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Body fat calculator

Body fat from a tape measure, given as the band it actually is — and beside it the other equation published under the same name, which over a swept grid of 1.35 million measurement combinations never comes within nineteen percentage points of it for a woman. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.

Two equations, same name, never closer than nineteen points

Search for the Navy body fat formula and you will find two different things, both presented as it:

They were swept against each other over a grid of measurement combinations across the plausible range — 112,251 for the men's equation and 1,352,538 for the women's. That is a grid rather than a sample of people: every combination of height, neck, waist and hip in range, not a population.

Over that grid the two never agree anywhere. For men the gap runs from 5.3 to 6.8 points; for women from 19.3 to 25.0. There is no region where it matters which one you used, and there is no region where it does not.

And the density form fails outright on the women's side. On that same grid it returns a figure below essential fat — a body composition nobody has — for about one combination in five, against about one in two hundred for the Navy equation. The bias in the grid is the same for both, so the comparison holds even though the rate itself does not describe anybody.

That is how the fault was found here. This page was built on the density form first, and it gave a 165 cm woman with a 74 cm waist 5.4%. The Navy equation gives 28.7%. It was caught because the number was absurd, not because anything flagged it — and for men, where the gap is six points rather than twenty-three, nothing would have looked absurd at all.

The error is wider than the categories

The tape method sits about ±3.5 points against a DEXA scan. The categories people get sorted into — athletic, fitness, average — are four to eight points wide.

So a single figure decides a category that the measurement error alone could move. This page shows the band and which categories it touches, because a number in the middle of a range that spans two labels has not told you which label you are.

And it is biased in opposite directions by sex

Compared against DEXA, the circumference method reads about 2.6 points low for men and 2.3 points high for women. The same tape, the same arithmetic, wrong in opposite directions depending which equation you fall under.

That is a systematic bias rather than noise, so it can be corrected for, and the page shows the corrected figure alongside. It does not substitute it, because the correction is itself an average.

Why the measurements are converted to inches

The coefficients were fitted to inches. There is no metric version of them — you cannot substitute centimetres and adjust a constant, because the logarithms do not work that way.

This page takes centimetres and converts, and shows the converted figures in the working so the arithmetic can be followed.

What a tape measure is not

It is not a measurement of fat. It is a measurement of a circumference that correlates with fat across a large group, and these equations were fitted on US Navy personnel. Two people with identical tape measurements can have genuinely different body composition, and the equation cannot tell them apart.

BMI is not offered here as an alternative, because it is not a body fat method at all — it is mass against height, and putting it beside a circumference estimate invites a comparison that is not one.

Where these come from

Hodgdon, J. A., & Beckett, M. B. (1984). “Prediction of percent body fat for U.S. Navy men and women from body circumference and height.” Naval Health Research Center. · Bias and spread against DEXA from Potter et al. (2022). The equations here are verified against a published worked example: an abdomen of 31 inches, a neck of 17 and a height of 70 gives 6.1%.

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