Navy Body Fat Calculator: Formula, Code and Steps

How to Measure

These sites and steps come from the two Naval Health Research Center reports behind the equations. The waist is taken at a different place for men and women, and that is the step most calculators skip.

1. Height. Stand straight against a wall, without shoes.
2. Neck. Place the tape just below the larynx (the Adam's apple), sloping slightly downward to the front.
3. Waist, men. Measure level with the navel, at the end of a normal breath out.
4. Waist, women. Measure at the narrowest point, about midway between the lower tip of the breastbone and the navel, at the end of a normal breath out.
5. Hips, women. Measure at the widest backward point of the buttocks.

Stand relaxed. Keep the tape level, except at the neck, and let it follow the skin without pressing in. The study teams measured each site twice, took a third reading if two differed by more than 1 cm, and used the mean. That habit is worth copying at home.

The Navy Body Fat Formula

The original reports predict body density, then convert density to percent body fat with the Siri equation. Both steps fit on one line. With every length in centimeters and log10 as the base-10 logarithm:

Men:
body fat % = 495 / (1.0324 - 0.19077 × log10(waist - neck) + 0.15456 × log10(height)) - 450

Women:
body fat % = 495 / (1.29579 - 0.35004 × log10(waist + hip - neck) + 0.22100 × log10(height)) - 450

The coefficients are from Report 84-11 for men and Report 84-29 for women. We checked them against scans of both reports. The summary pages of those reports show rounded values such as 0.191 and 0.350. The figures above are the full ones from the body of each report.

Worked Example: Man

Height 180 cm, waist 85 cm, neck 38 cm.

waist - neck  = 85 - 38 = 47
log10(47)     = 1.67210
log10(180)    = 2.25527
density       = 1.0324 - (0.19077 × 1.67210) + (0.15456 × 2.25527) = 1.06199
body fat %    = 495 / 1.06199 - 450 = about 16.1

Worked Example: Woman

Height 165 cm, waist 75 cm, hips 100 cm, neck 33 cm.

waist + hip - neck = 75 + 100 - 33 = 142
log10(142)         = 2.15229
log10(165)         = 2.21748
density            = 1.29579 - (0.35004 × 2.15229) + (0.22100 × 2.21748) = 1.03247
body fat %         = 495 / 1.03247 - 450 = about 29.4

The Centimeter and Inch Trap

Search for this formula and you will mostly find a second version, which is for inches only:

Men:   body fat % = 86.010 × log10(waist - neck) - 70.041 × log10(height) + 36.76
Women: body fat % = 163.205 × log10(waist + hip - neck) - 97.684 × log10(height) - 78.387

This is the form the Department of Defense adopted. Hodgdon and Friedl describe it in a later technical document, No. 99-2B: it predicts percent fat directly, and all measurements are in inches. It is not a unit conversion of the metric form, so the two give slightly different answers. Copying it into code that takes centimeters gives a wrong answer with no error. Here are our two example people, run all four ways:

The inch-form error is a fixed offset. Using centimeters adds (86.010 - 70.041) × log10(2.54), or about 6.5 points, to every man's result. For every woman it adds (163.205 - 97.684) × log10(2.54), or about 26.5 points. The men's error is the dangerous one, because 22.6% looks believable and passes a quick glance.

This page uses the metric form for every result. Inch entries are converted to centimeters first. Under the main number, the calculator also shows what the inch form gives, so you can compare it with other tools. When we ran both forms over a grid of typical adult inputs, for results of 10% to 45% (men 160 to 195 cm with waists of 70 to 120 cm, women 150 to 185 cm with waists of 60 to 110 cm), the gap stayed under 1 percentage point. At extreme inputs it grows, to more than 2 points near this calculator's limits. That is our own arithmetic on the two equations.

JavaScript and Python Code

Both functions take centimeters and reproduce the worked examples above. Each one rejects inputs where the log would fail, such as a neck measurement larger than the waist.

