MathBench

Body Fat Percentage Calculator

Estimate body fat from a tape measure using the US Navy circumference method — the same tape test the Navy uses — with your fat and lean mass broken out, and the method's real accuracy stated rather than glossed over.

Estimates, not medical advice. These calculators apply published equations to the numbers you enter. They describe averages across large groups, and any individual can differ from the average by a wide margin — metabolism, body composition, medication, and medical conditions all shift the result. Nothing here diagnoses, treats, or replaces advice from a doctor or registered dietitian, and no target produced by a formula should override how you actually feel. If you are managing a health condition, are pregnant, or have a history of disordered eating, talk to a clinician before acting on any of it.

Your estimate

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Category ranges

A general-wellness estimate, not a diagnosis. It cannot tell you whether you are healthy — only where a measurement falls on a published scale. Everything is calculated in your browser: nothing you type is sent anywhere or stored. If counting is making things worse rather than better, the National Eating Disorders Association keeps a current list of support options.

How this calculator works

The method estimates how much of your body is fat from a handful of tape measurements, on the principle that fat accumulates in predictable places relative to the size of your frame. The key term is the difference between waist and neck: neck circumference tracks skeletal and lean size, so a waist much larger than the neck suggests indicates stored fat rather than a large build. Height enters as a scale reference, because the same waist means different things on different frames. The women's equation adds hip circumference, since female fat distribution makes waist alone a weaker signal.

The equations were developed at the Naval Health Research Center in 1984 by Hodgdon and Beckett, who fitted them against hydrostatic weighing — submersion, the reference standard of the era — on Navy personnel. The US Navy still uses this tape test for body composition assessment, which is why the method carries its name. The result is then applied to your body weight to split it into fat mass and lean mass, the latter covering muscle, bone, organs and water together.

Alongside the tape result, the page shows a second estimate derived from BMI and age using the Deurenberg equation. It is a cruder method and generally less accurate, but it is useful as a cross-check: when the two disagree substantially, that is a signal that your build sits away from the population these equations were fitted on, and that both numbers deserve more scepticism than usual.

The formula

US Navy circumference method, measurements in inches:

  men    %fat = 86.010 × log₁₀(waist − neck)
                − 70.041 × log₁₀(height) + 36.76

  women  %fat = 163.205 × log₁₀(waist + hip − neck)
                − 97.684 × log₁₀(height) − 78.387

Derived masses:
  fat mass  = body weight × %fat ÷ 100
  lean mass = body weight − fat mass

Cross-check, Deurenberg (1991):
  %fat = 1.20 × BMI + 0.23 × age − 10.8 × (1 if male, 0 if female) − 5.4

The equations come from J. A. Hodgdon and M. B. Beckett, Prediction of percent body fat for U.S. Navy men and women from body circumferences and height, Naval Health Research Center reports 84-11 and 84-29 (1984), fitted against hydrostatic weighing. A metric formulation routed through Siri's body density equation is also widely published, and it is worth knowing that the two are not interchangeable. Checked cell by cell against the Navy's own published body fat tables, the logarithmic form above reproduces them, while the density form matches only about three quarters of the entries and drifts by as much as 1.1 percentage points. This page computes in inches and converts metric input, so the result agrees with the Navy's tables whichever units you type. Note also that Guide 4 publishes the lookup tables rather than the equation itself; the equation is printed verbatim in A. W. Potter and colleagues, Frontiers in Physiology 13 (2022) 868627.

The cross-check equation is from P. Deurenberg, J. A. Weststrate and J. C. Seidell, "Body mass index as a measure of body fatness: age- and sex-specific prediction formulas," British Journal of Nutrition 65 (1991) 105–114. Category ranges follow the American Council on Exercise, which are the ranges most widely used in fitness practice; note that they are descriptive conventions rather than clinical thresholds.

Worked example

A man 180 cm tall and 80 kg, with a 38 cm neck and an 86 cm waist — the calculator's default:

  1. Convert to inches: height 70.87, neck 14.96, waist 33.86
  2. Waist minus neck: 33.86 − 14.96 = 18.90 in
  3. log₁₀(18.90) = 1.2765, and log₁₀(70.87) = 1.8504
  4. 86.010 × 1.2765 = 109.79, and 70.041 × 1.8504 = 129.60
  5. 109.79 − 129.60 + 36.76 = 16.9% body fat, which is the fitness range for men
  6. Fat mass: 16.9% of 80 kg = 13.6 kg, leaving 66.4 kg of lean mass

The honest reading of that result is "somewhere around 13 to 20 percent", because the method's standard error is 3 to 4 points. What makes it worth doing anyway is consistency: measure the same way in six weeks, and a drop to 15.5 percent is meaningful information even though neither individual number is precise.

