Body Fat Formulas Compared: Same Person, Four Equations, Four Answers
Body fat formulas disagree because they read different inputs. The U.S. Navy method uses tape measurements, Relative Fat Mass uses height and waist, and Deurenberg and a Gallagher-type equation use BMI, age and sex. One person can get four different numbers. Each one is an estimate, not a measurement.
verified Published by the WorkoutX team. Formulas checked against the cited sources on November 5, 2026.
Four Equations, One Person
BMI 24.7. Formula spread: 5.5 points between the highest and lowest result.
Runs in your browser. No photo, no account, and nothing you type is sent or saved. Hip is only used in the women's Navy equation. Raw equation results for adults: estimates for general fitness interest, not medical advice and not a diagnosis.
What Each Equation Actually Reads
Start here, because it explains most of the disagreement. The Navy method and Relative Fat Mass never see your weight or age. Deurenberg and the Gallagher-type equation never see a tape measure.
| Equation | Height | Weight | Age | Sex | Neck | Waist | Hip |
|---|---|---|---|---|---|---|---|
| U.S. Navy | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | Women only |
| Relative Fat Mass | ✓ | ✗ | ✗ | ✓ | ✗ | ✓ | ✗ |
| Deurenberg | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |
| Gallagher-type | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |
Formula Spread: Ten Fictional People
These people are made up. We chose the inputs to show how the equations behave. This table is pure arithmetic: it contains no user data, no scan data and no measured body fat. Spread is the highest result minus the lowest, in percentage points.
| Fictional person | Sex | Height cm | Weight kg | Age | Neck cm | Waist cm | Hip cm | Navy % | RFM % | Deurenberg % | Gallagher-type % | Spread |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | M | 180 | 80 | 30 | 38 | 85 | – | 16.1 | 21.6 | 20.3 | 18.6 | 5.5 |
| B | M | 180 | 80 | 30 | 38 | 95 | – | 23.2 | 26.1 | 20.3 | 18.6 | 7.5 |
| C | M | 180 | 80 | 55 | 38 | 85 | – | 16.1 | 21.6 | 26.1 | 22.1 | 10.0 |
| D | M | 175 | 95 | 40 | 42 | 90 | – | 17.7 | 25.1 | 30.2 | 29.3 | 12.5 |
| E | M | 170 | 62 | 25 | 35 | 74 | – | 11.1 | 18.1 | 15.3 | 13.2 | 7.0 |
| F | F | 165 | 65 | 30 | 33 | 75 | 100 | 29.4 | 32.0 | 30.2 | 29.0 | 3.0 |
| G | F | 165 | 65 | 30 | 33 | 85 | 100 | 34.3 | 37.2 | 30.2 | 29.0 | 8.2 |
| H | F | 165 | 65 | 55 | 33 | 75 | 100 | 29.4 | 32.0 | 35.9 | 32.5 | 6.5 |
| I | F | 170 | 58 | 25 | 31 | 68 | 92 | 21.5 | 26.0 | 24.4 | 22.8 | 4.5 |
| J | F | 160 | 82 | 45 | 36 | 95 | 112 | 44.4 | 42.3 | 43.4 | 43.0 | 2.1 |
Read the rows in pairs and the pattern shows up:
- A to B, waist up 10 cm. Navy rises 7.1 points and RFM rises 4.5. Deurenberg and the Gallagher-type result don't move at all.
- A to C, 25 years older. Deurenberg rises 5.8 points and the Gallagher-type result rises 3.5. Navy and RFM don't move, because they have no age term.
- Person D, heavy with a moderate waist. The BMI equations land near 30% and Navy lands at 17.7%, the widest spread in the table. The BMI equations see the weight but can't tell what it is made of. The table can't say which number is closer for a real person like D.
- Person J, spread of 2.1. All four agree closely. That only shows that the arithmetic lines up for these inputs. Agreement between equations is not proof that any of them is right.
Worked Example: Person A by Hand
Person A is a fictional 30-year-old man: 180 cm, 80 kg, neck 38 cm, waist 85 cm. BMI is 80 / 1.80² = 24.69.
- Navy: density = 1.0324 − 0.19077 × log10(47) + 0.15456 × log10(180) = 1.0620. Then 495 / 1.0620 − 450 = about 16.1%.
- RFM: 64 − (20 × 180 / 85) = 64 − 42.35 = about 21.6%.
- Deurenberg: (1.20 × 24.69) + (0.23 × 30) − 10.8 − 5.4 = about 20.3%.
- Gallagher-type: (1.46 × 24.69) + (0.14 × 30) − 11.61 − 10.02 = about 18.6%.
