Body Adiposity Index (BAI) Calculator

Background.

The Body Adiposity Index estimates what percentage of your body is fat from two tape measurements and nothing else: your hip circumference and your height. No scale, no callipers, no electrical device, no weight at all. The formula is BAI = hip in centimetres ÷ height in metres to the power 1.5, minus 18. Enter the two numbers and the calculator returns that estimate — and, just as prominently, the published evidence about how far it misses.

That evidence needs to come before the number rather than after it. Richard Bergman and colleagues introduced BAI in the journal Obesity in 2011 under the title 'A better index of body adiposity', developing it on 1,733 Mexican-American adults from the BetaGene study and validating it on 223 African-American adults from the TARA study, both against DXA-measured percent body fat, with correlations of R = 0.790 and R = 0.849. The following year, in the same journal, David Freedman and colleagues published a paper titled 'The body adiposity index is not a more accurate measure of adiposity than is BMI, waist circumference, or hip circumference'. Working with 1,151 adults aged 18 to 110 across eleven studies at the New York Obesity Nutrition Research Center, they found that BAI overestimated DXA body fat in men by 3.9 percentage points and underestimated it in women by 2.5, with the size of those errors varying by how fat the person was, and concluded that estimates based on BAI 'are not more accurate than those based on BMI, waist circumference, or hip circumference'. Both papers are real, both are peer-reviewed, and this calculator shows you both: the raw BAI exactly as Bergman defined it, the mean bias Freedman measured for your sex, and the difference between them.

So why compute it at all? Because of what it does not need. Every other adiposity estimate on this site needs either a scale, a calliper or a second circumference. BAI needs a tape measure and a wall. If you are estimating body composition somewhere without equipment, or you want a number that is completely insensitive to weight — which means completely insensitive to muscle mass, hydration and what you last ate — this is the one index that provides it. It also looks somewhere BMI structurally cannot: the hip. Waist-based indices such as waist-to-height ratio and ABSI measure android, abdominal fat; BAI measures the gynoid, lower-body distribution, which is why it and a waist measure disagree most about exactly the people whose fat is distributed unusually.

One thing about the equation deserves attention because it is a genuine trap. The units are mixed: hip goes in as centimetres, height as metres. Using centimetres for both, or metres for both, produces an answer wrong by a factor of about 31.6, and it will look plausible enough to believe. This calculator takes both measurements in whichever unit you select and does the conversion internally, and it prints the converted hip in centimetres, the height in metres, and the height-to-the-1.5 denominator so you can check every step against the published formula.

A second quirk is that the equation subtracts a flat 18, which means it is a straight line that crosses zero. For a small hip on a tall frame it returns a negative body-fat percentage: 50 cm of hip at 2.30 m of height gives −3.7 %, and 55 cm at 2.20 m gives −1.1 %. Those are physically impossible, so rather than print them the calculator refuses and explains why. Because the intercept is fixed and the equation has no sex term, BAI also cannot represent the roughly ten-percentage-point difference in healthy body fat between men and women — a man and a woman with the same hips and the same height get exactly the same number, which is precisely the structural reason Freedman found bias in opposite directions for the two sexes.

Read the result, then, for what it is: a cheap, equipment-free, weight-independent estimate of total body fat with a known and fairly large bias, from a paper whose central claim a second paper in the same journal disputes. It is a reasonable thing to track over time with a consistent tape, and a poor thing to treat as a measurement.

What is body adiposity index (bai) calculator?

The Body Adiposity Index (BAI) is an anthropometric estimate of whole-body fat percentage calculated as hip circumference in centimetres divided by height in metres raised to the power 1.5, minus 18. It was published by Richard N. Bergman and colleagues in Obesity in 2011 as an alternative to BMI that requires no measurement of body weight. The exponent of 1.5 and the intercept of 18 were fitted so that the resulting number would sit on the same scale as DXA-measured percent body fat, using the BetaGene cohort of 1,733 Mexican-American adults, and were then checked against the TARA cohort of 223 African-American adults, where the correlation with DXA was R = 0.849 with a concordance coefficient of 0.947. Its distinguishing features are that it uses the hip rather than the waist, that it needs no scale, and that it applies a single equation to both sexes with no sex term. That last property is also its principal weakness: because healthy body-fat percentages differ by roughly ten points between men and women, a sexless equation must be biased for at least one of them. Freedman and colleagues demonstrated exactly that in 2012, finding BAI overestimated DXA body fat in men by 3.9 percentage points and underestimated it in women by 2.5 in a sample of 1,151 adults, and concluding it was not more accurate than BMI, waist circumference or hip circumference alone. BAI is therefore best understood as a weight-free, hip-based screening estimate with a known and sex-dependent bias, rather than as a replacement for BMI or a substitute for a body-composition scan.

