The U.S. Navy body fat method: from tape measure to percentage

Where the equations come from

James Hodgdon and Marcie Beckett published two reports in 1984. Report 84-11 covered men and report 84-29 covered women. Both were titled as predictions of percent body fat for U.S. Navy personnel from body circumferences and height.

The reference method was hydrostatic, or underwater, weighing. It measures body density, with the air left in the lungs measured separately by helium dilution. The men's sample was 602 Navy personnel aged 18 to 56. The women's development sample was 214 Navy women. The women's report also includes a field lookup table in inches, so the method could be used without logarithms.

The researchers then searched for the tape measurements that best predicted that lab density. For men, the winners were abdomen minus neck. For women, they were waist plus hip minus neck.

Step 1: body density

Both equations use base-10 logarithms, with every measurement in centimeters. The report abstracts round the coefficients, for example to −0.191 and 0.155 for men. The full-precision values below are from the report text and are what the calculator uses.

Step 2: Siri's equation

Density is not yet a percentage. The reports convert it with Siri's 1961 equation, a standard step for turning lab density into percent fat.

Written as in the men's report, percent body fat = (4.95 ÷ density − 4.50) × 100. Multiplied out, that is 495 ÷ density − 450, the form the calculator uses.

Where the tape goes

The calculator asks for ‘Height’, ‘Neck’ and ‘Waist’, plus ‘Hips’ when ‘Sex’ is set to Female. The reports describe how each was measured:

• Neck: just below the larynx, with the tape sloping slightly downward to the front.
• Waist for men (abdomen II in the report): at the level of the navel.
• Waist for women (abdomen I): at the narrowest point of the abdomen, about midway between the bottom of the breastbone and the navel.
• Posture: standing relaxed, with chest and abdomen measured at the end of a normal breath out.
• Tape: applied without compressing the skin; the men's report recorded readings to the nearest millimeter.

How accurate it is

Each report gives a standard error of estimate, the typical gap between the tape prediction and underwater weighing. For men, the development sample had a correlation of 0.90 and an error of about 3.5 percentage points of body fat.

The men's equation was then checked on 100 men from a different laboratory. The correlation stayed at 0.90, with an error of 2.7 points, though the predicted mean was slightly but significantly higher than the underwater result.

For women, the development sample had a correlation of 0.85 and an error of about 3.7 points. In cross-checks, the error was 4.36 points in 66 Canadian Forces women and 4.04 points in 80 U.S. Navy women. For comparison, the report tested an earlier equation by Wright and colleagues on the same women. It had a correlation of 0.80 and an error of 4.19 points.