Lean Body Mass Calculator: Boer, James, and Hume Formulas

Lean body mass is body weight minus fat mass. It is usually shortened to LBM, and “lean mass” and “lean body weight” are used for the same thing. A person who weighs 180 lb and carries 27 lb of fat has a lean body mass of 153 lb.

Lean body mass is found by subtraction, so it is everything that is not fat: skeletal muscle, bone, organs, connective tissue, and water.

Lean Body Mass vs. Muscle Mass

Lean body mass is not muscle mass. Muscle is one part of it. A 2024 review in Diabetes, Obesity and Metabolism (Neeland, Linge, and Birkenfeld) makes the point directly: lean mass includes organs, bone, fluids, and the water held in fat tissue, so a change in lean mass does not always reflect a change in muscle. That is why this page is a lean body mass calculator and not a muscle mass calculator. No formula that uses only height and weight can estimate muscle by itself.

Lean Body Mass vs. Fat-Free Mass

Lean body mass and fat-free mass are, in practice, the same number. The distinction is historical. A 2024 review in Advances in Nutrition (Heymsfield and colleagues) traces lean body mass to Albert Behnke in 1942, who described it as including a small amount of essential fat, meaning structural lipids. Fat-free mass was defined chemically, as body mass with all fat removed. The review concludes that the two have the same chemical composition and recommends the term fat-free mass.

The pharmacology literature treats them the same way. The authors of a 2005 model for lean body weight (Janmahasatian et al., Clinical Pharmacokinetics) state that fat-free mass closely approximates it. The Protocol MD FFMI calculator (fat-free mass index) works from the same quantity and divides it by height squared.

A lean body mass formula estimates lean body mass from sex, height, and weight when no body fat measurement exists. This calculator runs three of them. In each, W is weight in kilograms, H is height in centimeters, and the result is in kilograms.

The Boer Formula

The Boer formula comes from a 1984 paper by P. Boer in the American Journal of Physiology on how to normalize body fluid volumes. Its abstract reports blood volume measured in 66 healthy subjects, 38 men and 28 women, and concludes that lean body mass estimated from height and weight was a suitable index for men and women alike. It is the headline figure in this calculator when no body fat is entered.

The James Formula

The James formula comes from a 1976 report on obesity research by a joint Department of Health and Social Security and Medical Research Council group in the United Kingdom, credited to W. P. T. James and J. C. Waterlow. That report gave an estimate of body fat from BMI. Rearranged into a lean body mass equation, it is the form in the table, which the comparison by Puri and Blake (British Journal of Radiology, 2022) cites to Hallynck and colleagues in the British Journal of Clinical Pharmacology, 1981. It is the only one of the three that is not a straight line, and that is the source of its problem at a high BMI, covered below.

The Hume Formula

The Hume formula comes from a 1966 paper by R. Hume in the Journal of Clinical Pathology. Hume estimated lean body mass from total body water, measured using the antipyrine space, in 29 men and 27 women, then fitted an equation to height and weight. The fit had a multiple correlation coefficient of 0.96 in men and 0.83 in women.

The Body Fat Method

If you have a body fat percentage, no equation is needed. Lean body mass is weight multiplied by (1 − body fat percentage ÷ 100). This is the definition itself, so its only error is the error in the body fat figure. When you enter body fat above, the calculator leads with this method and shows the three equations beside it.

To calculate lean body mass by hand, convert your weight to kilograms and your height to centimeters, then run the formula for your sex. Here is every step for a man who is 5 ft 10 in and weighs 180 lb.

1. Convert to metric: 180 lb × 0.4536 = 81.65 kg. 70 in × 2.54 = 177.8 cm.
2. Boer: 0.407 × 81.65 + 0.267 × 177.8 − 19.2 = 33.23 + 47.47 − 19.2 = 61.50 kg, which is 135.6 lb.
3. James: 1.10 × 81.65 − 128 × (81.65 ÷ 177.8)² = 89.81 − 26.99 = 62.82 kg, which is 138.5 lb.
4. Hume: 0.32810 × 81.65 + 0.33929 × 177.8 − 29.5336 = 26.788 + 60.326 − 29.534 = 57.58 kg, which is 126.9 lb.
5. Body fat method, at 15% body fat: 180 × (1 − 0.15) = 153.0 lb, which is 69.4 kg.

Enter the same details above and the calculator returns the same 135.6, 138.5, and 126.9 lb, and 153.0 lb once 15% body fat is added. For a woman who is 5 ft 4 in and 150 lb, the three equations give 100.8 lb (Boer), 103.3 lb (James), and 98.8 lb (Hume).