Same person, four results, 5.5 points apart. RFM for fictional person F, a woman of 165 cm with a 75 cm waist: 64 − (20 × 165 / 75) + 12 = 64 − 44 + 12 = 32.0%.
U.S. Navy Method
The formula most people meet first. It predicts body density from circumferences and height, then converts density to body fat with the Siri equation. For a calculator built around this one equation, see the Navy body fat calculator.
- Inputs
- Sex, height, neck, waist, plus hip for women. All in centimeters for this form. Don't mix these coefficients with the inch-based form of the equation, which uses different numbers.
- Source
- Hodgdon and Beckett, Naval Health Research Center, 1984: Report 84-11 (men) and Report 84-29 (women). Developed on 602 Navy men and 214 Navy women, with underwater weighing as the reference.
- Doesn't know
- Your weight or age. It also knows nothing about how you hold the tape: every input is a hand measurement, and it was built on naval personnel rather than the general public.
Relative Fat Mass (RFM)
The shortest of the four. It needs only a height to waist ratio and sex, and height and waist can be in any unit as long as both match.
- Inputs
- Height, waist, sex.
- Source
- Woolcott and Bergman, Scientific Reports 8:10980 (2018). Developed on U.S. NHANES adults, with DXA as the reference method.
- Doesn't know
- Weight, age, neck or hip. The authors say it needs testing in groups they did not study, including athletes and Asian and Native American populations, and they note that waist measurement varies. They did not set cut-off values, and neither do we.
Deurenberg Formula
The classic BMI to body fat equation. It adds age and sex to BMI, so you need no tape measure at all.
Example: an 80 kg, 180 cm, 30-year-old man has a BMI of 24.69, which gives about 20.3%.
- Inputs
- Height and weight (as BMI), age, sex.
- Source
- Deurenberg, Weststrate and Seidell, British Journal of Nutrition 65:105–114 (1991). We checked the equation and sex coding against the paper itself. Reference method: densitometry, in 1,229 people aged 7 to 83. This adult formula covers ages 16 and up; the paper gives a separate one for children.
- Doesn't know
- Any body measurement. Waist, neck and hip never enter it, and BMI can't separate muscle from fat. The authors report that the formulas slightly overestimated body fat in obese subjects.
Gallagher-Type Linear BMI Equation
Another BMI, age and sex equation, in the same shape as Deurenberg with different coefficients. This is the linear form used in the Body Scan engine.
About the name. We have not confirmed where this exact equation was first published, so we call it "Gallagher-type". It is not the equation from Gallagher et al. 2000, whose abstract describes models built on 1/BMI. A 2025 review table credits a near-identical equation to Gallagher et al. 1996, but prints the age term as 0.12, not 0.14. We could not read the 1996 full text to settle it.
- Inputs
- Height and weight (as BMI), age, sex.
- Source
- Unconfirmed, as explained above.
- Doesn't know
- The same blind spots as Deurenberg: no body measurement enters it, and BMI can't separate muscle from fat.
The BMI Blind Spot
Deurenberg and the Gallagher-type equation don't look at any circumference. Two adults of the same sex, age, height and weight get exactly the same result, whether their waist is 75 cm or 95 cm. You can see it in rows A and B above.
That isn't a bug. They were designed for situations where only height and weight are available. It does mean that a change in body shape at the same weight is invisible to them, while it does show up in Navy and RFM.
One Word, Three Tape Positions
"Waist" is not the same place in every source. The calculator takes one waist number, so this alone can shift results.
| Equation | Where the source measured |
|---|---|
| Navy, men | Abdomen at the level of the navel |
| Navy, women | Abdomen at its narrowest, about midway between the bottom of the breastbone and the navel |
| RFM | Horizontally at the top of the right hip bone, at the end of a normal breath out |
So Which Formula Should You Use?
We won't name a winner. The equations were built on different people, with different reference methods, and a side-by-side comparison of raw formulas can't show which is right for you. What you can do is choose by practicality:
- Only have height and weight? You are limited to the BMI equations.
- Have a tape measure? RFM needs one measurement and Navy needs two or three.
- Tracking over time? Pick one equation, measure the same way each time, and don't compare a number from one equation with a number from another.
These equations are for adults. Results here carry no risk labels or healthy ranges, on purpose. They aren't medical advice, and a body fat estimate is not a health assessment. Talk to a qualified professional about anything medical.
