The WIMSTA Formula Registry
A verified, machine-readable registry of body-composition formulas — with sources, samples and error margins. 15 formulas · v2026.08.11 · updated 2026-08-11.
Use this data
The registry is open under CC BY 4.0 — the coefficients are facts; our value is the verification and the structure. Use them anywhere, just credit WIMSTA (wimsta.com) with a link.
- Machine-readable JSON: /api/registry.json (CORS open, cacheable)
- License: Creative Commons Attribution 4.0
- Attribution:
Data from WIMSTA (wimsta.com), CC BY 4.0
curl https://wimsta.com/api/registry.json | jq '.formulas[] | select(.id=="cun-bae")'Every formula, with its coefficients
Verification is honest: ✅ primary = checked against the original paper, 🟡 secondary = checked against secondary sources only. The same status the method page and the JSON report.
| Formula | Category | Inputs | Equation & coefficients | Source | Error | Status |
|---|---|---|---|---|---|---|
| Deurenberg 1991 id: deurenberg | body-fat | bmi, age, sex male=1, female=0 | BF% = 1.20·BMI + 0.23·age − 10.8·sex − 5.4 (BMI in kg/m², age in years) {"bmi":1.2,"age":0.23,"sex":-10.8,"intercept":-5.4} | Br J Nutr 65(2):105–114 Deurenberg, Weststrate & Seidell | SEE 4.1 pp · R² 0.79 | ✅ |
| CUN-BAE 2012 id: cun-bae | body-fat | bmi, age, sex female=1, male=0 (⚠️ inverse of Deurenberg) | BF% = −44.988 + 0.503·age + 10.689·female + 3.172·BMI − 0.026·BMI² + 0.181·BMI·female − 0.02·BMI·age − 0.005·BMI²·female + 0.00021·BMI²·age {"intercept":-44.988,"age":0.503,"female":10.689,"bmi":3.172,"bmi2":-0.026,"bmi_female":0.181,"bmi_age":-0.02,"bmi2_female":-0.005,"bmi2_age":0.00021} | Diabetes Care 35(2):383–388 Gómez-Ambrosi et al. | SE ≈ 4.7% · r 0.89 | ✅ |
| US Navy (Hodgdon–Beckett) 1984 id: us-navy | body-fat | waist, neck, height, sex, hip (women only) separate equations for men and women (women also require hip) | men: BF% = 495 / (1.0324 − 0.19077·log₁₀(waist−neck) + 0.15456·log₁₀(height)) − 450; women: BF% = 495 / (1.29579 − 0.35004·log₁₀(waist+hip−neck) + 0.221·log₁₀(height)) − 450 (cm) {"men":{"c0":1.0324,"cLogWaistNeck":-0.19077,"cLogHeight":0.15456},"women":{"c0":1.29579,"cLogWaistHipNeck":-0.35004,"cLogHeight":0.221},"transform":"495 / denominator − 450"} | U.S. Navy NHRC Reports 84-11 / 84-29 Hodgdon & Beckett | ±3–4 pp · r ≈ 0.90 | 🟡 |
| RFM (Relative Fat Mass) 2018 id: rfm | body-fat | height, waist, sex intercept 64 male / 76 female (the sex term is the +12 offset) | men: RFM = 64 − 20·(height/waist); women: RFM = 76 − 20·(height/waist) (cm) {"men":{"intercept":64,"heightOverWaist":-20},"women":{"intercept":76,"heightOverWaist":-20}} | Sci Rep 8:10980 Woolcott & Bergman | more accurate than BMI vs DXA | ✅ |
| Covert Bailey 1999 id: covert-bailey | body-fat | waist, hip, forearm, wrist, age, sex, thigh (women), calf (women) separate equations; women use thigh+calf, men use waist+hip+forearm | men (inches): waist + 0.5·hip − forearmCoef·forearm − wrist (forearmCoef 3 if age≤30 else 2.7); women (inches): hip + thighCoef·thigh − 2·calf − wrist (thighCoef 0.8 if age≤30 else 1.0) {"men":{"waist":1,"hip":0.5,"forearm":"coef","wrist":-1,"forearmCoef_le30":-3,"forearmCoef_gt30":-2.7},"women":{"hip":1,"thigh":"coef","calf":-2,"wrist":-1,"thighCoef_le30":0.8,"thighCoef_gt30":1}} | “Ultimate Fit or Fat” (book) Covert Bailey | not formally published | 🟡 |
| Gallagher healthy ranges 2000 id: gallagher-ranges | body-fat-ranges | age, sex ranges differ by sex | Age- and sex-specific HEALTHY body-fat % ranges (a reference band, not an estimator) — | Am J Clin Nutr 72(3):694–701 Gallagher et al. | age- and sex-specific ranges | 🟡 |
