Body fat calculator
This body fat percentage calculator estimates body fat from a tape measure with the U.S. Navy equations. Men enter height, neck and waist. Women add hip. The men's waist is taken at the navel and the women's at the narrowest point of the abdomen. A man 5 ft 10 in tall with a 15 inch neck and a 34 inch waist comes out at about 17.4 percent body fat.
Estimated body fat
17.4 percent
Estimated body density 1.0590 grams per cubic centimeter
The Navy body fat calculator equations
Men use abdomen II and neck
Body density = −0.19077 × log10(abdomen II − neck) + 0.15456 × log10(height) + 1.0324
This equation is copied from page 12 of Report 84-11, Prediction of Percent Body Fat for U.S. Navy Men from Body Circumferences and Height.
Women use abdomen I, hip and neck
Body density = −0.35004 × log10(abdomen I + hip − neck) + 0.22100 × log10(height) + 1.29579
This equation is copied from page 12 of Report 84-29, Prediction of Percent Body Fat for U.S. Navy Women from Body Circumferences and Height.
Convert density to percent fat
Percent fat = 100 × (4.95 ÷ body density − 4.50)
This step is copied from Assessing Readiness in Military Women, Table 2-1. It also appears in Reports 84-11 and 84-29, which credit it to Siri, 1961.
The equations take height and circumferences in centimeters. This page multiplies inches by 2.54 before the equation. NIST marks that conversion factor as exact. The two reports give their Appendix A lookup tables in inches.
The National Academies table prints the same equations with coefficients rounded to three decimals. For men they are −0.191, 0.155 and 1.032. For women they are −0.350, 0.221 and 1.296, also used in the women's report summary.
There is a misprint in the National Academies Table 2-1. It prints the women's circumference term as abdomen I plus hip plus neck. Report 84-29 prints abdomen I plus hip minus neck in the equation, in its summary and above each lookup table. This page follows the report.
The tape sites in the reports
| Measurement | Plain words | Report wording |
|---|---|---|
| Neck | Just below the voice box, tape sloping slightly down toward the front | Just inferior to the larynx with tape sloping slightly downward to the front |
| Men's waist | Level with the navel | Abdomen II, at the level of the umbilicus |
| Women's waist | The narrowest point of the abdomen, about midway between the lower end of the breastbone and the navel | Abdomen I, at the level of minimal abdominal width, approximately midway between the xyphoid and the umbilicus |
| Hip | Around the widest point of the buttocks | At the level of the greatest protrusion of the gluteal muscles |
| Height | Standing height to the nearest 0.25 inch | Standing height, measured to the nearest 0.25 inch |
The women's report uses hip in its equation but has no hip entry in its list of sites. The hip wording comes from the men's report by the same authors.
In both reports, the person stood relaxed. The tape conformed to the skin without depressing it. Readings were recorded to the nearest 1.0 millimeter. Abdominal measurements were taken at the end of a normal breath out.
Each site was measured twice. A third reading was taken when two circumference readings differed by more than 1 centimeter. The mean of the readings was used.
From tape readings to a percent
Both worked examples round each step to five decimals.
A man with a 34 inch waist
Height is 5 ft 10 in (70 in), neck is 15 in and waist at the navel is 34 in.
- Convert to centimeters. Height is 177.8, neck is 38.1 and waist is 86.36.
- Waist minus neck = 48.26 cm. log10(48.26) = 1.68359. log10(177.8) = 2.24993.
- Body density = −0.19077 × 1.68359 + 0.15456 × 2.24993 + 1.0324 = −0.32118 + 0.34775 + 1.0324 = 1.05897.
- Percent fat = 100 × (4.95 ÷ 1.05897 − 4.50) = 17.4.
The report's own lookup table lists 17 for a circumference value of 19.0 inches, from 34 minus 15, at a height of 70.0 inches.
A woman with a 76 cm waist
Height is 165 cm, neck is 33 cm, waist at the narrowest point is 76 cm and hip is 102 cm.
- Waist plus hip minus neck = 76 + 102 − 33 = 145 cm. log10(145) = 2.16137. log10(165) = 2.21748.
- Body density = −0.35004 × 2.16137 + 0.22100 × 2.21748 + 1.29579 = −0.75657 + 0.49006 + 1.29579 = 1.02928.
- Percent fat = 100 × (4.95 ÷ 1.02928 − 4.50) = 30.9.
For the check in US units, a woman 5 ft 5 in (65 in) tall with a 13 in neck, 30 in waist and 40 in hip works out to 30.8 percent. The report's own lookup table lists 31 for a circumference value of 57.0 inches, from 30 plus 40 minus 13, at a height of 65.0 inches.