The three formulas give different answers because each was fitted to a different small group of people, with a different way of measuring lean body mass, decades ago. For the man in the worked example they span 126.9 to 138.5 lb, a gap of 11.6 lb, from the same height and weight.

• Different samples. Hume fitted his equation to 56 people. The Puri and Blake comparison describes that cohort as 29 men aged 40 to 77 and 27 women aged 37 to 80. An equation fitted to a few dozen people carries the particulars of those people.
• Different reference methods. Hume worked from total body water. The James equation started as a body fat estimate from BMI. Neither was calibrated against a modern scan.
• Different shapes. Boer and Hume are straight lines in height and weight. James subtracts a term that grows with the square of weight.
• The same blind spot. None of the three uses age, waist size, or anything about training. Two people of the same sex, height, and weight get the same answer from all three, however different their bodies are.

That last point is why the body fat method wins whenever a body fat figure is available. In the worked example, the equations put the man at 126.9 to 138.5 lb. His measured 15% body fat puts him at 153.0 lb. The equations are describing an average man of his size, and he is leaner than that.

The James formula stops working at a high BMI. Above a BMI of about 43.0 in men and 36.1 in women, its estimate of lean body mass goes down as weight goes up. Above a BMI of about 85.9 in men and 72.3 in women, it is negative.

The reason is in the equation. Its second term subtracts 128 (men) or 148 (women) times the square of weight over height. As weight rises at a fixed height, that squared term grows faster than the first term, and eventually overtakes it. Those turning points follow directly from the coefficients.

The same thing shows in the body fat estimate the formula was built from. As tabulated by Puri and Blake, that estimate is body fat percent = 1.281 × BMI − 10.13 for men and 1.48 × BMI − 7.0 for women. A straight line in BMI has no ceiling, so at a high enough BMI it predicts more than 100% body fat, which is the same thing as a negative lean body mass.

What That Looks Like in Numbers

• A man who is 5 ft 10 in gets 164.7 lb at 300 lb and 163.9 lb at 320 lb. The formula says 20 lb of added weight removed lean mass.
• A woman who is 5 ft 0 in and 380 lb, a BMI of 74.2, gets −10.8 lb.

This limitation is documented. A 2016 letter in Radiology by U. Nyman argued that the James formula is not appropriate for determining CT contrast dose in patients with a high BMI, and Puri and Blake summarize its finding as a plateau at a BMI of 37 in women and 43 in men, followed by a decline. The Janmahasatian group’s 2005 paper opens from the same problem: the existing methods for lean body weight were inconsistent at the extremes of body size.

This calculator therefore does not show a James figure once your BMI is past the turning point for your sex, and it leaves James out of the range. The Boer and Hume figures are still shown. They are straight lines and do not turn down, but they were also fitted to small groups of people, so at a high BMI a body fat measurement is worth far more than any of the three.

Against DXA scans, the Boer, James, and Hume equations track lean body mass across a group reasonably well and can miss an individual by several kilograms. A large comparison is Puri and Blake’s 2022 study of ten equations against DXA in 747 men and 811 women, all aged 60 to 65.

The limits of agreement are the full width of the band that holds 95% of the differences between the equation and the scan. A width of 11 to 14 kg means that, for about 19 people in 20, the equation landed within roughly 6 to 7 kg of where the group’s average difference would put it. The average difference itself was 2 to 5 kg, depending on the equation and sex. In that study, none of these three was the best performer. Two newer equations, by Gallagher and by Janmahasatian, agreed with DXA more closely.

A smaller study looked at one equation alone. Carnevale and colleagues (Endocrine, 2015) compared the Hume formula with DXA in 100 people, 40 men and 60 women. The correlation for lean body mass was 0.913, the equation overestimated it by 1.36 kg on average, and the limits of agreement ran from −8.26 to 6.52 kg.

What to Take From That

Both studies have limits of their own. The larger one covered a five-year age band, so it says little about a 30-year-old. DXA is a reference method, not a perfect one. The practical reading is that an equation is a fair starting estimate for a typical body and a poor one for an unusual body: very lean, very muscular, or at a high BMI. A measured body fat percentage narrows the answer more than switching formulas does.

This lean body mass chart shows what the Boer formula returns across a range of heights, at a BMI of 22 and at a BMI of 27. It is the calculator’s own output, laid out as a table. It is not a set of targets, and there is no clinical definition of a good lean body mass.

Two patterns hold down the table, and both are properties of the formula. Its estimate rises with height. And at the same height, the heavier body gets more lean mass in pounds but a smaller share of its weight as lean mass. At 5 ft 10 in, the Boer estimate for a man is 81% of body weight at a BMI of 22 and 74% at a BMI of 27.

