health calculator

3D Body Composition Calculator

Estimate body fat, lean mass, skeletal muscle mass, and fat-free mass index (FFMI).

Formula Verified by Dr. Sarah Jenkins, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Biological Sex

Measurement Unit

Age (years)

Calculation Method

Height (feet)

Height (inches)

Weight (lbs)lb

Neck Circumference (in)in

Waist (in)in

Forearm (in)in

Thigh (in)in

Calf (in)in

Results

Estimated Body Fat

18.0%

Lean Body Mass (LBM)139.5 lb

Skeletal Muscle Mass (SMM)76.1 lb

Fat-Free Mass Index (FFMI)20.6

Normalized FFMI20.9

Bookmark this Body Composition Calculator

Save this page to track your muscle gains, fat loss, and skeletal muscle indicators over time.

Formula

US Navy Body Fat Equations

BF% (Male) = 86.010 × log10(waist - neck) - 70.041 × log10(height) + 36.76
BF% (Female) = 163.205 × log10(waist + hip - neck) - 97.684 × log10(height) - 78.387

Calculates body fat percentage based on circumferences. Values are converted to inches before processing in the formula.

Step by step

How the calculation works

1Select your measurement method: tape measure (US Navy) or skinfold calipers.
2Input your age, gender, height, and weight.
3Provide body circumferences (neck, waist, and hip) or the caliper skinfold measurements in millimeters.
4The calculator will compute your body fat, deduce lean body mass, and run the Lee equation to calculate skeletal muscle mass.

Example

Example Body Composition Profile

A 30-year-old male measuring 5ft 9in, weighing 170 lbs with a 15-inch neck and 34-inch waist has an estimated body fat of 15.6%, LBM of 143.5 lbs, SMM of 78.9 lbs, and a Normalized FFMI of 21.2 (above average muscularity).

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How to understand and use this calculator

Understanding Body Composition vs. Simple Body Weight

Standard body weight offers a highly incomplete picture of overall health and fitness. By analyzing body composition, we segment total mass into fat mass and lean tissues. A premium BMI calculator or ideal weight calculator provides basic height-to-weight ratios, but a complete body composition analysis distinguishes between fat-free mass and adiposity.

Body Fat Percentage: The portion of total weight composed of adipose tissue. High body fat is linked to metabolic syndrome, while excessively low body fat compromises hormonal health.

Lean Body Mass (LBM): Everything in the body that is not fat—including bone, organs, skin, water, and skeletal muscle. Tracking LBM helps prevent sarcopenia during a caloric deficit.

Skeletal Muscle Mass (SMM): The specific subset of LBM that comprises voluntary muscle fibers. This tissue is highly plastic and responds directly to resistance training.

By understanding these partitions, you can design target plans using our calorie calculator, macro calculator, and workout planner to maintain muscle while shedding fat.

The Mathematical Models: US Navy Circumference vs. Jackson-Pollock Skinfolds

This tool implements two primary mathematical approaches for estimating body density and fat percentage:

1. US Navy Circumference Method: An anthropometric model using waist, neck, and hip circumferences relative to height. The formulas are:

For Males:

$$\text{BF\%} = 86.010 \times \log_{10}(\text{waist} - \text{neck}) - 70.041 \times \log_{10}(\text{height}) + 36.76$$

For Females:

$$\text{BF\%} = 163.205 \times \log_{10}(\text{waist} + \text{hip} - \text{neck}) - 97.684 \times \log_{10}(\text{height}) - 78.387$$

*(Note: All measurements are in inches for the core formula)*. This method is highly accessible as it only requires a standard tape measure.

2. Jackson-Pollock 3-Site Skinfold Method: A caliper-based model estimating body density ($BD$) from localized subcutaneous fat deposits. The sites differ by sex:

* Males (Chest, Abdomen, Thigh):

$$BD = 1.10938 - 0.0008267(S) + 0.0000016(S^2) - 0.0002574(\text{age})$$

* Females (Triceps, Suprailiac, Thigh):

$$BD = 1.0994921 - 0.0009929(S) + 0.0000023(S^2) - 0.0001392(\text{age})$$

Where $S$ is the sum of the three skinfolds in millimeters. Body fat is then derived using the Siri Equation:

$$\text{BF\%} = \left( \frac{4.95}{BD} - 4.50 \right) \times 100$$

Skeletal Muscle Mass & Fat-Free Mass Index (FFMI)

Lean body mass includes organs and water, so it does not equal muscle. To calculate Skeletal Muscle Mass (SMM), we employ anthropometric adjustments based on corrected limb girths (calf, forearm, and thigh) that reflect local muscular hypertrophy.

