Hydrostatic weighing

The procedure is based on Archimedes' principle, which states that: The buoyant force which water exerts on an immersed object is equal to the weight of water that the object displaces.

Example 1: If a block of solid stone weighs 3 kilograms on dry land and 2 kilogram when immersed in a tub of water, then it has displaced 1 kilogram of water. Since 1 liter of water weighs 1 kilogram (at 4 °C), it follows that the volume of the block is 1 liter and the density (mass/volume) of the stone is 3 kilograms/liter.

Example 2: Consider a larger block of the same stone material as in Example 1 but with a 1-liter cavity inside of the same amount of stone. The block would still weigh 3 kilograms on dry land (ignoring the weight of air in the cavity) but it would now displace 2 liters of water so its immersed weight would be only 1 kilogram (at 4 °C).

In either of the examples above, the correct density can be calculated by the following equation:

${\displaystyle D_{b}={\frac {M_{a}}{{\frac {M_{a}-M_{w}}{D_{w}}}-RV}}}$

Where:

• D_b = Density of the body;
• M_a = "Mass in air" (i.e. dry weight);
• M_w = "Mass in water" (i.e. underwater weight);
• D_w = Density of water (based on water temperature);
• RV = Residual volume (the unfilled space enclosed by the body- e.g. volume of air in the lungs + respiratory passages after a maximum exhalation).

The residual volume in the lungs can add error if not measured directly or estimated accurately. Residual volume can be measured by gas dilution procedures or estimated from a person's age and height:[1]

• Inches: RV-Est(Men) = 0.033 X Ht. (inches) + 0.022 X Age (yrs.) - 1.232
• Metric: RV-Est(Men) = 1.310 X Ht. (meters) + 0.022 X Age (yrs.) - 1.232

• Inches: RV-Est(Women) = 0.046 X Ht. (inches) + 0.016 X Age (yrs.) - 2.003
• Metric: RV-Est(Women) = 1.812 X Ht. (meters) + 0.016 X Age (yrs.) - 2.003

Residual volume may also be estimated as a proportion of vital capacity (0.24 for men and 0.28 for women).[2]

Once body density has been calculated from the data obtained by hydrostatic/underwater weighing, body composition can be estimated. The most commonly used equations for estimating the percent of body fat from density are those of Siri[3] and Brozek et al.:[4]

Siri (1956): Fat % = [4.950 /Density - 4.500]×100

Brozek et al. (1963): Fat % = [4.570 /Density - 4.142]×100

• Body composition
• Composition of the human body
• Body fat percentage