{
  "registry_version": "2026.08.11",
  "last_updated": "2026-08-11",
  "license": "CC-BY-4.0",
  "attribution_notice": "Data from WIMSTA (wimsta.com), licensed CC BY 4.0. Cite as: \"WIMSTA (wimsta.com)\".",
  "canonical_page": "https://wimsta.com/registry/",
  "formula_count": 15,
  "formulas": [
    {
      "id": "deurenberg",
      "name": "Deurenberg",
      "category": "body-fat",
      "equation": "BF% = 1.20·BMI + 0.23·age − 10.8·sex − 5.4 (BMI in kg/m², age in years)",
      "inputs": [
        "bmi",
        "age",
        "sex"
      ],
      "source": {
        "authors": "Deurenberg, Weststrate & Seidell",
        "year": 1991,
        "journal": "Br J Nutr 65(2):105–114",
        "doi": "https://doi.org/10.1079/BJN19910073"
      },
      "sample": {
        "n": 1229,
        "population": "Netherlands adults",
        "reference_method": "densitometry (underwater weighing)"
      },
      "error": {
        "note": "SEE 4.1 pp · R² 0.79",
        "value": 4.1,
        "unit": "pp"
      },
      "verification": "primary",
      "independent_derivation": true,
      "limitations": [
        "Overestimates in obesity (per the authors) and not validated in Asian populations. BMI-based, so it cannot tell muscle from fat."
      ],
      "canonical_page": "https://wimsta.com/deurenberg-formula/",
      "coefficients": {
        "bmi": 1.2,
        "age": 0.23,
        "sex": -10.8,
        "intercept": -5.4
      },
      "sex_coding": "male=1, female=0",
      "units": "metric"
    },
    {
      "id": "cun-bae",
      "name": "CUN-BAE",
      "category": "body-fat",
      "equation": "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",
      "inputs": [
        "bmi",
        "age",
        "sex"
      ],
      "source": {
        "authors": "Gómez-Ambrosi et al.",
        "year": 2012,
        "journal": "Diabetes Care 35(2):383–388",
        "doi": "https://doi.org/10.2337/dc11-1334"
      },
      "sample": {
        "n": 6510,
        "population": "Spanish white adults 18–80",
        "reference_method": "air-displacement plethysmography"
      },
      "error": {
        "note": "SE ≈ 4.7% · r 0.89",
        "value": 4.7,
        "unit": "pp"
      },
      "verification": "primary",
      "independent_derivation": true,
      "limitations": [
        "BMI-based, so it shares the muscle blind spot; validated mainly in white adults. Not for under-18s or pregnancy."
      ],
      "canonical_page": "https://wimsta.com/cun-bae-calculator/",
      "coefficients": {
        "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
      },
      "sex_coding": "female=1, male=0 (⚠️ inverse of Deurenberg)",
      "units": "metric"
    },
    {
      "id": "us-navy",
      "name": "US Navy (Hodgdon–Beckett)",
      "category": "body-fat",
      "equation": "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)",
      "inputs": [
        "waist",
        "neck",
        "height",
        "sex",
        "hip (women only)"
      ],
      "source": {
        "authors": "Hodgdon & Beckett",
        "year": 1984,
        "journal": "U.S. Navy NHRC Reports 84-11 / 84-29"
      },
      "sample": {
        "population": "U.S. military personnel",
        "reference_method": "hydrostatic weighing"
      },
      "error": {
        "note": "±3–4 pp · r ≈ 0.90",
        "value": 3.5,
        "unit": "pp"
      },
      "verification": "secondary",
      "independent_derivation": true,
      "limitations": [
        "Developed on a military population; loses accuracy at extreme builds. Not valid in pregnancy."