Fat-Free Mass Index (FFMI) normalizes lean mass to height to evaluate muscular potential, akin to BMI but focused on lean tissue. The formula is:

$$\text{FFMI} = \frac{\text{LBM (kg)}}{\text{Height (m)}^2}$$

Because taller individuals naturally carry more muscle, we apply a height normalization:

$$\text{Normalized FFMI} = \text{FFMI} + 6.1 \times (1.8 - \text{Height (m)})$$

An FFMI of 18–20 is typical for average males, 22–25 represents high muscularity in natural athletes, and values above 25 frequently indicate chemical assistance, though rare outliers exist naturally. For women, baseline values are lower, with 15–17 being average and 20–22 representing elite athletic development.

Frequently Asked Questions

What is the difference between body fat and lean body mass?+

Body fat is the actual weight of adipose tissue. Lean body mass (LBM) is everything else, including bones, blood, organs, water, and skeletal muscle.

What is a good FFMI score?+

For natural males, 18-20 is average, 21-22 is excellent, and 23-25 represents the upper limits of natural muscular potential. For females, average is 15-17, and elite is 20-22.

How accurate is the US Navy Circumference method?+

It is typically accurate within 3-4% of hydrostatic weighing or DEXA scans, provided measurements are taken consistently at the correct landmarks.

How is Skeletal Muscle Mass (SMM) calculated?+

We use an anthropometric adjustment model that applies limb girths (forearm, thigh, calf) to LBM, reflecting changes in voluntary skeletal muscle relative to baseline skeletal structure.

Why does height affect FFMI?+

Taller people naturally carry more muscle due to longer skeletal structures. The Normalized FFMI adjusts the raw score to a standard height benchmark of 1.8 meters (5ft 11in).

Should I use skinfold calipers or a tape measure?+

Skinfold calipers are more accurate for lean individuals if measured by an experienced practitioner. Tape measurements are easier to do consistently by oneself.

What is the Siri equation?+

The Siri equation is a standard formula that converts body density (BD) obtained from skinfolds or underwater weighing into body fat percentage: BF% = (4.95 / BD - 4.50) * 100.

Can I use this calculator to reverse diet?+

Yes, tracking lean mass alongside daily energy output is standard for body recomposition and reversing caloric restriction.

How often should I measure my body composition?+

Measuring once every 2 to 4 weeks is ideal. Lean mass and fat distribution changes take time, and daily fluctuations in hydration can skew results.

How does hydration affect body composition measurements?+

Hydration changes limb circumferences and body weight. Ensure you take measurements first thing in the morning, fasted, and after using the restroom to maintain consistency.

How the calculation works

1Select your measurement method: tape measure (US Navy) or skinfold calipers.

2Input your age, gender, height, and weight.

3Provide body circumferences (neck, waist, and hip) or the caliper skinfold measurements in millimeters.

4The calculator will compute your body fat, deduce lean body mass, and run the Lee equation to calculate skeletal muscle mass.

How to understand and use this calculator

Understanding Body Composition vs. Simple Body Weight

Body Fat Percentage: The portion of total weight composed of adipose tissue. High body fat is linked to metabolic syndrome, while excessively low body fat compromises hormonal health.

Lean Body Mass (LBM): Everything in the body that is not fat—including bone, organs, skin, water, and skeletal muscle. Tracking LBM helps prevent sarcopenia during a caloric deficit.

Skeletal Muscle Mass (SMM): The specific subset of LBM that comprises voluntary muscle fibers. This tissue is highly plastic and responds directly to resistance training.

By understanding these partitions, you can design target plans using our calorie calculator, macro calculator, and workout planner to maintain muscle while shedding fat.

The Mathematical Models: US Navy Circumference vs. Jackson-Pollock Skinfolds

This tool implements two primary mathematical approaches for estimating body density and fat percentage:

1. US Navy Circumference Method: An anthropometric model using waist, neck, and hip circumferences relative to height. The formulas are:

For Males:

$$\text{BF\%} = 86.010 \times \log_{10}(\text{waist} - \text{neck}) - 70.041 \times \log_{10}(\text{height}) + 36.76$$

For Females:

$$\text{BF\%} = 163.205 \times \log_{10}(\text{waist} + \text{hip} - \text{neck}) - 97.684 \times \log_{10}(\text{height}) - 78.387$$

*(Note: All measurements are in inches for the core formula)*. This method is highly accessible as it only requires a standard tape measure.

