Enter your height, weight, sex and age group. Your lean body mass (LBM) is estimated with the Boer (main), James and Hume formulas, with the Peters formula added at the top for ages 14 and under, and you can compare them on one number line.
Enter height in centimeters and weight in kilograms. The results are estimates from statistical formulas, not a medical diagnosis.
Result and graph
Enter your height, weight, sex and age group in the fields on the left and press "Calculate". The result and a graph will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and figures
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter your height (feet and inches) and weight (pounds), and your lean body mass (LBM - your weight minus the weight of body fat) is estimated with three statistical formulas at once: Boer, James and Hume
- The Boer formula, the one most used in medicine, is the main result, and a number line lets you compare the formulas. For ages 14 and under, an estimate from the Peters formula for children is added at the top
- For each formula, a table shows the lean body mass, its share of your weight (%) and the estimated body fat (%)
- No tape measure or body fat scale needed (to estimate body fat from measurements taken with a tape measure, use the related "Body Fat Calculator")
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
All three formulas were built from statistical data on adults, so they can be far off for people with a lot of muscle or with severe obesity. The results are statistical estimates, not a medical diagnosis. If you have a medical condition or are pregnant, talk to your doctor or a registered dietitian before relying on them.
What is this calculation used for?
Fitting drug doses to body build (anesthesia and more - where these formulas come from)
Formulas for estimating lean body mass were originally made for medicine. For some drugs used in anesthesia (especially drugs that dissolve easily in water and do not spread well into fat), dosing by lean body mass rather than actual body weight is considered safer. Drugs do not spread much into fat tissue, so dosing a person with obesity in proportion to total weight could give too strong an effect.
That is why the Boer and Peters formulas have been used in anesthesia research and dosing references. The most important reason these formulas exist is that lean body mass is not just a fitness term but a practical tool that supports drug safety.
Using it as a floor for checking whether a weight goal is realistic
Lean body mass is the part of your weight that is not fat, so a target weight below your estimated lean body mass would mean less than zero body fat, which is not realistic. The body also needs essential fat to stay alive, so the real lower limit is higher still. For example, if someone with an estimated lean body mass of about 115 lb aims to "just get down to 110 lb", that is a sign the plan is unrealistic.
These estimates are statistical guides based on an average adult build, so do not set a goal from them directly; use them as a rough idea of "the weight you cannot go below" to spot an unrealistic diet plan early. Height and weight formulas cannot tell whether lost weight was fat or muscle, so to track the quality of weight loss, also use a body fat scale or tape measurements (the related "Body Fat Calculator").
Fitting protein needs more closely to your build (sports nutrition)
In nutrition plans for strength training and body shaping, protein targets are sometimes set per kilogram (or pound) of lean body mass rather than per unit of total weight. It is the lean tissue, such as muscle, that actually needs protein, so this estimate is not thrown off by how much body fat you have.
For example, if someone with a lean body mass of 116 lb (about 52.6 kg) aims for 2 g per kilogram of lean mass (about 0.9 g per pound), that comes to about 105 g a day (this is only one example; the related "Protein Calculator" page covers the usual guidelines).
Estimating basal metabolic rate (Katch-McArdle formula)
The Katch-McArdle formula, one way to estimate the minimum energy the body uses in a day (basal metabolic rate), uses only lean body mass: 370 + 21.6 × lean body mass (kg). For a lean body mass of 116 lb (about 52.6 kg), that is about \(370 + 21.6 \times 52.6 \approx 1{,}506\) kcal. Lean tissue such as muscle uses most of the energy, so for people whose body fat is far from average, this is said to be closer to reality than formulas based on total weight.
Being able to estimate lean body mass also connects, through this formula, to estimating your total daily calorie burn (the related "TDEE Calculator").
