The density of the body can be determined by weighing the body in air and underwater. From the body density the proportion of fat can be determined and the fat free mass calculated.

Underwater weighing apparatus:

(1) The person is submerged on a chair into a tank of water breathing through a snorkel.

(2) Weights are taken at maximum expiration to minimize lung volume.

(3) If residual volume is to be measured, a three-breath nitrogen dilution method can be performed when weight is being taken.


body density in kilograms per cubic meter =

= (weight in air) / ((((weight in air) - (weight in water)) / (density of water)) - (residual volume))



• The density of water varies with temperature and is usually under 1,000 kg per cubic meter.

• Fat has a density of about 900 kg per cubic meter.

• Fat-free body tissue has a density of about 1,100 kg per cubic meter.


Siri Equation


percent body fat =

= (4950 / (body density in kilograms per cubic meter)) - 4.50 =

= (4.95 / (body density in grams per cubic cm)) - 4.50



• If no fat is present and body density is 1,100 kg per cubic meter, 4950/1100 = 4.5 and there is 0% fat

• If only fat is present then the density is 900 kg per cubic meter and 4950/900 = 5.5, and there is 100% fat.


fat free mass =

= (1 - (percent body fat)) * (body weight in kilograms)


Correction for Air in Lungs and Intestines


The underwater weight is taken at maximum expiration. At this point a small volume due to residual lung volume and air in the intestines is present.


Residual volumes in adults can be calculated by one of several equations.


According to Goldman (1959):


predicted RV in liters in males =

= (0.069 * (height in inches)) + (0.017 * (age in years)) - 3.45


predicted RV in liters in females =

= (0.081 * (height in inches)) - (0.009 * (age in years)) - 3.9


More precise calculation of the residual volume can be calculated based on analysis of expired air, barometric pressure, temperature and the dead space in the breathing apparatus used.


Uncertainties in Implementation


Uncertainties at the time of implementation:

(1) Should mass (weight divided by gravity) be used instead of weight?

(2) Should residual volume be expressed in liters or in cubic meters? (used cubic meters in implementation, dividing liters/1000)

(3) What are appropriate weights for adults in water? To make equations work, weights of 4-5 kilograms were needed.

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