JavaScript

// All lengths in centimeters. Returns estimated body fat percent.
function navyBodyFat({ sex, height, neck, waist, hip }) {
  const size = sex === 'male' ? waist - neck : waist + hip - neck;
  if (!(size > 0)) throw new RangeError('Check the measurements');

  const density = sex === 'male'
    ? 1.0324 - 0.19077 * Math.log10(size) + 0.15456 * Math.log10(height)
    : 1.29579 - 0.35004 * Math.log10(size) + 0.221 * Math.log10(height);

  return 495 / density - 450;
}

const inToCm = (inches) => inches * 2.54; // convert first, never swap coefficients

navyBodyFat({ sex: 'male', height: 180, neck: 38, waist: 85 });              // 16.1
navyBodyFat({ sex: 'female', height: 165, neck: 33, waist: 75, hip: 100 }); // 29.4

Python

from math import log10

def navy_body_fat(sex, height, neck, waist, hip=None):
    """All lengths in centimeters. Returns estimated body fat percent."""
    size = waist - neck if sex == "male" else waist + hip - neck
    if size <= 0:
        raise ValueError("Check the measurements")

    if sex == "male":
        density = 1.0324 - 0.19077 * log10(size) + 0.15456 * log10(height)
    else:
        density = 1.29579 - 0.35004 * log10(size) + 0.221 * log10(height)

    return 495 / density - 450

print(round(navy_body_fat("male", 180, 38, 85), 1))         # 16.1
print(round(navy_body_fat("female", 165, 33, 75, 100), 1))  # 29.4

If your app accepts inches, convert at the edge and keep one equation in the core. Add a test using the two examples on this page. It catches the coefficient mix-up immediately.

Limits of the Navy Method

• It is an estimate. The equations are statistical fits to 602 male and 214 female U.S. Navy personnel from the 1980s, whose body density was found by underwater weighing. The women's report notes that such equations "tend to be population specific", so results for other groups may differ.
• Small tape errors move the result. For our example man, 1 cm more waist adds about 0.8 points, and for our example woman about 0.5. A larger neck lowers the result by about the same amount, whatever the reason for the larger neck. This is arithmetic on the equation, not an error rate.
• Weight and age aren't inputs. Both were offered to the regression and did not enter the final models. Losing weight only shows up if your tape numbers change.
• Adults only. The samples were adult Navy personnel. Don't use this for children or teenagers.
• No labels. This page gives a number and nothing else: no category, no risk rating, no target. It isn't medical advice and can't diagnose anything. For health questions, talk to a qualified professional.
• Not a guide to current service rules. The Pentagon moved to a waist-to-height ratio under a memo dated December 18, 2025, and the services are applying it through their own policies. If you need a military standard, check your service's current guidance.

Common Questions

Why does another calculator give me a different number?

A gap of under a point usually means it uses the inch form and this page uses the metric form. A larger gap points to inch coefficients applied to centimeters, or to a different formula altogether. Our body fat formulas page compares the common ones.

Is the calculator free, and what happens to my measurements?

Yes, this calculator is free and needs no sign-up. The math runs in your browser. Your measurements are not sent to us or saved.

Can I use it for a teenager?

No. The equations were built on adult Navy personnel, so this calculator is for adults only.

Sources

• Hodgdon JA, Beckett MB. Prediction of Percent Body Fat for U.S. Navy Men from Body Circumferences and Height. Report No. 84-11, Naval Health Research Center, San Diego, 1984. DTIC ADA143890.
• Hodgdon JA, Beckett MB. Prediction of Percent Body Fat for U.S. Navy Women from Body Circumferences and Height. Report No. 84-29, Naval Health Research Center, San Diego, 1984. DTIC ADA146456.
• Hodgdon JA, Friedl K. Development of the DoD Body Composition Estimation Equations. Technical Document No. 99-2B, Naval Health Research Center, San Diego. DTIC ADA370158. Source of the inch form.
• Siri WE. "Body composition from fluid spaces and density: analysis of methods", 1961. The density-to-fat step, as cited in both 1984 reports.
• Military Officers Association of America. Pentagon Announces New Approach to How the Military Will Measure Troops' Body Fat, 2026.