Body Adiposity Index (BAI) Calculator

Background.

In 2011 Richard Bergman's group published the Body Adiposity Index under a confident title, 'A better index of body adiposity'. Their idea was to estimate body-fat percentage from hip circumference and height alone, with no body weight anywhere in the calculation: hip in centimetres, divided by height in metres raised to the power 1.5, minus 18. In the two groups it was built and tested on, 1,733 Mexican-American adults in the BetaGene study and 223 African-American adults in the TARA study, it tracked fat measured by DXA scanning with correlations of 0.790 and 0.849.

A year later the same journal carried a rebuttal. David Freedman and colleagues compared BAI with DXA in 1,151 adults aged 18 to 110, drawn from eleven studies, and found it read about 3.9 percentage points too high in men and 2.5 too low in women, with errors that also shifted according to how much fat a person carried. The title of their paper gave the verdict: BAI is not a more accurate measure of adiposity than BMI, waist circumference or hip circumference.

You see both sides of that argument in the results: the index exactly as Bergman defined it, the average bias Freedman measured for your sex, and the index with that bias taken off.

The case for using BAI at all is practical. It needs a tape measure and a wall, nothing more, and because weight never enters it the number is not swayed by the day-to-day swings in water and stomach contents that move a scale. Measured the same way over months, it offers a weight-free view of change. As a single reading of how much fat you carry, it is a rough estimate with a known bias, and it does not replace a clinical assessment.

What is body adiposity index (bai) calculator?

The Body Adiposity Index is an estimate of total body fat, expressed as a percentage of body weight, calculated from hip circumference and height. Its two constants, the exponent 1.5 and the intercept 18, were fitted so the output would sit on the same scale as percent body fat measured by DXA (dual-energy X-ray absorptiometry), the scan used as the reference in both studies. One equation serves men and women alike, with no age or sex term. Because it rests on the hip rather than the waist, BAI reflects overall and lower-body fat, whereas waist-based measures are aimed at the abdominal fat most closely tied to heart and metabolic risk.

How to use this calculator.

1. 01Select your sex. It does not change the BAI itself, which has no sex term; it chooses which published bias figure is shown and subtracted.
2. 02Pick metric or imperial and enter both measurements in that unit. The calculator converts to the centimetres and metres the equation expects.
3. 03Measure your hips at the widest point of the buttocks, feet together, with the tape level all the way round and snug without pressing in. A mirror, or a helper, catches a tape that has slipped at the back.
4. 04Measure your height standing straight against a wall without shoes.
5. 05Read the BAI and the bias-adjusted figure beside it. For tracking, repeat with the same tape, the same landmark and the same clothing each time.

The formula.

BAI = hip ÷ height^1.5 − 18, with hip in centimetres and height in metres. The mixed units are part of the definition, because the constants were fitted with them. Height in centimetres makes the divisor a thousand times larger, so a 100 cm hip at 175 cm would give 0.0432 − 18 = −17.96; hip in metres shrinks the first term a hundredfold. The calculator therefore takes both measurements in one unit and does the conversion itself.

The hip term is linear. At a height of 1.75 m each extra centimetre of hip adds 1 ÷ 2.3150 = 0.432 points. Height works through the 1.5 power, so the same hip on a taller frame reads lower: going from 1.60 m to 2.00 m divides the first term by (2.00 ÷ 1.60)^1.5 = 1.3975, taking a 100 cm hip from 31.41% to 17.36%.

The fixed intercept means the line crosses zero. A 50 cm hip at 2.30 m works out at −3.67%, and 55 cm at 2.20 m at −1.15%, both impossible, so any combination giving zero or less is refused rather than shown. Hip entries are accepted from 50 to 200 cm and heights from 1.20 to 2.30 m.

The bias-adjusted figure is BAI minus Freedman's mean bias: minus 3.9 points for men, plus 2.5 for women. It is an average over 1,151 people, and the same paper found the bias changed with body fatness, so it is a population correction rather than a personal calibration.

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. An independent second authority, 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.