The Same Equations in JavaScript
This is the code running in the calculator above. Lengths are in cm, weight in kg. Note the opposite sex coding in RFM and Deurenberg, a mistake that is easy to make.
const bmi = (kg, cm) => kg / (cm / 100) ** 2;
function navy(sex, cm, neck, waist, hip) {
const girth = sex === 'male' ? waist - neck : waist + hip - neck;
if (!(girth > 0)) return null;
const density = sex === 'male'
? 1.0324 - 0.19077 * Math.log10(girth) + 0.15456 * Math.log10(cm)
: 1.29579 - 0.35004 * Math.log10(girth) + 0.221 * Math.log10(cm);
return 495 / density - 450;
}
const rfm = (sex, cm, waist) =>
64 - 20 * (cm / waist) + (sex === 'female' ? 12 : 0);
const deurenberg = (sex, bmi, age) =>
1.2 * bmi + 0.23 * age - 10.8 * (sex === 'male' ? 1 : 0) - 5.4;
const gallagherType = (sex, bmi, age) =>
1.46 * bmi + 0.14 * age - 11.61 * (sex === 'male' ? 1 : 0) - 10.02;
How This Relates to the Body Scan API
The WorkoutX Body Scan API uses these equations, but it doesn't return any one of them. The engine blends them, so the raw results on this page will not match an API result one to one. It also starts from different inputs: a photo plus height, weight, age and sex. It finds pose landmarks, estimates the body dimensions the equations need, then combines the U.S. Navy, Relative Fat Mass, Deurenberg and Gallagher-type results. A vision model only writes notes. It doesn't set the number.
A response includes a body fat estimate with an indicative range, fat and lean mass, BMI, body type, waist, hip and shoulder estimates, and muscle, symmetry and fitness scores. See the fields in the API reference, or read how the pieces fit together in the body fat percentage API guide and the body composition API guide.
Body Scan is a wellness and fitness estimate for adults. It has not been validated against DXA or any other reference method, and we publish no accuracy figure. It is not a medical device. Photos are not stored by us; they are sent to Anthropic for analysis, and results are deleted after 90 days. Credit packs start at $39 for 20 scans. View packs
Frequently Asked Questions
Why do body fat formulas give different answers?
They read different inputs and were built on different groups of people. The U.S. Navy method uses tape measurements and height. Relative Fat Mass uses height and waist. Deurenberg and the Gallagher-type equation use BMI, age and sex. Change one input and only the equations that read it will move.
Which body fat formula is the most accurate?
This page does not rank them. The equations were developed on different people with different reference methods, and a comparison of raw formulas cannot show which result is right for one person. A practical choice is to use the equation whose inputs you can measure consistently, and to stick with it.
What is the Relative Fat Mass formula?
RFM = 64 - (20 x height / waist) + (12 x sex), with sex 0 for men and 1 for women, and height and waist in the same unit. It was published by Woolcott and Bergman in Scientific Reports in 2018.
What is the Deurenberg formula?
Body fat % = 1.20 x BMI + 0.23 x age - 10.8 x sex - 5.4, with sex 1 for men and 0 for women. It was published by Deurenberg, Weststrate and Seidell in the British Journal of Nutrition in 1991. The adult formula applies from age 16; the paper gives a separate formula for children.
Do BMI-based body fat equations use waist size?
No. Deurenberg and the Gallagher-type equation read BMI, age and sex only. Two people with the same height, weight, age and sex get the same result, whatever their waist measures.
Will these results match the WorkoutX Body Scan API?
Not one to one. The Body Scan engine blends these equations and works from body dimensions estimated from a photo, so its result will differ from any single raw equation on this page.
Does this calculator store my data?
No. The calculation runs in your browser. There is no photo, no account, and the numbers you type are not sent anywhere or saved.
Sources
- Hodgdon JA, Beckett MB. Prediction of percent body fat for U.S. Navy men from body circumferences and height. Naval Health Research Center Report 84-11, 1984.
- Hodgdon JA, Beckett MB. Prediction of percent body fat for U.S. Navy women from body circumferences and height. Naval Health Research Center Report 84-29, 1984.
- Woolcott OO, Bergman RN. Relative fat mass (RFM) as a new estimator of whole-body fat percentage. Scientific Reports 8:10980, 2018.
- Deurenberg P, Weststrate JA, Seidell JC. Body mass index as a measure of body fatness: age- and sex-specific prediction formulas. British Journal of Nutrition 65:105–114, 1991.
- Gallagher D, Visser M, Sepúlveda D, et al. How useful is body mass index for comparison of body fatness across age, sex, and ethnic groups? American Journal of Epidemiology 143:228–239, 1996. Abstract only; see the note in the Gallagher-type section.
- Gallagher D, Heymsfield SB, Heo M, et al. Healthy percentage body fat ranges: an approach for developing guidelines based on body mass index. American Journal of Clinical Nutrition 72:694–701, 2000. Abstract only.
- The Association of Body Mass Index and Adiposity-Estimating Equations with Measures of Obstructive Sleep Apnea Severity. Nature and Science of Sleep 17:1003–1019, 2025. Cited only for its table of equations.