How the Navy Body Fat Formula Works

The unit trap, before anything else

The equation you'll find everywhere:

Men: 86.010 × log₁₀(waist − neck) − 70.041 × log₁₀(height) + 36.76 Women: 163.205 × log₁₀(waist + hip − neck) − 97.684 × log₁₀(height) − 78.387

Those constants are for inches. A great many sources say centimetres.

There's a separate metric form of the same method — the 495 / (…) − 450 version — with completely different constants. Feed centimetres into the inch equation and nothing errors:

Same man: 90 cm waist, 38 cm neck, 178 cm tall
Correct metric formula	20.1%
Centimetres through the inch formula	26.7%

Six and a half percentage points, and the answer looks entirely plausible. Measure in inches, or convert first.

What it is

The Hodgdon-Beckett equation, developed at the Naval Health Research Center in 1984 as a field method requiring nothing but a tape measure.

That constraint is the whole design. Two measurements for men, three for women, plus height — and no equipment.

The logarithms are there because body density doesn't vary linearly with circumference; log terms fit the observed relationship far better than a straight line. That's also why you can't sanity-check the result in your head, which is why the tool shows the single combined circumference your measurements reduce to.

Where the error actually comes from

Not the formula. The tape.

• Neck — just below the larynx, tape sloping slightly downward at the front. Don't flex.
• Waist — men at the navel. Women at the narrowest point, usually above the navel.
• Hip (women) — widest point, feet together.

Those waist sites are genuinely different, and swapping them changes the answer materially.

Measure at the end of a normal exhale, tape snug but not compressing the skin.

Why you measure three times

A half-inch difference on the waist moves the result by about 0.9–1.1 percentage points on the men's formula and 0.6–0.7 on the women's.

That's the same order as the change you might be trying to detect over a month. A single reading is noisier than it looks — take three and average, always at the same time of day.

How accurate is it, honestly

Useful. Not precise.

Against laboratory methods it typically lands within a few percentage points, which is genuinely good for a tape measure. Its known weakness is structural: it infers composition from shape, so two people with identical measurements and very different builds get the same answer, and it can't distinguish muscle from fat at the waist.

It's least accurate at the extremes — very lean and very heavy.

Fat mass and lean mass

Give it your weight as well and the percentage splits into two numbers: fat mass and lean mass — everything that isn't fat, meaning muscle, bone, organs and water.

That split is often more informative than the percentage, because it separates two things a bathroom scale conflates. Losing 6 lb of fat while gaining 2 lb of lean mass shows on the scale as a 4 lb loss and looks like a disappointing month. In the split it looks like what it is.

It also makes the percentage behave sensibly when weight changes: body fat percentage can fall while fat mass stays flat, purely because lean mass went up. Watching both stops that from being confusing.

What it can't see

The formula reduces you to one number — waist minus neck, or waist plus hip minus neck. Everything about your build that doesn't show up in those circumferences is invisible to it.

That's the trade the 1984 designers made deliberately, and it's why the method exists at all: two tape measurements that work in a field, versus a laboratory that doesn't travel. It was never trying to be the accurate answer. It was trying to be the available one.

Knowing which of those you're holding is most of using it well.

What it's actually for

Tracking a direction, on the same person, measured the same way.

The absolute number is the least reliable part of the output. The trend across months is the most reliable.

If it says 22% it might really be 19 or 25. But if it says 22 in March and 19 in June, measured identically both times, something real has changed — and that's a question the number can answer even when it can't tell you the truth about the digit.

Use it as an instrument for change, not a verdict.

Print the tracking sheet — same tape, same time of day, three readings averaged, which is what makes the trend mean anything.

Sources: Hodgdon & Beckett, Naval Health Research Center (1984), via Medicine LibreTexts

An estimate, not a medical assessment.