Men's estimates at a fixed neck size
Neck is held at 15 in (38.1 cm). Columns are heights. Cells are estimated body fat percent.
| Waist at the navel | 5 ft 6 in (167.6 cm) | 5 ft 10 in (177.8 cm) | 6 ft 2 in (188.0 cm) |
|---|---|---|---|
| 30 in (76.2 cm) | 10.6 | 8.9 | 7.4 |
| 32 in (81.3 cm) | 15.1 | 13.4 | 11.8 |
| 34 in (86.4 cm) | 19.2 | 17.4 | 15.8 |
| 36 in (91.4 cm) | 22.9 | 21.1 | 19.5 |
| 38 in (96.5 cm) | 26.3 | 24.5 | 22.8 |
| 40 in (101.6 cm) | 29.5 | 27.7 | 26.0 |
| 42 in (106.7 cm) | 32.5 | 30.6 | 28.9 |
| 44 in (111.8 cm) | 35.3 | 33.4 | 31.7 |
Women's estimates at fixed neck and hip sizes
Neck is held at 13 in (33.0 cm) and hip at 40 in (101.6 cm). Columns are heights. Cells are estimated body fat percent.
| Waist at the narrowest point | 5 ft 2 in (157.5 cm) | 5 ft 5 in (165.1 cm) | 5 ft 8 in (172.7 cm) |
|---|---|---|---|
| 26 in (66.0 cm) | 27.8 | 25.7 | 23.7 |
| 28 in (71.1 cm) | 30.4 | 28.3 | 26.3 |
| 30 in (76.2 cm) | 32.9 | 30.8 | 28.8 |
| 32 in (81.3 cm) | 35.4 | 33.2 | 31.2 |
| 34 in (86.4 cm) | 37.8 | 35.6 | 33.6 |
| 36 in (91.4 cm) | 40.2 | 38.0 | 35.9 |
| 38 in (96.5 cm) | 42.5 | 40.3 | 38.2 |
| 40 in (101.6 cm) | 44.8 | 42.5 | 40.4 |
Comparison with underwater weighing
Both reports used body density from underwater weighing as the reference, converted to percent fat with the Siri equation.
Report 84-11 studied 602 male U.S. Navy personnel aged 18 to 56, with a mean age of 32. It found a multiple correlation of 0.90 and a standard error of estimate of 0.00791 grams per cubic centimeter, equal to 3.52 percent body fat units.
On a separate sample of 100 male Navy personnel measured by another laboratory, the correlation was 0.90 and the standard error of measurement was 2.70 percent body fat units.
Report 84-29 studied 214 female U.S. Navy personnel aged 18 to 44, with a mean age of 26.5. It found a multiple correlation of 0.85 and a standard error of estimate of 0.00796 grams per cubic centimeter, equal to 3.72 percent body fat units.
The women's equation was checked on 66 female Canadian Forces personnel from another laboratory, with a correlation of 0.80 and standard error of measurement of 4.36. On 80 U.S. Navy women, the correlation was 0.87 and standard error was 4.04.
The National Academies Table 2-1 prints R = 0.90 and SEE = 3.52 for men, and R = 0.85 and SEE = 3.72 for women. SEE is the standard error of the estimate.
Both reports offered body weight and age to the model. Neither entered the final equation.
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Tape method questions
Which measurements go into each equation?
The men's equation uses height, neck and waist at the navel. The women's equation uses height, neck, waist at the narrowest point of the abdomen and hip.
Are the two waist measurements taken at the same place?
No. The men's waist is level with the navel. The women's waist is at the narrowest point of the abdomen, about midway between the lower end of the breastbone and the navel.
Do the equations use inches or centimeters?
The equations use centimeters. This page multiplies inches by 2.54 before calculating. The reports print their Appendix A lookup tables in inches.
Does the women's equation subtract the neck?
Yes. Report 84-29 uses abdomen I plus hip minus neck. The National Academies table prints plus neck, but this page follows the report.
Do weight and age enter these equations?
No. Both reports offered body weight and age to the model, but neither entered the final equation.
Reports and conversion reference
Institute of Medicine. Assessing Readiness in Military Women. National Academies Press, 1998. Chapter 2, Table 2-1, U.S. Military Body Composition Equations, checked October 12, 2026.
Hodgdon JA, Beckett MB. Prediction of Percent Body Fat for U.S. Navy Men from Body Circumferences and Height. Naval Health Research Center, San Diego, Report 84-11, 1984. DTIC file and archived copy, checked October 12, 2026.
Hodgdon JA, Beckett MB. Prediction of Percent Body Fat for U.S. Navy Women from Body Circumferences and Height. Naval Health Research Center, San Diego, Report 84-29, 1984. DTIC file and archived copy, checked October 12, 2026.
The archived copies of Reports 84-11 and 84-29 are the copies read on October 12, 2026.
NIST Guide to the SI, Appendix B.8, conversion factors, checked October 12, 2026.
TrueCal facts, checked October 12, 2026.