Formulas and figures
Boer formula (1984, the most used in medicine)
Figure
Standard notation
(the usual math form)
\(L\)
\(=\)
\(0.407\)
\(\times\)
\(W\)
\(+\)
\(0.267\)
\(\times\)
\(H\)
\(-\)
\(19.2\)
\(L\)
\(=\)
\(0.252\)
\(\times\)
\(W\)
\(+\)
\(0.473\)
\(\times\)
\(H\)
\(-\)
\(48.3\)
In words
(symbols replaced with words)
⑥
\(L\): lean body mass (kg)
\(=\)
①
weight coefficient for men \(0.407\)
\(\times\)
②
\(W\): weight (kg)
\(+\)
③
height coefficient for men \(0.267\)
\(\times\)
④
\(H\): height (cm)
\(-\)
⑤
constant for men \(19.2\)
⑧
\(L\): lean body mass (kg)
\(=\)
⑦
weight coefficient for women \(0.252\)
\(\times\)
\(W\): weight (kg)
\(+\)
height coefficient for women \(0.473\)
\(\times\)
\(H\): height (cm)
\(-\)
constant for women \(48.3\)
The formula in words
①
Multiply the
weight coefficient for men \(0.407\)
②
by the
\(W\): weight (kg)
③
add the
height coefficient for men \(0.267\)
④
times the
\(H\): height (cm)
⑤
subtract the
constant for men \(19.2\)
⑥
and you get the
\(L\): lean body mass (kg)
⑦
Do the same calculation with the three constants for women, starting with the
weight coefficient for women \(0.252\)
(0.252, 0.473 and 48.3)
⑧
and you get the
\(L\): lean body mass (kg)
for women
Quick example
For a man who is 170 cm (about 5 ft 7 in) tall and weighs 65 kg (about 143 lb), the Boer formula gives
lean body mass (kg)
\(=\)
weight coefficient (0.407)
\(\times\)
weight (65 kg)
\(+\)
height coefficient (0.267)
\(\times\)
height (170 cm)
\(-\)
constant (19.2)
\(0.407 \times 65 + 0.267 \times 170 - 19.2 = 26.455 + 45.39 - 19.2 \approx 52.6\ \mathrm{kg}\)
Key idea
So the lean body mass is about 52.6 kg, which is about 116 lb. The Boer formula was proposed by Boer in 1984, and it is the formula most often used in medicine to estimate lean body mass, for example to calculate doses of anesthetic drugs. It is the main formula on this page.
It is a simple linear formula: "a part proportional to weight + a part proportional to height − a constant", and only the three constants differ between men and women. The constants have many digits because they come straight from a statistical analysis of measurements on many people.
The formula was published in kilograms and centimeters. When you use US units, the calculator converts it: for men, lean body mass (lb) = 0.407 × weight (lb) + 1.4951 × height (in) − 42.329, which gives about 116.0 lb for 143 lb and 67 in.
James formula (1976)
Standard notation
(the usual math form)
\(L\)
\(=\)
\(1.1\)
\(\times\)
\(W\)
\(-\)
\(128\)
\(\times\)
\(\left(\dfrac{W}{H}\right)\)
\(2\)
\(L\)
\(=\)
\(1.07\)
\(\times\)
\(W\)
\(-\)
\(148\)
\(\times\)
\(\left(\dfrac{W}{H}\right)\)
\(2\)
In words
(symbols replaced with words)
⑥
\(L\): lean body mass (kg)
\(=\)
①
weight coefficient for men \(1.1\)
\(\times\)
②
\(W\): weight (kg)
\(-\)
③
correction coefficient for men \(128\)
\(\times\)
④
weight \(W\) ÷ height \(H\)
⑤
squared
⑧
\(L\): lean body mass (kg)
\(=\)
⑦
weight coefficient for women \(1.07\)
\(\times\)
\(W\): weight (kg)
\(-\)
correction coefficient for women \(148\)
\(\times\)
weight \(W\) ÷ height \(H\)
squared
The formula in words
①
Multiply the
weight coefficient for men \(1.1\)
②
by the
\(W\): weight (kg)
③
then subtract the
correction coefficient for men \(128\)
④
times
weight \(W\) ÷ height \(H\)
⑤
squared
⑥
and you get the
\(L\): lean body mass (kg)
⑦
Do the same calculation with the two coefficients for women, starting with the
weight coefficient for women \(1.07\)
(1.07 and 148)
⑧
and you get the
\(L\): lean body mass (kg)
for women
Quick example
For the same man (170 cm, 65 kg), the James formula gives
lean body mass (kg)
\(=\)
weight coefficient (1.1)
\(\times\)
weight (65 kg)
\(-\)
correction coefficient (128)
\(\times\)
weight (65) ÷ height (170)
squared
\((65 \div 170)^{2} \approx 0.382^{2} \approx 0.146\)
\(1.1 \times 65 - 128 \times 0.146 \approx 71.5 - 18.7 = 52.8\ \mathrm{kg}\)
Key idea
The James formula comes from a 1976 report on obesity research. It starts from a part proportional to weight and subtracts a part proportional to (weight ÷ height) squared.