Lean mass falls along with fat mass during substantial weight loss, including weight loss on a GLP-1 medication. The trials that measured body composition with DXA show how much, and they show that fat made up most of the loss.

What the Trials Measured

Semaglutide, STEP 1. The STEP 1 trial (Wilding et al., New England Journal of Medicine, 2021) enrolled 1,961 adults with overweight or obesity and without diabetes. A body composition substudy, published as a conference abstract in the Journal of the Endocrine Society, scanned 140 of them with DXA at screening and at week 68: 95 on semaglutide and 45 on placebo, all with a BMI of 40 or under, 76% of them women. With semaglutide, body weight fell 15.0%, total fat mass fell 19.3%, and total lean body mass fell 9.7%. Because fat fell further, lean body mass as a share of total body mass rose by 3.0 percentage points. Body weight fell 3.6% with placebo.

Tirzepatide, SURMOUNT-1. The body composition substudy of SURMOUNT-1 (Look et al., Diabetes, Obesity and Metabolism, 2025) scanned 160 of the trial’s 2,539 participants with DXA at baseline and at week 72: 124 on tirzepatide and 36 on placebo, 73% of them women. With tirzepatide, body weight fell 21.3%, fat mass fell 33.9%, and lean mass fell 10.9%. With placebo the figures were 5.3%, 8.2%, and 2.6%. Of the weight lost, about 75% was fat and 25% was lean mass, in both groups. Six of that paper’s eight authors are employees of the drug’s manufacturer.

Across studies. Results are not uniform. The Neeland review found lean mass making up 40% to 60% of the weight lost in some trials and about 15% or less in others, and it stresses that lean mass on a scan is not only muscle.

These are averages from groups of trial participants, mostly women, measured once at the start and once at the end. They are not a forecast for any one person. Compounded semaglutide and tirzepatide are not FDA-approved, are not the same as the brand-name products, and were not studied in these trials.

Why an Equation Cannot Track It

The Boer, James, and Hume formulas cannot tell you how much lean mass you have lost. They see only height and weight. When your weight changes, the Boer formula moves its estimate by a fixed 0.407 kg per kilogram for men and 0.252 for women, whatever was actually lost. It would report the same change in lean body mass for someone who lost only fat as for someone who lost a great deal of muscle.

Tracking a change needs a measured body fat percentage at two points in time, taken the same way. With those, the body fat method on this page gives a lean body mass for each date, and the FFMI calculator (fat-free mass index) compares two measurements and splits the weight change into fat and lean mass. Our guide to muscle loss on GLP-1 medications covers why it happens and what protects muscle.

What Guidance Says About Holding On to Lean Mass

Enough protein and resistance training are the two measures current guidance names. The 2025 joint advisory on nutritional priorities to support GLP-1 therapy for obesity (Mozaffarian et al., American Journal of Clinical Nutrition) lists preserving muscle and bone through resistance training and an appropriate diet as a priority, and notes that protein targets of 1.2 to 1.6 grams per kilogram a day have been proposed during active weight reduction. The macro calculator (protein, carbs, and fat in grams) builds a day around a protein-first split, the calorie calculator (maintenance and a daily target) and the BMR calculator (your resting burn) cover the energy side, and the body recomposition calculator (calories and protein) is built for losing fat while keeping muscle. For the combined height-and-weight figure, see the BMI calculator, with its limitations spelled out.

Semaglutide and tirzepatide carry a boxed warning for thyroid C-cell tumors, based on rodent studies, and are contraindicated in anyone with a personal or family history of medullary thyroid carcinoma or multiple endocrine neoplasia syndrome type 2 (MEN 2).

Protocol MD is a physician-guided telehealth practice. A lean body mass figure is one description of body composition. Whether any treatment is appropriate depends on your history, your labs, and your goals, and only a licensed physician can make that call after reviewing them.

Protocol MD sells compounded semaglutide and compounded tirzepatide and therefore has a commercial interest in this topic. For patients a physician determines are appropriate candidates, Protocol MD prescribes compounded semaglutide or compounded tirzepatide, prepared by a licensed compounding pharmacy. Compounded medications are not FDA-approved. They are not generic equivalents of, and are not the same product as, the brand-name medications. Protocol MD serves patients in all 50 states, and your card is authorized at checkout and charged only if a physician approves your prescription.

Nothing in this calculator depends on taking a medication. Lean body mass is the same calculation for anyone, and the tool is free to use without an account.