Assumptions & tips

  • Average three measurements. Half-inch errors in opposing directions compound to roughly two percentage points of body fat — comparable to the method's entire standard error — and the waist term drives most of it. Measure three times, discard anything wildly different, and average the rest.
  • Measure under identical conditions. First thing in the morning, before eating, after using the bathroom, at the end of a normal exhale. Consistency matters far more than perfection when the purpose is tracking change.
  • Do not pull the tape tight. Snug against the skin without compressing it. Tightening the tape by a centimetre can shift the result by more than a percentage point, and it is the easiest way to fool yourself in either direction.
  • Track the trend, not the number. The error in this method is largely systematic — it tends to be wrong in the same direction for the same person — which means differences over time are much more reliable than any single reading. Six-week intervals show real change without the noise.
  • Lean does not mean healthy without limit. Essential fat exists for a reason: below roughly 5 percent in men and 13 in women, hormonal function, immunity and bone density suffer. Athletes who dip lower do so temporarily and under supervision.
  • If a number matters clinically, get it measured. DEXA gives an actual measurement rather than an estimate, typically for a modest fee at a sports medicine clinic. Every tape and impedance method is a prediction fitted to somebody else's population.

Frequently asked questions

How accurate is the tape measure method?

It carries a standard error of roughly 3 to 4 percentage points against hydrostatic weighing, which is the reference it was fitted against. In practice that means a reading of 20 percent tells you the true figure is probably somewhere between about 16 and 24. That is accurate enough to track change over months — the error is fairly consistent for the same person measured the same way — and not accurate enough to argue about a single percentage point. The equations were developed on US Navy personnel, so they perform best on adults of similar build and less well at the extremes of leanness or obesity.

Why does it ask for my neck?

Because the waist measurement alone cannot separate fat from frame. Neck circumference acts as a proxy for skeletal size and lean mass: two people with identical waists but different builds get different results, which is the whole point. For women the hip measurement is added as well, since female fat distribution makes the waist alone a poorer predictor. The subtraction of neck from waist is doing the real work in the equation — it is effectively asking how much bigger your waist is than your frame would suggest.

How do I measure correctly?

Use a flexible tape, keep it level and snug without compressing the skin, and measure at the end of a normal exhale. Neck: just below the larynx, sloping slightly downward at the front. Waist: for men at the navel, for women at the narrowest point. Hips: at the widest point of the buttocks. Take each measurement three times and average them — repeat measurements typically vary by half a centimetre, which moves the result by several tenths of a percent. Measuring at the same time of day, under the same conditions, matters more for tracking than getting any single reading perfectly right.

What is a healthy body fat percentage?

It depends on sex and on what you are optimising for. Women carry substantially more essential fat than men — roughly 10 to 13 percent versus 2 to 5 — because of reproductive and hormonal requirements, so the healthy ranges differ throughout. The American Council on Exercise categories put men's fitness range at 14 to 17 percent and women's at 21 to 24, with average ranges above that. Very low body fat is not a health achievement: below the essential threshold it disrupts hormones, immunity, and bone density in both sexes, and in women commonly stops menstruation.

Should I use this or a body fat scale?

Both are estimates, and neither is a measurement. Bioelectrical impedance scales pass a small current through the body and infer composition from resistance, which makes them extremely sensitive to hydration — the same person can read three percentage points apart morning and evening. The tape method is not affected by hydration and is more consistent between sessions, which makes it better for tracking. If you want an actual measurement rather than an estimate, DEXA is the practical gold standard, with air displacement plethysmography close behind.

Sources

  1. Prediction of percent body fat for U.S. Navy men from body circumferences and height (Report No. 84-11) and Prediction of percent body fat for U.S. Navy women from body circumferences and height (Report No. 84-29) — J. A. Hodgdon and M. B. Beckett, Naval Health Research Center, San Diego, California, 1984. Cited without a link: the Defense Technical Information Center copies were unreachable at the time of writing. The original derivation of the two circumference equations this calculator evaluates, fitted against hydrostatic weighing on Navy personnel.
  2. Circumference-Based Predictions of Body Fat Revisited: Preliminary Results From a US Marine Corps Body Composition Survey — A. W. Potter, W. J. Tharion, L. D. Holden and colleagues, Frontiers in Physiology 13, article 868627, 2022. pmc.ncbi.nlm.nih.govPrints the Hodgdon-Beckett coefficients verbatim — 86.010 and 70.041 for men, 163.205 and 97.684 for women, in inches — which is the form this page computes in and the reason metric input is converted rather than routed through a density equation.
  3. Body Composition in the Military Services: Standards and Methods, in Body Composition and Physical Performance: Applications for the Military Services — Institute of Medicine (US) Committee on Military Nutrition Research; B. M. Marriott and J. Grumstrup-Scott, editors. National Academies Press, Washington DC, 1990. ncbi.nlm.nih.govThe source of the accuracy figure this page reports: it records that the equations used by the US Navy to predict body fat have standard errors of measurement of approximately 3.5 percentage points.
  4. Body mass index as a measure of body fatness: age- and sex-specific prediction formulas — P. Deurenberg, J. A. Weststrate and J. C. Seidell, British Journal of Nutrition 65(2), 105–114, 1991. doi.orgThe BMI-and-age equation shown as the cross-check beside the tape result, and the basis for the warning when the two estimates diverge by more than six points.
  5. Percent body fat norms published by the American Council on Exercise (ACE). Cited without a link and without a claimed title: ACE's article addresses for this table now redirect to its blog index, so no stable public address could be verified. The essential-fat, athletic, fitness and average bands, which differ by sex, that this page uses to label the estimate and to build the category table.

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