Weight ÷ height gets bigger the heavier you are for your height, so the correction pulls the estimate down more for heavier-built people, who are expected to carry more fat. However, with severe obesity the correction is known to go too far and stop matching reality, so when the estimate is 0 or less or more than the body weight, this calculator shows "Out of range". In US units, the calculator uses 1.1 × weight (lb) − 8.9993 × (weight (lb) ÷ height (in)) squared for men.
Hume formula (1966)
Standard notation
(the usual math form)
\(L\)
\(=\)
\(0.32810\)
\(\times\)
\(W\)
\(+\)
\(0.33929\)
\(\times\)
\(H\)
\(-\)
\(29.5336\)
\(L\)
\(=\)
\(0.29569\)
\(\times\)
\(W\)
\(+\)
\(0.41813\)
\(\times\)
\(H\)
\(-\)
\(43.2933\)
In words
(symbols replaced with words)
⑥
\(L\): lean body mass (kg)
\(=\)
①
weight coefficient for men \(0.32810\)
\(\times\)
②
\(W\): weight (kg)
\(+\)
③
height coefficient for men \(0.33929\)
\(\times\)
④
\(H\): height (cm)
\(-\)
⑤
constant for men \(29.5336\)
⑧
\(L\): lean body mass (kg)
\(=\)
⑦
weight coefficient for women \(0.29569\)
\(\times\)
\(W\): weight (kg)
\(+\)
height coefficient for women \(0.41813\)
\(\times\)
\(H\): height (cm)
\(-\)
constant for women \(43.2933\)
The formula in words
①
Multiply the
weight coefficient for men \(0.32810\)
②
by the
\(W\): weight (kg)
③
add the
height coefficient for men \(0.33929\)
④
times the
\(H\): height (cm)
⑤
subtract the
constant for men \(29.5336\)
⑥
and you get the
\(L\): lean body mass (kg)
⑦
Do the same calculation with the three constants for women, starting with the
weight coefficient for women \(0.29569\)
(0.29569, 0.41813 and 43.2933)
⑧
and you get the
\(L\): lean body mass (kg)
for women
Quick example
For the same man (170 cm, 65 kg), the Hume formula gives
lean body mass (kg)
\(=\)
weight coefficient (0.32810)
\(\times\)
weight (65 kg)
\(+\)
height coefficient (0.33929)
\(\times\)
height (170 cm)
\(-\)
constant (29.5336)
\(0.32810 \times 65 + 0.33929 \times 170 - 29.5336 \approx 21.33 + 57.68 - 29.53 \approx 49.5\ \mathrm{kg}\)
Key idea
The Hume formula, proposed by Hume in 1966, is the oldest of the three. It has the same shape as the Boer formula, "a part proportional to weight + a part proportional to height − a constant", with different constants.
It grew out of research that measured total body water and used it to find lean body mass, so that lean body mass could be estimated easily from height and weight alone. Lean body mass (muscle, organs and so on) is mostly water, so research on body water and estimates of lean body mass are closely connected. The three formulas give slightly different values because they were made in different decades from different data; no single one is "the right answer".
