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Body Fat Percentage Formulas

Review the legacy circumference, Relative Fat Mass, and Deurenberg body-fat equations with variables, units, worked calculations, and limitations.

How do the Body Fat Calculator formulas work?

This formula page defines the variables used by the Body Fat Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

The calculator runs three adult prediction equations. The selected method controls the headline percentage, fat mass, and lean mass. The other equations remain visible as comparisons because the formulas use different predictors and can disagree.

Variable Definitions

SymbolMeaningUnit or code
BFEstimated body-fat percentagePercent
HHeightCentimeters for circumference equations; same unit as waist for RFM
WWaist circumferenceCentimeters for circumference equations
NNeck circumferenceCentimeters
PHip circumferenceCentimeters
AAgeCompleted years
SRFMPublished RFM sex termMale 0; female 1
SBMIPublished Deurenberg sex termMale 1; female 0
MBody weightKilograms

Unit Conversions

The production engine converts U.S. inputs before applying the equations.

centimeters=inches×2.54centimeters=inches\times2.54
kilograms=pounds×0.45359237kilograms=pounds\times0.45359237
total inches=12(feet)+inchestotal\ inches=12(feet)+inches

Conversion happens before logarithms, ratios, BMI, fat mass, or lean mass are calculated.

Legacy Circumference Equations

The equations commonly called the Navy method estimate body density from height and circumferences, then convert density to body-fat percentage with the Siri relationship.

Male Equation

BFmale=4951.0324−0.19077log⁡10(W−N)+0.15456log⁡10(H)−450BF_{male}=\frac{495}{1.0324-0.19077\log_{10}(W-N)+0.15456\log_{10}(H)}-450

Waist must be greater than neck so the logarithm receives a positive value.

Female Equation

BFfemale=4951.29579−0.35004log⁡10(W+P−N)+0.221log⁡10(H)−450BF_{female}=\frac{495}{1.29579-0.35004\log_{10}(W+P-N)+0.221\log_{10}(H)}-450

Waist plus hip must be greater than neck. The hip measurement is used only in this equation.

Relative Fat Mass Formula

RFM=64−20(HW)+12SRFMRFM=64-20\left(\frac{H}{W}\right)+12S_{RFM}

RFM uses height, waist, and the published sex term. Height and waist may be in centimeters or inches as long as both use the same unit, because only their ratio appears in the equation.

The original 2018 study developed the equation with NHANES adult data and validated it against DXA estimates in a separate adult dataset. That does not make RFM a direct measurement for an individual.

BMI-Based Body-Fat Formula

BMI=M(H/100)2BMI=\frac{M}{(H/100)^2}
BF=1.2(BMI)+0.23A−10.8SBMI−5.4BF=1.2(BMI)+0.23A-10.8S_{BMI}-5.4

The adult Deurenberg equation uses BMI, age, and the published sex term. The cited study reported a standard error of estimate of 4.1 percentage points for the adult formula and noted slight overestimation in participants with obesity.

Estimated Fat Mass and Lean Mass

Fat mass=M(BF100)Fat\ mass=M\left(\frac{BF}{100}\right)
Lean mass=M−Fat massLean\ mass=M-Fat\ mass

Lean mass includes water, muscle, bone, organs, and other non-fat tissue. It is not a direct muscle-mass estimate.

Method Spread

Spread=max⁡(BFcirc,BFRFM,BFBMI)−min⁡(BFcirc,BFRFM,BFBMI)Spread=\max(BF_{circ},BF_{RFM},BF_{BMI})-\min(BF_{circ},BF_{RFM},BF_{BMI})

The spread is reported in percentage points. It describes disagreement among models for the entered measurements; it is not an error margin or confidence interval.

Worked Male Circumference Calculation

For height 177.8 cm, neck 38.1 cm, waist 91.44 cm, age 30, and weight 81.6466 kg:

BFcirc≈21.12%BF_{circ}\approx21.12\%
Circumference estimate21.12%
RFM estimate25.11%
BMI-based estimate21.69%
Estimated fat mass17.25 kg
Estimated lean mass64.40 kg
Method spread3.99 percentage points

Precision, Validation, and Limitations

  • The engine keeps unrounded values through intermediate calculations.
  • Body-fat estimates and masses are displayed to practical precision rather than implying laboratory accuracy.
  • The calculator accepts adults age 18-100 within the configured measurement ranges.
  • All three equations use binary sex terms exactly as defined by the published models.
  • The equations do not directly measure tissue or diagnose a condition.
  • An unusual result or a spread of at least 5 points triggers a recheck notice.

See the worked body-fat examples for reproducible input sets.

References

Use the Body Fat Calculator