      ],
      "canonical_page": "https://wimsta.com/us-navy-body-fat-formula/",
      "coefficients": {
        "men": {
          "c0": 1.0324,
          "cLogWaistNeck": -0.19077,
          "cLogHeight": 0.15456
        },
        "women": {
          "c0": 1.29579,
          "cLogWaistHipNeck": -0.35004,
          "cLogHeight": 0.221
        },
        "transform": "495 / denominator − 450"
      },
      "sex_coding": "separate equations for men and women (women also require hip)",
      "units": "metric"
    },
    {
      "id": "rfm",
      "name": "RFM (Relative Fat Mass)",
      "category": "body-fat",
      "equation": "men: RFM = 64 − 20·(height/waist); women: RFM = 76 − 20·(height/waist) (cm)",
      "inputs": [
        "height",
        "waist",
        "sex"
      ],
      "source": {
        "authors": "Woolcott & Bergman",
        "year": 2018,
        "journal": "Sci Rep 8:10980",
        "doi": "https://doi.org/10.1038/s41598-018-29362-1"
      },
      "sample": {
        "n": 12000,
        "population": "NHANES, US multi-ethnic",
        "reference_method": "DXA"
      },
      "error": {
        "note": "more accurate than BMI vs DXA"
      },
      "verification": "primary",
      "independent_derivation": true,
      "limitations": [
        "Needs only waist and height — a strong all-rounder, but still an estimate, not a measurement."
      ],
      "canonical_page": "https://wimsta.com/rfm-calculator/",
      "coefficients": {
        "men": {
          "intercept": 64,
          "heightOverWaist": -20
        },
        "women": {
          "intercept": 76,
          "heightOverWaist": -20
        }
      },
      "sex_coding": "intercept 64 male / 76 female (the sex term is the +12 offset)",
      "units": "metric"
    },
    {
      "id": "covert-bailey",
      "name": "Covert Bailey",
      "category": "body-fat",
      "equation": "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)",
      "inputs": [
        "waist",
        "hip",
        "forearm",
        "wrist",
        "age",
        "sex",
        "thigh (women)",
        "calf (women)"
      ],
      "source": {
        "authors": "Covert Bailey",
        "year": 1999,
        "journal": "“Ultimate Fit or Fat” (book)"
      },
      "sample": {
        "population": "popular book, not peer-reviewed",
        "reference_method": "—"
      },
      "error": {
        "note": "not formally published"
      },
      "verification": "secondary",
      "independent_derivation": true,
      "limitations": [
        "From a popular book, not a peer-reviewed paper; the primary validation is hard to source. Needs extra circumferences (wrist/forearm or thigh/calf)."
      ],
      "coefficients": {
        "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
        }
      },
      "sex_coding": "separate equations; women use thigh+calf, men use waist+hip+forearm",
      "units": "imperial"
    },
    {
      "id": "gallagher-ranges",
      "name": "Gallagher healthy ranges",
      "category": "body-fat-ranges",
      "equation": "Age- and sex-specific HEALTHY body-fat % ranges (a reference band, not an estimator)",
      "inputs": [
        "age",
        "sex"
      ],
      "source": {
        "authors": "Gallagher et al.",
        "year": 2000,
        "journal": "Am J Clin Nutr 72(3):694–701",
        "doi": "https://doi.org/10.1093/ajcn/72.3.694"
      },
      "sample": {
        "population": "multi-ethnic adults",
        "reference_method": "four-compartment model"
      },
      "error": {
        "note": "age- and sex-specific ranges"
      },
      "verification": "secondary",
      "independent_derivation": true,
      "limitations": [
        "Source of the healthy-range ZONES, not a body-fat estimate. Ranges depend on age and sex; Asian ranges differ."
      ],
      "sex_coding": "ranges differ by sex"
    },
    {
      "id": "who-bmi",
      "name": "WHO BMI cut-points",
      "category": "bmi",
      "equation": "BMI cut-points (kg/m²): underweight <18.5 · normal 18.5–25 · overweight 25–30 · obese I 30–35 · II 35–40 · III ≥40",
      "inputs": [
        "bmi"
      ],
      "source": {
        "authors": "World Health Organization",
        "year": 2000,
        "journal": "WHO Technical Report Series 894",
        "doi": "https://www.who.int/publications/i/item/WHO_TRS_894"
      },
      "sample": {
        "population": "international expert consultation",
        "reference_method": "population mortality/morbidity risk"
      },
      "error": {
        "note": "bands 18.5 / 25 / 30 / 35 / 40"
      },
      "verification": "primary",
      "independent_derivation": true,
      "limitations": [
        "Population cut-points, not a personal verdict. Class I/II/III come from TRS 894, not the current fact sheet. Asian risk thresholds are lower."