Peters formula (2011, for age 14 and under)
Standard notation
(the usual math form)
\(V\)
\(=\)
\(0.0215\)
\(\times\)
\(W\)
\(0.6469\)
\(\times\)
\(H\)
\(0.7236\)
\(L\)
\(=\)
\(3.8\)
\(\times\)
\(V\)
In words
(symbols replaced with words)
⑥
\(V\): estimated extracellular fluid volume (L)
\(=\)
①
constant \(0.0215\)
\(\times\)
②
\(W\): weight (kg)
③
to the power \(0.6469\)
\(\times\)
④
\(H\): height (cm)
⑤
to the power \(0.7236\)
⑧
\(L\): lean body mass (kg)
\(=\)
⑦
constant \(3.8\)
\(\times\)
\(V\): estimated extracellular fluid volume (L)
The formula in words
①
Multiply the
constant \(0.0215\)
②
by the
\(W\): weight (kg)
③
raised
to the power \(0.6469\)
④
and the
\(H\): height (cm)
⑤
raised
to the power \(0.7236\)
⑥
and you get the
\(V\): estimated extracellular fluid volume (L)
⑦
Multiply that volume by the
constant \(3.8\)
⑧
and you get the
\(L\): lean body mass (kg)
Quick example
For a boy aged 14 or under who is 150 cm (about 4 ft 11 in) tall and weighs 40 kg (about 88 lb), the Peters formula gives
estimated extracellular fluid volume (L)
\(=\)
constant (0.0215)
\(\times\)
weight (40 kg)
to the 0.6469
\(\times\)
height (150 cm)
to the 0.7236
lean body mass (kg)
\(=\)
constant (3.8)
\(\times\)
estimated extracellular fluid volume (8.78 L)
\(V = 0.0215 \times 40^{0.6469} \times 150^{0.7236} \approx 0.0215 \times 10.87 \times 37.55 \approx 8.78\)
\(L = 3.8 \times 8.78 \approx 33.4\ \mathrm{kg}\)
Key idea
So the lean body mass is about 33.4 kg, or about 74 lb. The Peters formula was proposed in 2011 by Peters and colleagues, for example to calculate drug doses for children, and it works for both boys and girls. The Boer and other two formulas were built from adult data, while this one was built from measurements on children, so this page shows its estimate at the top for ages 14 and under.
It works in two steps: first it estimates the extracellular fluid volume (the part of the body's water that is outside the cells) from height and weight, then it multiplies that by 3.8 to turn it into lean body mass. Powers with decimal exponents such as \(0.6469\) are not practical by hand, so use this calculator, Excel or the power key on a calculator.
Also keep in mind that body composition in growing children varies a lot and changes quickly. Do not judge a child's build from this number alone; if you are concerned, talk to a pediatrician or another professional.
Share of weight and estimated body fat
Figure
Standard notation
(the usual math form)
\(R\)
\(=\)
\(L\)
\(\div\)
\(W\)
\(\times\)
\(100\)
\(F\)
\(=\)
\(100\)
\(-\)
\(R\)
In words
(symbols replaced with words)
④
\(R\): share of weight (%)
\(=\)
①
\(L\): lean body mass (kg)
\(\div\)
②
\(W\): weight (kg)
\(\times\)
③
\(100\) to make a percent
⑦
\(F\): estimated body fat (%)
\(=\)
⑤
the whole, \(100\)%
\(-\)
⑥
\(R\): share of weight (%)
The formula in words
①
Divide the
\(L\): lean body mass (kg)
②
by the
\(W\): weight (kg)
③
multiply by
\(100\) to make a percent
④
and you get the
\(R\): share of weight (%)
⑤
From
the whole, \(100\)%
⑥
subtract the
\(R\): share of weight (%)
⑦
and you get the
\(F\): estimated body fat (%)
Quick example
Continuing the Boer example (weight 65 kg, lean body mass 52.6 kg)
share of weight (%)
\(=\)
lean body mass (52.6 kg)
\(\div\)
weight (65 kg)
\(\times\)
100 to make a percent
estimated body fat (%)
\(=\)
the whole, 100%
\(-\)
share of weight (81%)
\(52.6 \div 65 \times 100 \approx 81\ (\%)\)
\(100 - 81 = 19\ (\%)\)
Key idea
Body weight splits into lean body mass + the weight of body fat, so if lean body mass is 81% of your weight, the remaining 19% is fat: that is the estimated body fat percentage. The share does not depend on the units, so 116 lb out of 143 lb is also 81%. This calculator rounds the share to a whole number before subtracting it from 100.
The body fat percentage here is only worked backward from a lean body mass estimated with a statistical formula. It is found in a different way from a body fat scale or from the tape-measure method (the related "Body Fat Calculator"), so a difference of a few percent is normal.