2. Jackson-Pollock 3-Site Skinfold Method: A caliper-based model estimating body density ($BD$) from localized subcutaneous fat deposits. The sites differ by sex:

* Males (Chest, Abdomen, Thigh):

$$BD = 1.10938 - 0.0008267(S) + 0.0000016(S^2) - 0.0002574(\text{age})$$

* Females (Triceps, Suprailiac, Thigh):

$$BD = 1.0994921 - 0.0009929(S) + 0.0000023(S^2) - 0.0001392(\text{age})$$

Where $S$ is the sum of the three skinfolds in millimeters. Body fat is then derived using the Siri Equation:

$$\text{BF\%} = \left( \frac{4.95}{BD} - 4.50 \right) \times 100$$

Skeletal Muscle Mass & Fat-Free Mass Index (FFMI)

Fat-Free Mass Index (FFMI) normalizes lean mass to height to evaluate muscular potential, akin to BMI but focused on lean tissue. The formula is:

$$\text{FFMI} = \frac{\text{LBM (kg)}}{\text{Height (m)}^2}$$

Because taller individuals naturally carry more muscle, we apply a height normalization:

$$\text{Normalized FFMI} = \text{FFMI} + 6.1 \times (1.8 - \text{Height (m)})$$

Frequently Asked Questions

What is the difference between body fat and lean body mass?+

Body fat is the actual weight of adipose tissue. Lean body mass (LBM) is everything else, including bones, blood, organs, water, and skeletal muscle.

What is a good FFMI score?+

For natural males, 18-20 is average, 21-22 is excellent, and 23-25 represents the upper limits of natural muscular potential. For females, average is 15-17, and elite is 20-22.

How accurate is the US Navy Circumference method?+

It is typically accurate within 3-4% of hydrostatic weighing or DEXA scans, provided measurements are taken consistently at the correct landmarks.

How is Skeletal Muscle Mass (SMM) calculated?+

We use an anthropometric adjustment model that applies limb girths (forearm, thigh, calf) to LBM, reflecting changes in voluntary skeletal muscle relative to baseline skeletal structure.

Why does height affect FFMI?+

Taller people naturally carry more muscle due to longer skeletal structures. The Normalized FFMI adjusts the raw score to a standard height benchmark of 1.8 meters (5ft 11in).

Should I use skinfold calipers or a tape measure?+

Skinfold calipers are more accurate for lean individuals if measured by an experienced practitioner. Tape measurements are easier to do consistently by oneself.

What is the Siri equation?+

The Siri equation is a standard formula that converts body density (BD) obtained from skinfolds or underwater weighing into body fat percentage: BF% = (4.95 / BD - 4.50) * 100.

Can I use this calculator to reverse diet?+

Yes, tracking lean mass alongside daily energy output is standard for body recomposition and reversing caloric restriction.

How often should I measure my body composition?+

Measuring once every 2 to 4 weeks is ideal. Lean mass and fat distribution changes take time, and daily fluctuations in hydration can skew results.

How does hydration affect body composition measurements?+

Hydration changes limb circumferences and body weight. Ensure you take measurements first thing in the morning, fasted, and after using the restroom to maintain consistency.

3D Body Composition Calculator

Inputs

Results

Bookmark this Body Composition Calculator

US Navy Body Fat Equations

How the calculation works

Example Body Composition Profile

Learn more about this calculation

BMI Calculation Guide: Formula, Ranges, and Limits

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

BMI Calculator

Body Fat Calculator

Ideal Weight Calculator

Workout Planner

3D Body Composition Calculator

Inputs

Results

Bookmark this Body Composition Calculator

Key output metrics

Body composition distribution

Muscle mass context

How to understand and use this calculator

Understanding Body Composition vs. Simple Body Weight

The Mathematical Models: US Navy Circumference vs. Jackson-Pollock Skinfolds

Skeletal Muscle Mass & Fat-Free Mass Index (FFMI)

Frequently Asked Questions

US Navy Body Fat Equations

How the calculation works

Example Body Composition Profile

Learn more about this calculation

BMI Calculation Guide: Formula, Ranges, and Limits

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

BMI Calculator

Body Fat Calculator

Ideal Weight Calculator

Workout Planner

Key output metrics

Body composition distribution

Muscle mass context

How to understand and use this calculator

Understanding Body Composition vs. Simple Body Weight

The Mathematical Models: US Navy Circumference vs. Jackson-Pollock Skinfolds

Skeletal Muscle Mass & Fat-Free Mass Index (FFMI)

Frequently Asked Questions