Body fat from tape measurements: how the US Navy formula works and how far to trust it
The body fat calculator uses the Hodgdon and Beckett formula (US Navy, 1984): height plus neck and waist measurements and, for women, hips. In the sample where the formula was derived, its standard error was 3.5 percentage points for men and 3.7 for women. In checks on other groups the error can be larger and runs in one direction: in US Army recruits the formula underestimated body fat by 6 points on average compared with DXA. The result is an estimate with a wide margin, not a measurement.
What the calculator computes
Inputs: sex, age, height, weight, and neck, waist and (for women) hip measurements. Outputs: body fat percentage, fat mass and lean mass in kilograms, and where the result sits against a range for your sex and age.
An example using the default values in the form: a 30-year-old woman, 170 cm tall, 70 kg, neck 33 cm, waist 76 cm, hips 98 cm. The formula gives 27.6%, which is 19.3 kg of fat and 50.7 kg of lean mass. The calculator places that result in the 21-32% range.
Where the formula comes from
In 1984 James Hodgdon and Marcie Beckett of the Naval Health Research Center in San Diego issued two reports: one for Navy men and one for women (report no. 84-29, listed in a US National Academies reference on body composition in the military services). The reference was body fat measured by underwater weighing. The formula estimates body density from the logarithms of circumferences and height, then converts density to body fat with the Siri equation (1961).
The equations as given in a Navy report that tested them on 505 service members, and as the calculator uses them (height and circumferences in centimeters, log is the base-10 logarithm):
- men: density = 1.0324 - 0.19077 x log(waist - neck) + 0.15456 x log(height);
- women: density = 1.29579 - 0.35004 x log(waist + hips - neck) + 0.221 x log(height);
- body fat % = 495 / density - 450.
The formulas were derived on 602 men and 214 women from the US Navy and Marine Corps, all serving personnel. The standard error in those samples was 3.52 points for men and 3.72 for women. In cross-validation on another sample it was 2.70 for men and between 4.04 and 4.36 for women.
Where the healthy range comes from
The ranges in the calculator come from Gallagher and colleagues (Am J Clin Nutr, 2000). The authors measured body fat with reference methods (a four-compartment model and DXA) in 1,626 adults with a BMI up to 35, from three ethnic groups: white, African American and Asian. From these data they built an equation in which body fat depends on BMI, sex, age and ethnic group (standard error 2.8 to 5.4%), and applied it to the BMI limits of 18.5, 25 and 30.
| Age | Range matching a BMI of 18.5 to 24.9: women / men |
|---|---|
| 20-39 | 21-32% / 8-19% |
| 40-59 | 23-33% / 11-21% |
| 60-79 | 24-35% / 13-24% |
The authors call the ranges provisional. One detail matters: this "healthy range" is BMI limits converted into body fat, not the result of following the health of people with different body fat levels. It therefore inherits the limits of BMI, covered in our article on body mass index. The calculator rates a result only for ages 20 to 79, because the ranges were derived for that span.
Where the formula goes wrong
The error is quoted as one number, but it looks different across groups.
| Who was checked | What was found |
|---|---|
| The sample the formula was derived on (Hodgdon, Beckett, 1984) | Standard error 3.52 points for men, 3.72 for women |
| 1,904 serving US Army soldiers, compared with DXA (PMC11026907) | The Army regulation equations, built on the Hodgdon formulas, underestimated body fat on average: by 4.79 points in men and 1.69 in women |
| 1,407 US Army recruits, compared with DXA at the start of training (Frontiers in Physiology, 2023) | Underestimation by 6.0 points on average, in both women (spread of 4.4) and men (3.5) |
The error is not random. The authors of the 2023 paper recall that these equations underestimate body fat where there is a lot of it and overestimate it where there is little. All three rows are military samples, and in the 2023 study participants had also been selected against entry standards. These checks do not show how the formula behaves in people of other ages and builds.
A centimeter of tape is 0.5 to 0.8 of a percentage point
The formula takes logarithms of the circumferences, and a small slip in measuring visibly shifts the answer. Calculations with the calculator's formula:
- a man 178 cm tall, neck 38 cm, waist 85 cm: 16.4%. A waist of 86 cm gives 17.2%, and a neck of 37 cm also gives 17.2%;
- a woman 170 cm tall, neck 33 cm, hips 98 cm, waist 76 cm: 27.6%. A waist of 77 cm gives 28.1%, and hips of 99 cm also give 28.1%.
A tape that sits 2 cm off changes the result by 1 to 1.6 points. The 2023 paper cited above reports an estimate that trained observers reproduce the formula's result within 1 point. At home the measuring point wanders more, so a difference of a point or two between two results is reasonably treated as noise.
For tracking change, the formula does worse than it seems
Calculators like this are often recommended for trends: the absolute number is off, but the change supposedly shows. A test in 1,407 recruits did not support that. Over 8 weeks of training, DXA showed body fat falling by 4.0 points in women and 3.3 in men. The circumference formula showed 0.0 in women (statistically no change) and a fall of 2.2 points in men. In 43% of women and 14.5% of men the formula showed body fat rising when DXA showed it falling.