How to use this calculator.

1. 01Select your sex. This does not change the BAI number at all — the equation has no sex term. It selects which published bias figure is displayed alongside.
2. 02Choose metric or imperial. Enter both measurements in the unit you picked; the calculator handles the equation's own mixed centimetre-and-metre convention for you.
3. 03Measure your hip at the widest point of the buttocks, standing with feet together and weight even, with the tape horizontal all the way round. Check it in a mirror or have someone help — a tilted tape is the commonest error here.
4. 04Measure your height standing straight without shoes, ideally first thing in the morning.
5. 05Read the BAI percentage, then read the published bias tile immediately beside it. For a man, subtract about 3.9 points to get closer to what a DXA scan would say; for a woman, add about 2.5.
6. 06Use the hip-in-centimetres, height-in-metres and height^1.5 tiles to check the calculator read your measurements as you intended.
7. 07Track it with the same tape at the same landmark over months. BAI's insensitivity to weight is its real strength: a change in BAI cannot be caused by muscle gain, hydration or a heavy meal.

The formula.

BAI = hip circumference in centimetres ÷ (height in metres)^1.5 − 18. THE MIXED UNITS ARE PART OF THE DEFINITION AND ARE THE MAIN TRAP: hip is in centimetres, height in metres. Using the same unit for both is wrong by a factor of roughly 31.6 and produces a plausible-looking number. Working the shipped example: a person 175 cm tall has a height of 1.75 m, and 1.75^1.5 = 1.75 × √1.75 = 2.3150323972. With a 100 cm hip, the first term is 100 ÷ 2.3150323972 = 43.1959397725, and subtracting the fixed 18 gives a BAI of 25.1959397725 %. For a man, Freedman's measured mean bias of +3.9 percentage points means the DXA-comparable figure is around 25.1959397725 − 3.9 = 21.2959397725 %. For a woman the bias runs the other way at −2.5 points, so the adjustment adds: a woman with a 102 cm hip at 165 cm has height^1.5 = 2.1194633755, a BAI of 102 ÷ 2.1194633755 − 18 = 30.1253892754 %, and a DXA-comparable figure of 32.6253892754 %. TWO DIRECTIONAL FACTS, verified against the equation rather than assumed: a larger hip at fixed height raises BAI exactly linearly, by Δhip ÷ height^1.5 per centimetre — about 0.43 points per centimetre at 1.75 m; and a taller person with the same hip has a lower BAI, falling with the 1.5 power, so going from 1.60 m to 2.00 m divides the first term by (2.00/1.60)^1.5 = 1.3975. INVALID DOMAIN: because the equation subtracts a fixed 18, it returns negative percentages for a small hip on a tall frame — 50 cm at 2.30 m gives −3.67 %, 55 cm at 2.20 m gives −1.15 %, and 60 cm at 2.20 m only just clears zero at +0.39 %. The calculator rejects any combination giving zero or less and says why, rather than printing an impossible figure. Hip is additionally guarded to 50–200 cm and height to 1.20–2.30 m. ROUNDING STAGE: the fractional power, the subtraction and the bias adjustment are all carried at full decimal precision and rounded once, at the end.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Bergman RN, Stefanovski D, Buchanan TA, Sumner AE, Reynolds JC, Sebring NG, Xiang AH, Watanabe RM. "A better index of body adiposity." Obesity (Silver Spring). 2011;19(5):1083–1089. PMID 21372804, PMC3275633. Source of the equation BAI = Hip/Height^1.5 − 18 with hip in centimetres and height in metres, the BetaGene derivation cohort (n = 1,733 Mexican-American adults) and TARA validation cohort (n = 223 African-American adults), and the DXA correlations of R = 0.790 and R = 0.849 (concordance Cb = 0.947). Open access.
2. [2]Freedman DS, Thornton J, Pi-Sunyer FX, Heymsfield SB, Wang J, Pierson RN, Blanck HM, Gallagher D. "The body adiposity index (hip circumference ÷ height^1.5) is not a more accurate measure of adiposity than is BMI, waist circumference, or hip circumference." Obesity (Silver Spring). 2012;20(12):2438–2444. PMID 22484365, PMC3477292. The independent second authority consulted for this build, and the source of the bias figures displayed on this page: "BAI overestimated PBFDXA among men (3.9%) and underestimated PBFDXA among women (2.5%), but the magnitudes of these biases varied with the level of body fatness", in 1,151 adults aged 18–110 across eleven studies. Open access.
3. [3]National Institute of Standards and Technology — "Guide for the Use of the International System of Units (SI)," NIST Special Publication 811, 2008 edition, Appendix B.9. Source of the exact conversion 1 in = 2.54 cm used for imperial input.