Body Fat Calculator

This is general information, not medical advice

This page does arithmetic and explains where the arithmetic came from. It is general educational information about two published estimating equations. It is not medical advice, it is not a diagnosis, and it cannot account for anything a tape measure cannot reach.

Both equations were fitted to particular groups of people. Hodgdon and Beckett built the circumference method in 1984 on active-duty US Navy personnel — a young, physically screened population, validated against hydrostatic weighing. Deurenberg, Weststrate and Seidell built the BMI-based formula in 1991 on a Dutch sample spanning childhood to old age, validated against densitometry. If you are far from either of those groups — much older, much heavier, pregnant, a competitive athlete, a bodybuilder, an amputee, or living with an eating disorder or a condition that shifts body water — the equations are extrapolating, and this page will not tell you by how much.

If you are trying to decide whether to change how you eat or train, or you have been handed a body composition figure and do not know what to make of it, talk to a doctor, nurse, or registered dietitian. They can look at the things this page cannot.

How each number is worked out

The Navy method is two steps. Hodgdon and Beckett’s regression predicts body densityfrom circumferences and height; the Siri equation then converts density into a fat percentage. Deurenberg’s formula skips the tape entirely and regresses fat percentage on BMI, age and sex.

The units matter, and they are widely got wrong. The constants above were fitted against centimetres. The Navy’s own field tables use an algebraically different, inch-based form of the same relationship, with the constants 86.010 and 70.041 for men and 163.205 and 97.684 for women. Fed the units each was built for, the two agree to about a tenth of a point. Fed inches, the metric constants return 9.8% where the correct answer is 16.2% — an error twice the size of the method’s own uncertainty, and always in the flattering direction. Whatever you type here is converted to centimetres before any logarithm is taken.

Two smaller decisions. The ACE band is chosen from the percentage rounded to one decimal place — the figure actually on screen — so the number and its label can never contradict each other. And fat mass is computed from that rounded percentage, with lean mass as the remainder, so the three figures always add back to the weight you entered.

A 30-year-old man, 175 cm, 72 kg, 84 cm waist, 38 cm neck

Start with the girth the logarithm is taken of: 84 − 38 = 46 cm. Then log₁₀(46) = 1.6628 and log₁₀(175) = 2.2430. Feed both in: 1.0324 − 0.19077 × 1.6628 + 0.15456 × 2.2430 = 1.0324 − 0.3172 + 0.3467 = 1.0619 g/cm³. Convert with Siri: 495 ÷ 1.0619 = 466.2, minus 450 = 16.2%. At 72 kg that is 11.7 kg of fat and 60.3 kg of lean mass, and 16.2% sits in the ACE fitness band of 14% to 17% for men.

Now the other method. The same man has a BMI of 72 ÷ 1.75² = 23.5, so Deurenberg gives 1.20 × 23.51 + 0.23 × 30 − 10.8 − 5.4 = 28.2 + 6.9 − 16.2 = 18.9%. The two differ by 2.7 percentage points on the same body, which is well inside what either can resolve. Neither is the truth; the truth is somewhere in a band several points wide that contains both.

Change one thing to see what actually drives the answer. Measure the waist at 86 cm instead of 84 and the figure becomes 17.7% — a 1.5 point move from 2 cm of tape. Measure the neck at 40 cm instead of 38 and it drops to 14.5%. Get the height wrong by 4 cm, at 173 or 177, and it moves by only 0.7 points in total. The tape is what matters. The height barely registers.

Tape placement beats the formula

Every article about this method leads with its ±3 to 4 point standard error, as if that were the whole story. It is the error of the equation when a trained assessor takes the measurements. Yours are probably not taken by a trained assessor, and the measurement error stacks on top.

In the worked example above, one centimetre at the waist is worth about 0.8 percentage points, and one centimetre at the neck is worth about the same in the opposite direction. A centimetre is nothing. It is the difference between the tape at the navel and the tape an inch above it, between snug and slightly tight, between reading it after breathing out and reading it while holding still. Two people measuring the same body will routinely differ by more than that, and so will you measuring yourself on two consecutive days.

