Body Fat Formula

Health Formula • Published on September 01, 2026 • Last updated September 01, 2026

Mathematical Equation

$$\begin{aligned} \text{Male Body Fat \%} &= \frac{495}{1.0324 - 0.19077\log_{10}(\text{Waist}-\text{Neck}) + 0.15456\log_{10}(\text{Height})} - 450 \\ \text{Female Body Fat \%} &= \frac{495}{1.29579 - 0.35004\log_{10}(\text{Waist}+\text{Hip}-\text{Neck}) + 0.22100\log_{10}(\text{Height})} - 450 \end{aligned}$$

Variable Definitions

Waist

Waist circumference in cm, measured at the navel

Neck

Neck circumference in cm, measured below the larynx

Hip

Hip circumference in cm at the widest point (women only)

Height

Standing height in cm

Detailed Explanation

In-Depth Guide

The U.S. Navy Method estimates body fat percentage from simple circumference measurements rather than calipers or DEXA scans, using a regression formula developed by Hodgdon & Beckett that predicts body density from waist, neck, hip (for women), and height, then converts that density to a body fat percentage using the Siri equation (the 495/D − 450 term).

How to Calculate: Step-by-Step

1. Measure Neck circumference (below the larynx), Waist circumference (at the navel), and — for women — Hip circumference (at the widest point). 2. Take the appropriate gender formula and compute the density index using log base-10 of the circumference differences/sums and height. 3. Divide 495 by the density index, then subtract 450 to get Body Fat%. 4. Result is clamped between 2% and 60% as a sanity bound.

Worked Calculation Example

Male, Height = 175 cm, Neck = 38 cm, Waist = 90 cm: - Density index = 1.0324 − 0.19077×log10(90−38) + 0.15456×log10(175) - log10(52) ≈ 1.716, log10(175) ≈ 2.243 - Density index ≈ 1.0324 − (0.19077×1.716) + (0.15456×2.243) ≈ 1.0324 − 0.3274 + 0.3467 ≈ 1.0517 - BF% = 495/1.0517 − 450 ≈ 470.6 − 450 = 20.6%

Common Use Cases

Estimating body fat percentage without special equipment like calipers or DEXA
Tracking body composition changes over time using consistent tape-measure inputs
Getting a body composition estimate to complement BMI, which cannot distinguish fat from muscle

Frequently Asked Questions

The Navy circumference method typically has a margin of error of around 3-4% body fat compared to gold-standard methods like DEXA, making it a reasonably good field estimate but not a clinical-grade measurement.

Neck circumference correlates with upper-body fat distribution and helps the regression normalize for frame size, improving accuracy compared to using waist circumference alone.

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