| WHO BMI cut-points 2000 id: who-bmi | bmi | bmi | BMI cut-points (kg/m²): underweight <18.5 · normal 18.5–25 · overweight 25–30 · obese I 30–35 · II 35–40 · III ≥40 {"cutPoints":[18.5,25,30,35,40]} | WHO Technical Report Series 894 World Health Organization | bands 18.5 / 25 / 30 / 35 / 40 | ✅ |
| Trefethen “new BMI” 2013 id: trefethen-bmi | bmi | height, weight | new BMI = 1.3·weight / height^2.5 (weight kg, height m) {"factor":1.3,"heightExponent":2.5} | The Economist (letter) / Oxford page Nick Trefethen (Oxford) | 1.3 · w / h^2.5 | ✅ |
| Ashwell boundary 2016 id: ashwell-whtr | waist-to-height | waist, height | waist ÷ height; screening boundary at 0.5 ("keep waist under half your height") {"boundary":0.5,"lowFlag":0.4} | BMJ Open 6:e010159 Ashwell & Gibson | boundary 0.5 (“keep waist under half your height”) | ✅ |
| Tanaka 2001 id: tanaka | max-heart-rate | age | HRmax = 208 − 0.7·age (bpm) {"intercept":208,"age":-0.7} | J Am Coll Cardiol 37(1):153–156 Tanaka, Monahan & Seals | 208 − 0.7·age · SD ±10 bpm | 🟡 |
| Gulati 2010 id: gulati | max-heart-rate | age, sex women only (derived in a female cohort) | HRmax = 206 − 0.88·age (bpm), women {"intercept":206,"age":-0.88} | Circulation 122(2):130–137 Gulati et al. | 206 − 0.88·age | 🟡 |
| Fox (220 − age) 1971 id: fox | max-heart-rate | age | HRmax = 220 − age (bpm) {"intercept":220,"age":-1} | no strict primary derivation Fox, Naughton & Haskell | 220 − age · SD ±10–12 bpm | 🟡 |
| Harris–Benedict 1919 id: harris-benedict-1919 | bmr | weight, height, age, sex separate equations for men and women | men: BMR = 66.473 + 13.7516·weight + 5.0033·height − 6.755·age; women: BMR = 655.0955 + 9.5634·weight + 1.8496·height − 4.6756·age (kcal/day; kg, cm, years) {"men":{"intercept":66.473,"weight":13.7516,"height":5.0033,"age":-6.755},"women":{"intercept":655.0955,"weight":9.5634,"height":1.8496,"age":-4.6756}} | Carnegie Inst. of Washington, Pub. 279 Harris & Benedict | overestimates modern BMR ~5% | 🟡 |
| Harris–Benedict revised 1984 id: harris-benedict-1984 | bmr | weight, height, age, sex separate equations for men and women | men: BMR = 88.362 + 13.397·weight + 4.799·height − 5.677·age; women: BMR = 447.593 + 9.247·weight + 3.098·height − 4.33·age (kcal/day; kg, cm, years) {"men":{"intercept":88.362,"weight":13.397,"height":4.799,"age":-5.677},"women":{"intercept":447.593,"weight":9.247,"height":3.098,"age":-4.33}} | Am J Clin Nutr 40(1):168–182 Roza & Shizgal | re-derivation of Harris–Benedict | ✅ |
| Katch–McArdle (Cunningham 1991) 1991 id: katch-mcardle | bmr | weight, bodyFat | BMR = 370 + 21.6·LBM, where LBM = weight·(1 − bodyFat/100) (kcal/day; kg) {"intercept":370,"leanBodyMass":21.6} | Am J Clin Nutr 54(6):963–969 Cunningham (popularised by Katch & McArdle) | strong with a measured body-fat % | ✅ |
Why this exists
Popular calculators copy each other, and they copy each other’s mistakes. The YMCA body-fat formula is everywhere despite having no locatable primary source and the worst fit against NHANES data in our testing (mean absolute error 8.4 percentage points). “Ideal weight” coefficients get quoted as health targets when they were built for drug dosing. The same equation shows up under two names — “Katch–McArdle” is, term for term, Cunningham 1991 — which lets sites fake a wider “range” by counting one estimate twice.
We publish the verified version instead: every coefficient checked against the source we cite, every verification status shown as it is, and the machine-readable file kept in lockstep with the human pages by generating both from one registry.
Changelog
- 2026-08-11 — first public release of the machine-readable registry (JSON + this page), generated from the same source as the method page.
- August 2026 — YMCA formula removed; CUN-BAE added and verified against the primary source; Deurenberg status corrected to verified.
How we calculate
Where the data comes from
For developers