\,$$.

Residual lung volume can be estimated as a proportion of vital capacity (0.24 for men and 0.28 for women).

Application
From this density information body composition and percentage body fat may be estimated. This is occasionally used for assessment of obesity. The residual volume in the lungs can add error if not measured directly. Hydrostatic weights gives body density, and percent body fat can be estimated using the Siri or Brozek formula.