# Lean body mass calculator

> Lean body mass (LBM) from height, weight and sex by the Boer, James and Hume formulas, with the implied body fat percentage.

Interactive version: https://www.calcopenly.com/health/lean-body-mass-calculator
Subject: Health and fitness calculators

Lean body mass (LBM) is body weight minus fat: muscle, bone, organs, skin and body water. It is estimated here from height, weight and sex with three regression formulas, Boer (1984), James (1976) and Hume (1966). Subtracting the Boer estimate from your weight gives an implied body fat percentage.

Clinicians use LBM to scale some drug doses and fluid volumes, and the Katch-McArdle equation uses it to estimate resting energy needs. For a man weighing 70 kg at 175 cm the three formulas give 52.8 to 56.5 kg, and Boer's 56.0 kg implies about 20 % body fat.

The formulas assume average body composition for a given height and weight, so they cannot see unusual muscle or fat. The James formula peaks and then falls as weight rises, which underestimates lean mass in obesity (Green and Duffull, 2002). A tape or skinfold measurement adds information about your own build.

## Inputs

- **Sex (for the formula)** (options: Male, Female)
- **Weight**
- **Height**: Accepts 5'11" or 5 ft 11 in

## Results

- Lean body mass (Boer) (kg) — main result
- James (kg)
- Hume (kg)
- Implied body fat (Boer)

## Formula

$$
\begin{aligned}\text{Boer (M)} &= 0.407w + 0.267h - 19.2 & \text{(F)} &= 0.252w + 0.473h - 48.3\\ \text{James (M)} &= 1.1w - 128\left(\tfrac{w}{h}\right)^2 & \text{(F)} &= 1.07w - 148\left(\tfrac{w}{h}\right)^2\\ \text{Hume (M)} &= 0.32810w + 0.33929h - 29.5336 & \text{(F)} &= 0.29569w + 0.41813h - 43.2933\end{aligned}
$$

## Worked examples

### Man, 70 kg, 175 cm

- Sex (for the formula): Male
- Weight: 70 kg
- Height: 175 cm
- **Lean body mass (Boer): 56.0 kg**
- **James: 56.5 kg**
- **Hume: 52.8 kg**
- **Implied body fat (Boer): 20.0%**
- Checked against: Python 3.8 decimal: 0.407·70 + 0.267·175 − 19.2; 1.1·70 − 128·(70/175)²; 0.32810·70 + 0.33929·175 − 29.5336

### Woman, 60 kg, 165 cm

- Sex (for the formula): Female
- Weight: 60 kg
- Height: 165 cm
- **Lean body mass (Boer): 44.9 kg**
- **James: 44.6 kg**
- **Hume: 43.4 kg**
- **Implied body fat (Boer): 25.2%**
- Checked against: Python 3.8 decimal: 0.252·60 + 0.473·165 − 48.3; 1.07·60 − 148·(60/165)²; 0.29569·60 + 0.41813·165 − 43.2933

### Obesity: James falls below the others

- Sex (for the formula): Male
- Weight: 150 kg
- Height: 175 cm
- **Lean body mass (Boer): 88.6 kg**
- **James: 71.0 kg**
- **Hume: 79.1 kg**
- Checked against: Python 3.8 decimal; James peaks at 1.1·175²/256 = 131.6 kg and declines beyond it (Green & Duffull 2002)

### Imperial: 180 lb, 5 ft 10 in woman

- Sex (for the formula): Female
- Weight: 180 lb
- Height: 70 in
- **Lean body mass (Boer): 56.4 kg**
- **James: 56.2 kg**
- **Hume: 55.2 kg**
- Checked against: Python 3.8 decimal after 180 lb = 81.6466 kg and 70 in = 177.8 cm

## Questions

### Is lean body mass the same as muscle mass?

No. Lean body mass is everything that is not fat: muscle, bone, organs, skin, blood and body water. Skeletal muscle is the largest part but not all of it. In an MRI study of 468 adults, Janssen and colleagues (2000) measured skeletal muscle at 38.4 % of body weight in men and 30.6 % in women, while a man with 20 % body fat has lean mass equal to 80 % of his weight.

### How is lean body mass calculated from height and weight?

With a regression formula fitted to measured body composition. Boer's is 0.407 × weight + 0.267 × height − 19.2 for men and 0.252 × weight + 0.473 × height − 48.3 for women, with weight in kg and height in cm. For a 60 kg woman 165 cm tall that gives 44.9 kg, which implies 25.2 % body fat, in the ACE average range for women.

### Why does the James formula give low values for heavy people?

Its squared term, 128 × (weight ÷ height)² for men, grows faster than the 1.1 × weight term, so estimated lean mass peaks and then falls as weight rises. At 175 cm the peak for men is at 131.6 kg, and a 150 kg man gets 71.0 kg against Boer's 88.6 kg. Green and Duffull (2002) cautioned against using it as a size descriptor for obese patients.

### What is a normal lean body mass percentage?

It is 100 % minus body fat percentage. The American Council on Exercise's average body fat ranges, 18–24 % for men and 25–31 % for women, correspond to lean mass of 76–82 % and 69–75 % of body weight. Athletes sit higher: ACE's athlete ranges of 6–13 % and 14–20 % fat mean 87–94 % and 80–86 % lean mass.

### How accurate is the lean body mass calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 4 worked examples whose answers come from independent sources; for example, “Man, 70 kg, 175 cm” is checked against Python 3.8 decimal: 0.407·70 + 0.267·175 − 19.2; 1.1·70 − 128·(70/175)²; 0.32810·70 + 0.33929·175 − 29.5336.

### Where does the method come from?

Boer P. Estimated lean body mass as an index for normalization of body fluid volumes in humans. Am J Physiol 1984;247:F632–F636; James WPT. Research on obesity. London: HMSO, 1976 (DHSS/MRC Group report); Hume R. Prediction of lean body mass from height and weight. J Clin Pathol 1966;19:389–391; Green B, Duffull SB. Caution when lean body weight is used as a size descriptor for obese subjects. Clin Pharmacol Ther 2002;72:743–744.

## Sources

- Boer P. Estimated lean body mass as an index for normalization of body fluid volumes in humans. Am J Physiol 1984;247:F632–F636
- James WPT. Research on obesity. London: HMSO, 1976 (DHSS/MRC Group report)
- [Hume R. Prediction of lean body mass from height and weight. J Clin Pathol 1966;19:389–391](https://jcp.bmj.com/content/19/4/389)
- Green B, Duffull SB. Caution when lean body weight is used as a size descriptor for obese subjects. Clin Pharmacol Ther 2002;72:743–744

_Note: medical information, not professional advice._