• Waist. Men: level with the navel, all the way round, horizontal. Women: at the narrowest point of the torso, which is usually a little above the navel. Do not suck in and do not push out — read it at the end of a normal breath out.
• Neck. Just below the larynx, at the narrowest point, with the tape sloping very slightly downwards toward the front. Shoulders relaxed, looking straight ahead. Tilting your chin changes this measurement.
• Hip (women). Around the widest part of the buttocks, feet together, tape horizontal all the way round.
• Everything. Snug against the skin without compressing it. Measure each site three times and take the middle reading — not the smallest, however tempting. Use the same tape and the same time of day every time.

This is why the trend matters more than the figure. A single reading carries the formula’s error plus your tape error. A series of readings taken the same way, by the same person, with the same tape, cancels most of the tape error out and leaves you with something that genuinely tracks change. Once you have a lean mass figure you trust, the lean body mass calculator shows how three published formulas estimate the same quantity from height and weight alone, and how far apart they land.

What a tape measure cannot see

• It infers, it does not measure. Nothing here observes fat. The circumference method observes that people with more abdominal girth relative to neck and height tended to have lower body density in a sample of Navy personnel in the early 1980s, and applies that relationship to you.
• It only sees two or three places on your body. Two people with identical waist, neck and height measurements get identical answers, whatever is happening at their thighs, arms or back. Fat distribution varies with genetics, sex, age and hormones, and this method reads exactly one axis of it.
• The reference method has its own error. The equations were validated against hydrostatic weighing, which assumes a fixed density for lean tissue. That assumption is itself imperfect and varies with bone density, hydration and ancestry, so even a perfect prediction of the reference is not a perfect prediction of the truth.
• The bands are norms, not thresholds. The ACE categories describe how a population distributes, not where a risk begins. Nothing changes about your health when you cross from 17.9% to 18.1%.
• The Deurenberg estimate inherits every weakness of BMI. It cannot distinguish muscle from fat, so it reads high on trained bodies and low on sedentary ones at the same weight. It is here as a second opinion and a sanity check, not as a rival answer.

What this calculator assumes

• You are an adult. Both equations were fitted to adults, and the Deurenberg constants in particular behave differently in children.
• You are not pregnant. Pregnancy changes both body water and circumference for reasons neither equation can interpret.
• Your measurements were taken as described above — horizontal tape, snug not tight, at the end of a normal breath out, at the sites each equation specifies.
• Your build is not far from the populations the equations were fitted to. Very muscular, very lean, and very heavy bodies are all extrapolations, and the method is known to read low on lean muscular people and high on some older adults.
• Imperial input is converted with the exact definitions — 1 inch = 2.54 cm and 1 pound = 0.45359237 kg — before the metric constants are applied.
• A result the equation cannot stand behind is refused rather than clamped. A waist no wider than the neck, for instance, produces a mathematically defined but physically meaningless answer, so the page asks you to check the tape instead of showing it.

Body fat FAQ

Sources and review notes

1. Hodgdon, J. A. & Beckett, M. B. (1984). Prediction of Percent Body Fat for U.S. Navy Men from Body Circumferences and Height. Naval Health Research Center Report No. 84-11 — the source of the circumference equations, with the companion Report No. 84-29 covering women
2. Deurenberg, P., Weststrate, J. A. & Seidell, J. C. (1991). Body mass index as a measure of body fatness: age- and sex-specific prediction formulas. British Journal of Nutrition 65(2), 105–114 — the BMI-based estimate
3. American Council on Exercise — percent body fat norms, the source of the essential, athlete, fitness, average and obese bands and of their different edges for men and women
4. NIST Special Publication 811 — the exact inch and pound definitions used for the imperial conversion

The equations here are forty years old and are not going to change; what changes is the population they are applied to, which is no longer the one they were fitted to. Where a clinician has given you a figure from a DEXA scan or a hydrostatic tank, that figure supersedes anything on this page — it is a measurement, and this is a regression.