The Navy equations
The US Department of Defense uses circumference measurements to screen body composition, because a tape costs nothing and works in a gymnasium. The equations, in centimetres, are:
- Male: 495 / (1.0324 − 0.19077 × log10(waist − neck) + 0.15456 × log10(height)) − 450
- Female: 495 / (1.29579 − 0.35004 × log10(waist + hip − neck) + 0.22100 × log10(height)) − 450
The structure is a body density estimate fed into the Siri equation, which converts density to fat percentage. The circumference terms are standing in for density, on the reasoning that abdominal girth relative to frame size tracks fat mass across a population. It does, well enough for screening. It does so with a standard error around 3 to 4 percentage points on an individual, which is the figure to keep in mind whenever the output shows a decimal place.
Where to put the tape
Measurement technique is the largest controllable source of error here, larger than the choice of formula.
| Reading | Placement | Common mistake |
|---|---|---|
| Waist | Horizontal at navel height, standing relaxed, after a normal breath out | Pulling the stomach in, or pulling the tape tight enough to compress |
| Neck | Just below the larynx, tape sloping slightly down at the front | Measuring across the widest part of the neck instead |
| Hip | The widest circumference viewed from the side, feet together | Measuring at the iliac crest rather than the widest point |
Use a cloth or fibreglass tape, not a steel one, and have someone else read it if you can — reading your own waist tape while looking down changes the placement. Because the waist term dominates the male equation, an inch of inconsistency there is worth about one and a half points of result, which is comparable to a month of genuine change.
Why the second estimate is shown
The Deurenberg equation, published in 1991, is body fat percentage estimated from BMI, age and sex: 1.20 times BMI, plus 0.23 times age, minus 10.8 for males, minus 5.4. It needs no tape at all, which is its appeal, and it inherits every limitation of BMI, which is its problem. It cannot distinguish muscle from fat because its only body input is a weight-for-height ratio.
Running both is more informative than running either. When they agree closely, your build is near the middle of the population the formulas were fitted on and both are probably in a reasonable range. When they separate by more than about six points, one of the assumptions has broken: usually substantial muscle mass, which pushes the BMI-based estimate up while the tape method reads the actual shape. The disagreement is a warning that neither number deserves confidence, and that is worth more than a spuriously precise single figure.
Bands, and what they are not
The descriptor table in the output uses the American Council on Exercise categories, which are the ones most widely reproduced in English-language fitness material. They are conventions, not thresholds validated against health outcomes the way blood pressure or A1c cut points are. Different organisations publish different boundaries, and the sex difference in the essential-fat row is real physiology — reproductive and hormonal tissue means the floor for women sits substantially higher than for men, and sustained readings below it are associated with menstrual disruption and reduced bone density.
What none of this supports is reading your own number against a band and drawing a conclusion about your health. A percentage from a tape measure, carrying four points of error, placed against a category boundary somebody chose, is several inferential steps away from anything clinical. Track the direction of your own readings over months under identical conditions. That trend is the part of this measurement that is actually reliable.
Questions people ask
Why does this disagree with my bioimpedance scale?
They measure different things. A bioimpedance scale passes a small current through the body and estimates composition from the resistance, which depends heavily on hydration. The same person on the same scale can read two to three points apart across a single day depending on fluid balance, food, exercise and salt intake. The tape method is insensitive to hydration but only sees girth, so it captures abdominal fat well and limb fat poorly. A gap of three to five points between the two is completely ordinary, and neither is a reference standard. If you need one, DEXA is the accessible option.
How often should I remeasure?
Every two to four weeks is enough. Real changes in body composition happen at a rate well below the measurement error of any tape method, so a weekly reading is mostly noise with a small signal buried in it. Measure at the same time of day, under the same conditions, ideally with the same person holding the tape, and plot the readings rather than reacting to any one of them. Three consecutive readings trending the same direction means something; one reading moving two points does not.
Does the calculator work if my waist is smaller than my neck?
No, and it returns a message rather than a number in that case. The male equation takes the logarithm of waist minus neck, which requires a positive value. In practice this almost always means the two measurements were entered in different units, or the neck was measured across the widest part rather than just below the larynx. Very occasionally it reflects an unusual build that falls outside the range the equation was fitted on, in which case the circumference method is not the right tool.
Is there a body fat percentage I should aim for?
This page does not set one and cannot. The bands shown are descriptive categories published by a fitness organisation, not health targets, and they say nothing about an individual's training history, medical situation or what a sustainable composition looks like for them. Very low readings carry documented costs to hormonal function and bone density, and the level at which those appear varies between people. If you are making decisions about body composition in a context where it matters — a sport with weight categories, a medical condition, an eating disorder history — that belongs with a clinician or a registered dietitian who can see the whole picture.