Lean body mass (LBM) is your weight minus the weight of body fat, and it can be estimated from height and weight alone with statistical formulas. The Boer formula (the one most used in medicine) is the main one; together with the James and Hume formulas and the Peters formula for ages 14 and under, the trick is to read the results as a range, not as one correct answer.
Symbols and terms
Symbols
| \(L\) | el | The lean body mass you want to find (kg in the formulas). It is the first letter of "lean" (the related "Body Fat Calculator" uses the same symbol). |
| \(W\) | double-u | Weight (kg). It is the first letter of "weight". 1 lb = 0.45359237 kg. |
| \(H\) | aitch | Height (cm). It is the first letter of "height". Every formula on this page uses centimeters as they are (do not convert to meters). 1 in = 2.54 cm. |
| \(\left(\dfrac{W}{H}\right)^{2}\) | W over H, squared | Weight divided by height, multiplied by itself. It is used in the James formula and gets bigger the heavier you are for your height. |
| \(W^{0.6469}\) | W to the power 0.6469 | Weight raised to the power 0.6469. The exponent (the small raised number) is a decimal, which is not practical by hand, so use the power key on a calculator or "^" in Excel. It is used in the Peters formula. |
| \(V\) | vee | Estimated extracellular fluid volume (liters). It appears partway through the Peters formula and is written eECV in the research paper. It is the first letter of "volume". |
| \(R\) | ar | The share of your weight that is lean body mass (%). It is the first letter of "ratio". |
| \(F\) | ef | Estimated body fat percentage (%) - what is left after subtracting the share \(R\) from 100%. It is the first letter of "fat". |
Terms
| lean body mass | Your weight minus the weight of body fat - the total weight of everything that is not fat, such as muscle, bone, water, blood and organs. It is usually 60 to 90% of body weight and tends to be a larger share in men. |
| LBM | Short for lean body mass. Articles on training and nutrition often use this abbreviation. A closely related term is fat-free mass (FFM). |
| body fat percentage | The share of body weight that is fat (%). On this page it is worked backward from the lean body mass estimated with a statistical formula. To estimate it from measurements taken with a tape measure, use the related "Body Fat Calculator". |
| estimation formula | A formula for estimating an approximate value, built by statistically analyzing measurements from many people. Instead of measuring each person precisely, it gives an estimate from easy-to-measure values such as height and weight, so it always includes some error from individual differences. |
| Boer formula | A formula for estimating lean body mass, proposed by Boer in 1984. It is the one most used in medicine, for example to calculate doses of anesthetic drugs, and it is the main formula on this page. |
| Peters formula | A formula for estimating lean body mass, proposed in 2011 by Peters and colleagues, for example to calculate drug doses for children. It works in two steps, multiplying the estimated extracellular fluid volume (eECV) by 3.8, and it works for both boys and girls. |
| extracellular fluid volume | The volume of the body's water that is outside the cells (the liquid part of the blood and the spaces between cells). The Peters formula first estimates this from height and weight, then converts it to lean body mass. |
| body fat scale | A device that sends a weak electric current through the body to measure body fat and more (the kind built into home bathroom scales uses bioelectrical impedance). It measures in a completely different way from the statistical formulas on this page, so a difference of a few percent is normal. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Ratios and percentages (Grade 6) |
|
| Multiplying and dividing with decimals (Grades 5–6) |
|
| Substituting into expressions (Grades 6–7) |
|
| Powers and exponents (Grade 6 and up) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table for the Boer formula
| Height (in) | 67 |
| Weight (lb) | 143 |
| Sex (male = 1, female = 2) | 1 |
| Lean body mass (lb) | =IF(B3=1,0.407*B2+1.4951*B1-42.329,0.252*B2+2.6487*B1-106.48) |
Table for the James formula
| Height (in) | 67 |
| Weight (lb) | 143 |
| Sex (male = 1, female = 2) | 1 |
| Lean body mass (lb) | =IF(B3=1,1.1*B2-8.9993*(B2/B1)^2,1.07*B2-10.405*(B2/B1)^2) |
Table for the Hume formula
| Height (in) | 67 |
| Weight (lb) | 143 |
| Sex (male = 1, female = 2) | 1 |
| Lean body mass (lb) | =IF(B3=1,0.32810*B2+1.8999*B1-65.110,0.29569*B2+2.3414*B1-95.445) |
Table for the Peters formula (age 14 and under)
| Height (in) | 59 |
| Weight (lb) | 88 |
| Estimated extracellular fluid eECV (L) | =0.0215*(B2*0.45359237)^0.6469*(B1*2.54)^0.7236 |
| Lean body mass (lb) | =3.8*B3/0.45359237 |
Table for the share of weight and estimated body fat
| Lean body mass (lb) | 116.0 |
| Weight (lb) | 143 |
| Share of weight (%) | =ROUND(B1/B2*100,0) |
| Estimated body fat (%) | =100-B3 |
After pasting, the upper rows are your inputs and the formula rows are calculated automatically.
