Navy Body Fat Formula: Metric Equations and Examples

The Navy body fat formula estimates body-fat percentage from a few tape measurements and your height. Men use waist and neck; women add hip. A man who is 180 cm tall with a 90 cm waist and 38 cm neck comes out at about 19.8% body fat. Expect an error of roughly 3–4 percentage points.

Key takeaways

• You need only a tape measure: height, neck, waist and, for women, hip.
• The metric formulas use centimeters and base-10 logarithms.
• Typical error is about ±3–4 percentage points, similar to skilled skinfold calipers.
• It is best for tracking trends over time with the same technique.
• Compare your result with the ACE body-fat ranges to see where you stand.

Where the Navy formula comes from

The equations come from two 1984 Naval Health Research Center reports by Hodgdon and Beckett. The researchers measured body fat by underwater weighing. Then they found which tape measurements predicted it best.

The men's study used 602 Navy personnel aged 18–56. The women's study used 214 Navy personnel aged 18–44.

US Navy body fat formula (metric)

All measurements are in centimeters. "log10" means the base-10 logarithm, the LOG function in most spreadsheets.

US Navy body fat formula for men

%BF = 495 / (1.0324 − 0.19077 × log10(waist − neck) + 0.15456 × log10(height)) − 450

Navy body fat formula for women

%BF = 495 / (1.29579 − 0.35004 × log10(waist + hip − neck) + 0.22100 × log10(height)) − 450

The 495 and 450 at each end convert body density into body-fat percentage.

How to measure correctly

The formula is only as good as your tape work. Small errors at the neck or waist shift the result by a point or more.

• Height: barefoot, standing tall, in cm.
• Neck: just below the Adam's apple, with the tape sloping slightly down toward the front.
• Waist (men): horizontally at the level of the navel.
• Waist (women): at the narrowest point of the torso.
• Hip (women): at the widest point of the buttocks.
• Technique: tape snug but not pressing into the skin, stomach relaxed.

Measure at the same time of day, ideally in the morning before eating. Take each measurement twice and use the average.

Worked examples (checked with Python)

Man: 180 cm, waist 90 cm, neck 38 cm

waist − neck = 90 − 38 = 52 log10(52) = 1.7160 log10(180) = 2.2553 denominator = 1.0324 − 0.19077 × 1.7160 + 0.15456 × 2.2553 = 1.0536 495 / 1.0536 = 469.81 %BF = 469.81 − 450 ≈ 19.8%

Woman: 165 cm, waist 75 cm, hip 100 cm, neck 33 cm

waist + hip − neck = 75 + 100 − 33 = 142 log10(142) = 2.1523 log10(165) = 2.2175 denominator = 1.29579 − 0.35004 × 2.1523 + 0.22100 × 2.2175 = 1.0325 495 / 1.0325 = 479.43 %BF = 479.43 − 450 ≈ 29.4%

Both results fall in the ACE "acceptable" range for their sex.

What your result means: ACE body-fat ranges

The American Council on Exercise (ACE) publishes these general categories.

• Essential fat: Men (% body fat) 2–5, Women (% body fat) 10–13
• Athletes: Men (% body fat) 6–13, Women (% body fat) 14–20
• Fitness: Men (% body fat) 14–17, Women (% body fat) 21–24
• Acceptable: Men (% body fat) 18–24, Women (% body fat) 25–31
• Obese: Men (% body fat) 25+, Women (% body fat) 32+

Women carry more essential fat than men, so their ranges sit higher. Essential fat is the minimum needed for normal body function, not a goal.

US Navy body fat formula accuracy

The Navy formula has a typical error of about ±3–4 percentage points. A reading of 20% could mean a true value anywhere from roughly 16% to 24%.

• DEXA scan: Typical error (± % body fat) 1–2
• Underwater weighing / BodPod: Typical error (± % body fat) 2–3
• Skinfold calipers (skilled tester): Typical error (± % body fat) 3–4
• Navy tape formula: Typical error (± % body fat) 3–4
• Bioimpedance scales: Typical error (± % body fat) 4–6 or more

That puts the Navy formula on par with skilled caliper work, and ahead of most bathroom scales. It is free and easy to repeat.

Its main weakness is that it only sees circumferences. Two people with the same waist and neck get the same estimate, even if one carries more muscle.

The fix is to use it for trends. If your Navy estimate drops 2 points over 8 weeks with consistent measuring, the change is likely real. Pair it with waist size, photos and the scale for the clearest picture.

How to apply this

• Measure height, neck, waist and (for women) hip in cm, twice each.
• Plug the averages into the correct formula, or a spreadsheet using LOG.
• Compare your result with the ACE ranges.
• Calculate lean mass: weight × (1 − body fat % ÷ 100).
• Use lean mass for the Katch–McArdle TDEE formula or your FFMI (fat-free mass index).
• Re-measure every 4 weeks under the same conditions.
• Track the trend while you diet or do body recomposition. If you are cutting, check your pace against how fast you can lose fat.

FAQ

What is the US Navy body fat formula in metric?

For men: %BF = 495 / (1.0324 − 0.19077 × log10(waist − neck) + 0.15456 × log10(height)) − 450. For women, use 1.29579, 0.35004 × log10(waist + hip − neck) and 0.22100 × log10(height) instead. All measurements are in centimeters.

How do you use the US Navy body fat formula for men?

Measure height, neck below the Adam's apple and waist at the navel, all in cm. Subtract neck from waist, take base-10 logs and plug them into the men's equation. A 180 cm man with a 90 cm waist and 38 cm neck gets about 19.8%.

How is the Navy body fat formula for women different?

Women add a hip measurement at the widest point and measure the waist at its narrowest. The formula uses waist + hip − neck and different constants. A 165 cm woman with a 75 cm waist, 100 cm hips and 33 cm neck gets about 29.4%.

How accurate is the US Navy body fat formula?

Its typical error is about ±3–4 percentage points, similar to skilled skinfold calipers. That is less precise than DEXA but better than most bioimpedance scales. It works best for tracking change over time with consistent measuring.

Is the Navy formula good for tracking body fat percentage?

Yes, as long as you measure the same way each time. Small changes of a point or less may just be measurement noise. Look for a steady trend over several weeks, alongside waist size and photos.

Sources

• Hodgdon JA, Beckett MB. 1984. Prediction of percent body fat for U.S. Navy men from body circumferences and height. Naval Health Research Center Report 84-11. https://apps.dtic.mil/sti/pdfs/ADA143890.pdf
• Hodgdon JA, Beckett MB. 1984. Prediction of percent body fat for U.S. Navy women from body circumferences and height. Naval Health Research Center. https://apps.dtic.mil/sti/html/tr/ADA146456/index.html
• American Council on Exercise. Percent body fat calculator and norms. https://www.acefitness.org/resources/everyone/tools-calculators/percent-body-fat-calculator/

Body-fat estimates are most useful next to the other numbers you track. The Field Manual puts the Navy, BMI, FFMI and TDEE formulas on one formula sheet. Its knowledge checks let you practice each calculation with answers.