The authors conclude that such formulas are unsuited to tracking body composition during short, intense training. The conditions were unusual: young people under a load that changes fat and muscle at the same time. Whether the finding carries over to ordinary life was not tested. In the same study, DXA changes in men closely matched changes in abdominal circumference. If you follow a trend, the circumferences themselves in centimeters are a safer thing to watch than the derived percentage. On why weight and waist diverge, see when the scale stays put but the waist shrinks.
How this differs from smart scales and DXA
Bioimpedance scales also give a calculated estimate: the device measures electrical resistance and puts it into a formula. What error to expect there and why the result drifts through the day is covered in the article on smart scales and bioimpedance. DXA, the reference in the last two checks in the table, is done in a clinic on a dedicated scanner.
Measuring so the number means something
- Soft tape, at the end of a breath out, without pulling the skin tight. Measure the neck just below the Adam's apple.
- Waist: for men at navel level, for women at the narrowest point. Hips: at the fullest point of the buttocks. These are the points the formula was derived on; others give a different result.
- The waist and hip calculator measures the waist differently: midway between the lowest rib and the top of the hip bone. Do not mix numbers between the two calculators.
- The same time of day, the same tape, two measurements in a row. If they differ by more than a centimeter, measure again.
How to use the result
Read it as a band, not a point. With an error of 3 to 4 points, a result of 27.6% cannot be told from 24% or from 31%, and the band may be shifted in one direction. The position against the range says where the result sits on a scale built from BMI. It is not a rating of a person and not a target.
The formula is too coarse to support a numeric goal for body fat, since it cannot measure a step of one or two points. For a rough sense of how your body is doing, it is more useful to keep several indicators side by side: waist circumference, how you feel, strength, eating and sleep habits.
When to see a doctor
The calculator result is not a diagnosis or a measure of health. See a doctor if weight or waist change quickly for no clear reason, or if swelling, breathlessness or unexplained weakness appear. The same goes if measuring and numbers take up a lot of your thoughts or cause anxiety: you do not have to measure yourself, and a conversation about food and body can start with a doctor or a psychologist. Exact body composition, if it is really needed, is determined in a clinic.
The calculator itself is on the body fat calculator page.
Frequently asked questions
- How is body fat calculated from measurements?
- With the Hodgdon and Beckett formula (US Navy, 1984). For men, density = 1.0324 - 0.19077 x log(waist - neck) + 0.15456 x log(height); for women, density = 1.29579 - 0.35004 x log(waist + hips - neck) + 0.221 x log(height); all in centimeters. Body fat % = 495 / density - 450 (the Siri equation).
- How accurate is the US Navy formula?
- The standard error in the sample it was derived on is 3.52 points for men and 3.72 for women. In checks on US Army personnel with DXA as the reference, formulas of this family underestimated body fat on average: by 1.69 to 4.79 points in one study and by 6.0 points in another.
- Where do the healthy ranges in the calculator come from?
- From Gallagher and colleagues (2000): the authors converted the BMI limits of 18.5, 25 and 30 into body fat using data on 1,626 adults with a BMI up to 35. For ages 20 to 39 that gives 21-32% in women and 8-19% in men. The ranges are provisional.
- Can I track change with this formula?
- With reservations. In a study of 1,407 US Army recruits over 8 weeks, DXA showed body fat falling by 4.0 points in women and 3.3 in men, while the circumference formula showed 0.0 and 2.2. The circumferences themselves in centimeters are a safer thing to watch.
- Why do women need a hip measurement?
- The women's formula is built on the sum of waist and hips minus neck. That is how its authors derived it, on a sample of 214 Navy and Marine Corps women. Without hips the women's formula cannot be computed.
Read next
- Body mass index: how to calculate it and where it goes wrong — Body mass index takes ten seconds to calculate and is therefore used where it shouldn't be: for an individual.
- Smart scales: what bioimpedance actually measures — Smart scales display body fat percentage, water percentage, muscle mass, bone mass, and "metabolic age.
- Visceral fat: why it matters and how to measure it — Two people at the same weight, with the same BMI, can carry very different metabolic risk.
- The scale is steady but your waist is shrinking: what it means — If your weight is steady but your waist measures smaller, change may be happening without a visible shift on the scale.
- Waist-to-height, waist circumference and waist-to-hip: how the three measures differ — The waist and hip calculator gives three numbers: waist-to-height ratio, waist circumference and, if you enter hips, waist-to-hip ratio.
This article is for general information. It is not medical advice, a diagnosis, or a prescription for treatment or a diet, and it does not replace a consultation with your doctor. If you have a health condition, are pregnant, take medication, or follow a diet prescribed to you, decisions about food belong with your doctor.
Figures from regulations, guidelines and studies are given as they stood when this article was prepared and may since have changed; check them against the primary sources. This article is not advertising, an offer, or individual advice, and neither the author nor the site owner is responsible for decisions taken on the basis of it.