Lean body mass (LBM) from height, weight and sex by the Boer, James and Hume formulas, with the implied body fat percentage.
By AdminDrafted with AI writing toolsUpdated Checked examples: 4
About 56 kg of your 70 kg is lean mass by the Boer formula, leaving roughly 20 % as fat; the 3 formulas range from 52.8 to 56.5 kg.
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.
The Boer formula (1984) estimates lean body mass from weight in kilograms and height in centimeters: 0.407 × weight + 0.267 × height − 19.2 for men, or 0.252 × weight + 0.473 × height − 48.3 for women. A man who weighs 70 kg at 175 cm: 28.49 + 46.725 − 19.2 = 56.0 kg.
Lean body mass is everything that is not fat: muscle, bone, organs, skin, blood and body water. The rest of his weight, 14.0 kg, is the fat the formula implies.
Three published regression formulas estimate lean mass from height and weight. With W in kilograms and H in centimeters:
For the same man, James gives 1.1 × 70 − 128 × (70 ÷ 175)² = 77 − 20.48 = 56.5 kg, and Hume 52.8 kg. A woman of 60 kg and 165 cm gets 44.9 kg from Boer, 44.6 kg from James and 43.4 kg from Hume.
Boer's study developed his equation as an index for normalizing body-fluid volumes in healthy subjects. Hume's 1966 paper fitted separate linear equations for men and women.
All three are fitted to groups, so they assume average body composition for a given height and weight. They cannot see unusual muscle or fat.
Subtracting lean mass from weight gives the fat mass the formula implies: body fat % = (weight − lean mass) ÷ weight × 100. For the man above, (70 − 56.015) ÷ 70 = 20.0 %.
The female example is the 60 kg, 165 cm woman. The high-weight example is the same 175 cm man at 150 kg. All three rows use Boer:
| Scenario | Boer lean mass (kg) | Implied body fat (%) |
|---|---|---|
| Default | 56.0 | 20.0 |
| Female example | 44.9 | 25.2 |
| High weight | 88.6 | 41.0 |
The James formula has a squared weight term that grows faster than its linear term, so the estimate rises, peaks and then falls as weight goes up. For men the peak sits at 1.1 × H² ÷ 256 kg, and for women at 1.07 × H² ÷ 296 kg.
At 175 cm a man's James estimate peaks at 131.6 kg of body weight, where it reaches its ceiling of 72.4 kg of lean mass. Every heavier man of that height gets less.
At 150 kg the same man gets 71.0 kg from James against 88.6 kg from Boer and 79.1 kg from Hume. Green and Duffull (2002) cautioned against using the James formula as a size descriptor for obese patients.
For a clinical dosing decision, the treating team decides which weight measure applies.
Checked against: 0.407·70 + 0.267·175 − 19.2; 1.1·70 − 128·(70/175)²; 0.32810·70 + 0.33929·175 − 29.5336
Checked against: 0.252·60 + 0.473·165 − 48.3; 1.07·60 − 148·(60/165)²; 0.29569·60 + 0.41813·165 − 43.2933
Checked against: decimal; James peaks at 1.1·175²/256 = 131.6 kg and declines beyond it (Green & Duffull 2002)
Checked against: After 180 lb = 81.6466 kg and 70 in = 177.8 cm
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.
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.
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.
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.
For information only, not medical advice. These formulas describe populations, not you; talk to a clinician before acting on a result.
This calculator includes 4 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.