How to use it
- Choose Units (Metric or US) and your Sex. The equations were fitted separately for men and women.
- Enter your Height, then your Neck and Waist measurements. Age and Weight are optional: with them you also get fat and lean mass and a second estimate from BMI.
- If you chose Female, also enter Hips. The men's equation doesn't use a hip measurement.
- Read the estimated body fat percentage. Open How this was calculated to see the density and percentage worked out with your numbers.
- Keep the result with Copy link or Save image, or measure again and compare.
How the calculation works
The equations come from two Naval Health Research Center reports by James Hodgdon and Marcie Beckett, both from 1984. Report 84-11 covers men and report 84-29 covers women. Each first predicts body density, then turns density into percent fat.
Men: density = 1.0324 − 0.19077 × log10(waist − neck) + 0.15456 × log10(height)
Women: density = 1.29579 − 0.35004 × log10(waist + hips − neck) + 0.22100 × log10(height)
Both reports state the measurements in centimeters, so the calculator converts inches to centimeters before it uses them. The last step is the Siri (1961) equation used in the reports: % fat = 495 ÷ density − 450.
| Step | Man: height 180, neck 38, waist 85 | Woman: height 165, neck 33, waist 75, hips 100 |
|---|---|---|
| Circumference term | 85 − 38 = 47 | 75 + 100 − 33 = 142 |
| log10 of that term | 1.6721 | 2.1523 |
| log10 of height | 2.2553 | 2.2175 |
| Body density | 1.0324 − 0.19077 × 1.6721 + 0.15456 × 2.2553 = 1.0620 | 1.29579 − 0.35004 × 2.1523 + 0.22100 × 2.2175 = 1.0325 |
| Body fat | 495 ÷ 1.0620 − 450 = 16.1% | 495 ÷ 1.0325 − 450 = 29.4% |
Where to measure
The Navy reports describe the neck, waist and height sites. The U.S. Coast Guard Body Composition Desk Guide (2020) describes the same tape sites step by step.
Stand relaxed and keep the tape level, snug on the skin without pressing in. The reports took each site twice and recorded it to the nearest millimeter. The Coast Guard guide takes three readings and averages them.
| Measurement | Where | Notes |
|---|---|---|
| Neck | Just below the larynx (Adam's apple) | Tape slopes slightly downward to the front. Look straight ahead, shoulders down. |
| Waist (men) | At the level of the navel | Read at the end of a normal, relaxed breath out. Don't hold your breath. |
| Waist (women) | At the narrowest point, about halfway between the navel and the bottom of the breastbone | Read at the end of a normal breath out. |
| Hips (women) | Around the widest part of the buttocks | The Coast Guard guide places the tape over the greatest protrusion of the gluteal muscles. |
| Height | Standing, without shoes | Feet together, flat on the floor. |
How accurate is this?
The equations predict what underwater weighing would have measured. The men's equation was built on 602 Navy men aged 18 to 56. Its typical error was about 3.5 percentage points of body fat, and 2.7 points in a second group of 100 men.
The women's equation was built on 214 Navy women aged 18 to 44. Its typical error was about 3.7 points, and 4.0 to 4.4 points in two cross-check groups. So a result of 29.4% is best read as a rough range, not an exact figure.
The samples were adult military personnel. The equations were not fitted to children, teens, pregnancy or older adults outside those age ranges. Small measuring errors also matter: a centimeter on the waist changes the result more than a centimeter on height.
Your result also carries over: "Try this next" opens the BMR calculator with this body fat % filled in, for the lean-mass equations. The same few points of uncertainty carry over with it.
Body fat and BMI measure different things
BMI uses only height and weight, so it cannot tell muscle from fat. The Navy equations skip weight entirely and rely on how the waist compares with the neck. Two people with the same BMI can get quite different results here.
The published protein references are stated per kilogram of body weight. The protein calculator shows what they work out to for your weight.
The second estimate: Deurenberg's BMI formula
Deurenberg, Weststrate and Seidell (British Journal of Nutrition, 1991) measured body fat by densitometry (underwater weighing) in 1,229 people aged 7 to 83 and fitted a separate formula for adults from BMI, age and sex: body fat % = 1.20 × BMI + 0.23 × age − 10.8 × sex − 5.4, with sex = 1 for men and 0 for women. Its standard error of estimate was 4.1 percentage points.
The authors noted that it slightly overestimates body fat in people with obesity. And because it starts from BMI, it can't see the difference between muscle and fat. The tape-measure method can, at least partly, because it uses the waist.
For the man in the example (180 cm, 80 kg, 30 years), BMI is 24.7 and Deurenberg gives 20.3%, against 16.1% from the U.S. Navy equation. A gap of a few points is normal: both carry an error of about 4 points.
Questions
- How accurate is the U.S. Navy body fat method?
- In the original reports, predictions were typically within about 3.5 (men) and 3.7 (women) percentage points of underwater weighing. In cross-check groups the error was 2.7 points for men and 4.0 to 4.4 points for women.
- Why does the women's equation use hips?
- The stepwise regression in report 84-29 picked waist, hips, neck and height as the best predictors for women. For men, waist minus neck and height were enough.
- Should I measure the waist at the navel?
- For men, yes: the equation was fitted with the tape at the navel. For women, the equation uses the narrowest part of the waist, about halfway between the navel and the bottom of the breastbone.
- Can I enter measurements in inches?
- Yes. Choose US under Units. The reports give the equations in centimeters, so inches are converted before the math runs.
- What is the 495 ÷ density − 450 step?
- That is the Siri (1961) equation. It converts body density in grams per cubic centimeter into percent body fat, and both Navy reports use it.
- Why did my result change when I measured again?
- The equations use logarithms of differences between tape readings, so a small change on the waist or neck shifts the result. Measuring at the same landmarks each time, two or three times, gives more stable numbers.
- Why do the two methods give different results?
- They use different information. The U.S. Navy equation uses your neck, waist (and hips for women) and height; Deurenberg uses only BMI, age and sex. Each has a typical error of about 3.5 to 4 percentage points, so they can easily differ by a few points.