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FREETOOLS LABS

FreeTools Labs Glossary

Body metrics and body fat

Explore different body-metrics models and learn why their inputs and methods can produce different estimates.

Relevant tool

Body Metrics Calculator

Estimate body fat, FFM, FFMI, WHtR, resting energy and reference weight.

Open Body Metrics Calculator →

The Body Metrics Calculator compares equation-based body-fat estimates, derives related mathematical measures and shows resting-energy and reference-weight equations. It uses the entered measurements and chosen equation; it is neither a direct body-composition measurement nor a medical assessment.

Inputs, units and the selected body-fat estimate

The calculator needs age, the sex category used by the equations, height and weight. Age must be an integer of at least 18; height and weight must be positive. Metric entries use cm and kg, while imperial entries use ft/in and lb. The service normalises imperial measurements with 1 in = 2.54 cm and 1 lb = 0.45359237 kg before most equations run.

Available estimates are RFM, Deurenberg, Hodgdon-Beckett and a manually entered body-fat value. Comparison values appear only when their required measurements were entered, and the tool does not average them. Fat mass, fat-free mass, FFMI and Katch-McArdle use only the valid selected estimate.

RFM, Deurenberg and Hodgdon-Beckett are equation estimates, not direct measurements. A manual value is merely reused as supplied; its quality depends on the external measurement.

Four separate body-fat models

RFM – Relative Fat Mass

RFM = 64 − 20 × height / waist + (12 for FEMALE, otherwise 0)

RFM uses height and waist in the same length unit and the formula sex category; the project documents it as an adult estimate for the studied US population. A positive waist is required.

Deurenberg

BF% = 1.2 × BMI + 0.23 × age − (10.8 for MALE, otherwise 0) − 5.4

Deurenberg uses BMI, age and formula sex. BMI is calculated from kg and metres only as an intermediate value: this tool provides neither BMI classification nor Real-BMI categories.

Hodgdon-Beckett, MALE

BF% = 86.01 × log10(abdomen − neck) − 70.041 × log10(height) + 36.76

Hodgdon-Beckett, FEMALE

BF% = 163.205 × log10(waist + hip − neck) − 97.684 × log10(height) − 78.387

For Hodgdon-Beckett the service converts all measurements to inches before logarithms. MALE needs positive waist/abdomen and neck values; FEMALE also needs a positive hip value and all logarithm arguments must be positive. These historical anthropometric equations are not presented as a current military fitness test.

Manual body-fat value

BF% = entered value, with 0 < BF% < 100

Values derived from a valid selected estimate

Fat mass

fat mass kg = body weight kg × BF% / 100

Fat-free mass (FFM)

FFM kg = body weight kg − fat mass kg

FFMI

FFMI = FFM kg / (height in m)²

WHtR

WHtR = waist / height

An estimate at or outside 0–100% is marked outside the estimation range and produces no fat mass, FFM, FFMI or Katch-McArdle result. A positive waist separately enables WHtR. FFM is not muscle mass: it also includes water, bone and organs. The tool assigns no risk light, universal category or diagnosis to WHtR or FFMI.

Example 1: RFM and derived values

For age 30, MALE, 180 cm, 80 kg and a 90 cm waist with RFM selected, the service calculates RFM = 64 − 20 × 180 / 90 = 24%. That is the selected estimate, not a measurement.

It then returns 19.2 kg fat mass, 60.8 kg FFM, FFMI = 60.8 / 1.8² = 18.765432… kg/m² and WHtR = 90 / 180 = 0.5. Display formatting uses at most two decimals for body fat, fat mass and FFM and three for FFMI and WHtR; there is no intermediate rounding.

Estimated resting energy and equation-based reference weights

Mifflin-St Jeor

MALE: 10W + 6.25H − 5A + 5; FEMALE: 10W + 6.25H − 5A − 161

Revised Harris-Benedict

MALE: 88.362 + 13.397W + 4.799H − 5.677A; FEMALE: 447.593 + 9.247W + 3.098H − 4.330A

Katch-McArdle

370 + 21.6 × FFM kg

W is kg, H is cm and A is years. Mifflin-St Jeor and Revised Harris-Benedict use the basic inputs; Katch-McArdle appears only with valid FFM and identifies whether that FFM is estimated or manual. All are estimated kcal/day, not total energy needs, PAL or calorie targets.

Devine and Robinson

their respective base + step per inch above 60 in

Lemmens

22 × (height in m)²

Devine uses 50 kg (MALE) or 45.5 kg (FEMALE) plus 2.3 kg per inch above 60 in; Robinson uses 52/49 kg plus 1.9/1.7 kg. Both return no value below 152.4 cm. Lemmens is sex-neutral. These are equation-based references, not personal target weights or health advice.

Example 2: female Hodgdon-Beckett branch

For age 30, FEMALE, 165 cm, 65 kg, waist 75 cm, neck 32 cm and hip 98 cm with Hodgdon-Beckett selected, the service first converts lengths to 64.960629…, 29.527559…, 12.598425… and 38.582677… inches. The female equation returns BF% = 29.23849372767515…%.

It derives 19.005020922988848… kg fat mass and 45.99497907701115… kg FFM; the page displays 29.24%, 19.01 kg and 45.99 kg. The other estimates are neither averaged nor used as corrections.

Model limits and display

No model is shown as a gold standard. Missing measurements create no substitutes; invalid logarithm domains block Hodgdon-Beckett, and Devine/Robinson are not extrapolated below their documented height range. The page formats only at the end: at most two decimals for body fat, fat mass, FFM, BMI and reference weights; three for FFMI and WHtR; whole kcal/day for resting energy.

The calculator performs no direct body-fat measurement, indirect calorimetry or medical assessment. It contains no diagnosis, treatment, nutrition or weight-loss recommendation. An equation estimate cannot replace measured body composition or individually measured resting energy.

Sources and foundations

  • Relative Fat Mass as a new estimator of whole-body fat percentage — Woolcott O, Bergman R · Scientific Reports (2018), PMID 30030479

    Project source for RFM; no project URL is stored.

  • Body mass index as a measure of body fatness — Deurenberg P, Weststrate JA, Seidell JC · British Journal of Nutrition (1991), PMID 2043597 (External link)

    Project source for the adult Deurenberg equation.

  • NHRC 84-11 und 84-29; Development of the DoD Body Composition Estimation Equations — Hodgdon JA, Beckett MB (1984); Hodgdon/Friedl (1999), ADA370158

    Project source for circumference equations and their historical measurement context; no project URL is stored.

  • A new predictive equation for resting energy expenditure in healthy individuals — Mifflin MD et al. · AJCN (1990), PMID 2305711

    Project source for Mifflin-St Jeor; no project URL is stored.

  • The Harris Benedict equation reevaluated — Roza AM, Shizgal HM · AJCN (1984), PMID 6741850

    Project source for Revised Harris-Benedict; no project URL is stored.

  • Exercise Physiology: Nutrition, Energy, and Human Performance — McArdle WD, Katch FI, Katch VL

    Project source for the FFM equation labelled Katch-McArdle; no project URL is stored.

  • Gentamicin therapy — Devine BJ · Drug Intelligence & Clinical Pharmacy (1974)

    Project source for the historical Devine reference equation; no project URL is stored.

  • Determination of ideal body weight for drug dosage calculations — Robinson JD et al. · AJHP (1983), PMID 6869387

    Project source for the historical Robinson reference equation; no project URL is stored.

  • Estimating ideal body weight—a new formula — Lemmens HJM et al. · Obesity Surgery (2005), PMID 16105412

    Project source for the Lemmens reference equation; no project URL is stored.