      ],
      "coefficients": {
        "cutPoints": [
          18.5,
          25,
          30,
          35,
          40
        ]
      }
    },
    {
      "id": "trefethen-bmi",
      "name": "Trefethen “new BMI”",
      "category": "bmi",
      "equation": "new BMI = 1.3·weight / height^2.5 (weight kg, height m)",
      "inputs": [
        "height",
        "weight"
      ],
      "source": {
        "authors": "Nick Trefethen (Oxford)",
        "year": 2013,
        "journal": "The Economist (letter) / Oxford page",
        "doi": "https://people.maths.ox.ac.uk/trefethen/bmi.html"
      },
      "sample": {
        "population": "—",
        "reference_method": "—"
      },
      "error": {
        "note": "1.3 · w / h^2.5"
      },
      "verification": "primary",
      "independent_derivation": true,
      "limitations": [
        "A proposal, not an official standard — gentler on very tall and very short people. Uses the same category cut-points as classic BMI."
      ],
      "coefficients": {
        "factor": 1.3,
        "heightExponent": 2.5
      },
      "units": "metric"
    },
    {
      "id": "ashwell-whtr",
      "name": "Ashwell boundary",
      "category": "waist-to-height",
      "equation": "waist ÷ height; screening boundary at 0.5 (\"keep waist under half your height\")",
      "inputs": [
        "waist",
        "height"
      ],
      "source": {
        "authors": "Ashwell & Gibson",
        "year": 2016,
        "journal": "BMJ Open 6:e010159",
        "doi": "https://doi.org/10.1136/bmjopen-2015-010159"
      },
      "sample": {
        "population": "systematic review / meta-analysis",
        "reference_method": "cardiometabolic risk outcomes"
      },
      "error": {
        "note": "boundary 0.5 (“keep waist under half your height”)"
      },
      "verification": "primary",
      "independent_derivation": true,
      "limitations": [
        "A single screening boundary across sex and age; the full scale also flags very low ratios (<0.4). A screening signal, not a diagnosis."
      ],
      "coefficients": {
        "boundary": 0.5,
        "lowFlag": 0.4
      }
    },
    {
      "id": "tanaka",
      "name": "Tanaka",
      "category": "max-heart-rate",
      "equation": "HRmax = 208 − 0.7·age (bpm)",
      "inputs": [
        "age"
      ],
      "source": {
        "authors": "Tanaka, Monahan & Seals",
        "year": 2001,
        "journal": "J Am Coll Cardiol 37(1):153–156",
        "doi": "https://doi.org/10.1016/S0735-1097(00)01054-8"
      },
      "sample": {
        "n": 18712,
        "population": "meta-analysis, healthy adults",
        "reference_method": "measured max heart rate"
      },
      "error": {
        "note": "208 − 0.7·age · SD ±10 bpm",
        "value": 10,
        "unit": "bpm"
      },
      "verification": "secondary",
      "independent_derivation": true,
      "limitations": [
        "Population-recommended over 220−age, but any prediction is ±10 bpm for an individual."
      ],
      "canonical_page": "https://wimsta.com/tanaka-formula/",
      "coefficients": {
        "intercept": 208,
        "age": -0.7
      }
    },
    {
      "id": "gulati",
      "name": "Gulati",
      "category": "max-heart-rate",
      "equation": "HRmax = 206 − 0.88·age (bpm), women",
      "inputs": [
        "age",
        "sex"
      ],
      "source": {
        "authors": "Gulati et al.",
        "year": 2010,
        "journal": "Circulation 122(2):130–137",
        "doi": "https://doi.org/10.1161/CIRCULATIONAHA.110.939249"
      },
      "sample": {
        "n": 5437,
        "population": "women's cohort",
        "reference_method": "symptom-limited stress test"
      },
      "error": {
        "note": "206 − 0.88·age",
        "unit": "bpm"
      },
      "verification": "secondary",
      "independent_derivation": true,
      "limitations": [
        "Derived specifically in women, where 220−age fits worst."
