Body Fat Percentage - Free Online Calculator | yourcalculator.app
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HomeHealth & FitnessBody Fat Percentage
Navy Method: % Fat = 86.010 × log10(Waist - Neck) - 70.041 × log10(Height) + 36.76

Body Fat Percentage

US Navy method calculation using waist, neck, hip, and height measurements.

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Formula & Mathematical Method

This calculator uses standard deterministic mathematical algorithms to process user inputs in real time. Calculations are performed client-side for maximum speed and privacy.

Reviewed by Applied Kinesiology Panel
Checked for AccuracyLast Reviewed: July 2026

Measuring Body Composition with the U.S. Navy Method

Theoretical background and practical computational guidance

Body fat percentage measures the proportion of total body mass comprised of adipose tissue versus lean body mass (muscle, bones, organs, and water).

The U.S. Navy circumference tape method estimates body fat by analyzing the ratio of neck, waist, and hip circumferences relative to height.

Ideal essential fat is 2-5% for men and 10-13% for women. Athletic body fat ranges are 6-13% for men and 14-20% for women, while healthy fitness averages are 14-17% for men and 21-24% for women.

U.S. Navy Body Fat EquationsMathematical Standard
% Fat (Men) = 86.010 × log10(Waist - Neck) - 70.041 × log10(Height) + 36.76

For women, hip measurement is included: % Fat = 163.205 × log10(Waist + Hip - Neck) - 97.684 × log10(Height) - 78.387.

Worked Calculation Walkthrough & Analytical Steps

To evaluate a typical problem using the Body Fat Percentage, identify your known baseline inputs, convert all measurements to congruent units, and apply the governing formula sequentially. Below is a structured breakdown of the computational workflow:

  1. Data Ingestion & Unit Harmonization: Enter the primary parameters into the input fields. If working with mixed metric or imperial dimensions, use the unit selector above to align scales.
  2. Intermediate Term Evaluation: The algorithm evaluates inner parentheses, rate exponents, and coefficient ratios in strict compliance with mathematical precedence.
  3. Final Transformation & Precision Rounding: The final numerical figure is determined, formatted to user-selected decimal precision, and mapped against relevant diagnostic or diagnostic thresholds.

Key Insights & Operational Tips

  • Measurements should be taken horizontally around bare skin without pulling the tape tightly enough to compress soft tissue.
  • Body fat percentage is a far superior indicator of health and athletic fitness than scale weight alone.
  • Correlates within 3-4% accuracy compared to DEXA clinical scans when measured correctly.

Frequently Asked Questions (FAQs)

Authoritative answers to common computational and formula questions

When performed carefully with a flexible measuring tape at proper anatomical landmarks, the Navy formula correlates closely (within 3–4%) with DEXA X-ray scans and hydrostatic weighing.
Athletic: 6–13% (M) / 14–20% (W); Fitness: 14–17% (M) / 21–24% (W); Acceptable: 18–24% (M) / 25–31% (W); Obese: 25%+ (M) / 32%+ (W).
Neck: below the larynx; Waist: at the navel for men, narrowest point above navel for women; Hips: widest point around buttocks for women.

Authoritative Citations & Institutional References

U.S. Navy Body Composition Assessment GuideSource: Department of the Navy
Disclaimer & Methodological Transparency Notice

Fitness Notice: Body composition estimates provide informative targets; consult a physician for clinical health assessments.

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