      ],
      "canonical_page": "https://wimsta.com/max-heart-rate-women/",
      "coefficients": {
        "intercept": 206,
        "age": -0.88
      },
      "sex_coding": "women only (derived in a female cohort)"
    },
    {
      "id": "fox",
      "name": "Fox (220 − age)",
      "category": "max-heart-rate",
      "equation": "HRmax = 220 − age (bpm)",
      "inputs": [
        "age"
      ],
      "source": {
        "authors": "Fox, Naughton & Haskell",
        "year": 1971,
        "journal": "no strict primary derivation"
      },
      "sample": {
        "population": "observational, small",
        "reference_method": "—"
      },
      "error": {
        "note": "220 − age · SD ±10–12 bpm",
        "value": 11,
        "unit": "bpm"
      },
      "verification": "secondary",
      "independent_derivation": true,
      "limitations": [
        "The famous one, and the least accurate for an individual — shown with its spread, plus six more formulas in the heart-rate calculator."
      ],
      "canonical_page": "https://wimsta.com/220-minus-age/",
      "coefficients": {
        "intercept": 220,
        "age": -1
      }
    },
    {
      "id": "harris-benedict-1919",
      "name": "Harris–Benedict",
      "category": "bmr",
      "equation": "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)",
      "inputs": [
        "weight",
        "height",
        "age",
        "sex"
      ],
      "source": {
        "authors": "Harris & Benedict",
        "year": 1919,
        "journal": "Carnegie Inst. of Washington, Pub. 279"
      },
      "sample": {
        "population": "adults measured in the 1910s",
        "reference_method": "indirect calorimetry"
      },
      "error": {
        "note": "overestimates modern BMR ~5%"
      },
      "verification": "secondary",
      "independent_derivation": true,
      "limitations": [
        "Derived on an early-1900s sample; overestimates basal metabolism by about 5% vs modern measurements. Kept as the historical baseline, shown beside the 1984 revision."
      ],
      "canonical_page": "https://wimsta.com/harris-benedict-calculator/",
      "coefficients": {
        "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
        }
      },
      "sex_coding": "separate equations for men and women",
      "units": "metric"
    },
    {
      "id": "harris-benedict-1984",
      "name": "Harris–Benedict revised",
      "category": "bmr",
      "equation": "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)",
      "inputs": [
        "weight",
        "height",
        "age",
        "sex"
      ],
      "source": {
        "authors": "Roza & Shizgal",
        "year": 1984,
        "journal": "Am J Clin Nutr 40(1):168–182",
        "doi": "https://doi.org/10.1093/ajcn/40.1.168"
      },
      "sample": {
        "n": 337,
        "population": "indirect-calorimetry sample",
        "reference_method": "measured resting energy expenditure"
      },
      "error": {
        "note": "re-derivation of Harris–Benedict"
      },
      "verification": "primary",
      "independent_derivation": true,
      "limitations": [
        "A re-derivation of Harris–Benedict on new data (n=337), not a reissue — so it counts as a separate estimate. Still tends to run above Mifflin–St Jeor for modern populations."
      ],
      "canonical_page": "https://wimsta.com/harris-benedict-calculator/",
      "coefficients": {
        "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
        }
      },
      "sex_coding": "separate equations for men and women",
      "units": "metric"
    },
    {
      "id": "katch-mcardle",
      "name": "Katch–McArdle (Cunningham 1991)",
      "category": "bmr",
      "equation": "BMR = 370 + 21.6·LBM, where LBM = weight·(1 − bodyFat/100) (kcal/day; kg)",
      "inputs": [
        "weight",
        "bodyFat"
      ],
      "source": {
        "authors": "Cunningham (popularised by Katch & McArdle)",
        "year": 1991,
        "journal": "Am J Clin Nutr 54(6):963–969",
        "doi": "https://doi.org/10.1093/ajcn/54.6.963"
      },
      "sample": {
        "population": "synthesis of pooled body-composition data",
        "reference_method": "lean body mass vs measured RMR"
      },
      "error": {
        "note": "strong with a measured body-fat %"
      },
      "verification": "primary",
      "independent_derivation": true,
      "limitations": [
        "Uses lean body mass, so it needs a body-fat % and is only as accurate as that number. It is the Cunningham 1991 equation under a popular name — do not add Cunningham separately (same estimate)."
      ],
      "canonical_page": "https://wimsta.com/katch-mcardle-calculator/",
      "coefficients": {
        "intercept": 370,
        "leanBodyMass": 21.6
      },
      "units": "metric"
    }
  ]
}