"IF(B3=1,A,B)" means "use formula A if the sex is male (1) and formula B if female (2)". "^" is the power symbol, and "ROUND(value,0)" rounds to a whole number. The first three tables use the published coefficients converted for pounds and inches (the same ones this calculator uses in US units). The Peters table converts to kilograms and centimeters inside the formula (0.45359237 kg per lb, 2.54 cm per in).
In the first table (67 in, 143 lb, male), for example, the lean body mass cell shows about 116.0. With the same inputs, the second table gives about 116.3 and the third about 109.1. The fourth table (59 in, 88 lb) gives about 73.4, and the fifth gives a share of 81% and an estimated body fat of 19%. Just replace the height, weight and sex with your own.
"IF(B3=1,A,B)" means "use formula A if the sex is male (1) and formula B if female (2)". "^" is the power symbol, and "ROUND(value,0)" rounds to a whole number. The first three tables use the published coefficients converted for pounds and inches (the same ones this calculator uses in US units). The Peters table converts to kilograms and centimeters inside the formula (0.45359237 kg per lb, 2.54 cm per in).
In the first table (67 in, 143 lb, male), for example, the lean body mass cell shows about 116.0. With the same inputs, the second table gives about 116.3 and the third about 109.1. The fourth table (59 in, 88 lb) gives about 73.4, and the fifth gives a share of 81% and an estimated body fat of 19%. Just replace the height, weight and sex with your own.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table for the Boer formula
| Height (in) | 67 |
| Weight (lb) | 143 |
| Sex (male = 1, female = 2) | 1 |
| Lean body mass (lb) | =IF(B3=1,0.407*B2+1.4951*B1-42.329,0.252*B2+2.6487*B1-106.48) |
Table for the James formula
| Height (in) | 67 |
| Weight (lb) | 143 |
| Sex (male = 1, female = 2) | 1 |
| Lean body mass (lb) | =IF(B3=1,1.1*B2-8.9993*(B2/B1)^2,1.07*B2-10.405*(B2/B1)^2) |
Table for the Hume formula
| Height (in) | 67 |
| Weight (lb) | 143 |
| Sex (male = 1, female = 2) | 1 |
| Lean body mass (lb) | =IF(B3=1,0.32810*B2+1.8999*B1-65.110,0.29569*B2+2.3414*B1-95.445) |
Table for the Peters formula (age 14 and under)
| Height (in) | 59 |
| Weight (lb) | 88 |
| Estimated extracellular fluid eECV (L) | =0.0215*(B2*0.45359237)^0.6469*(B1*2.54)^0.7236 |
| Lean body mass (lb) | =3.8*B3/0.45359237 |
Table for the share of weight and estimated body fat
| Lean body mass (lb) | 116.0 |
| Weight (lb) | 143 |
| Share of weight (%) | =ROUND(B1/B2*100,0) |
| Estimated body fat (%) | =100-B3 |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the height, weight and sex with your own.
How to calculate it in Python
from decimal import Decimal, ROUND_HALF_UP
def round_half_up(x):
# round half up to a whole number (Python's built-in round sends .5 to the nearest even number)
return int(Decimal(str(x)).quantize(Decimal("1"), rounding=ROUND_HALF_UP))
height_in = 67 # height (inches), 5 ft 7 in
weight_lb = 143 # weight (lb)
sex = "m" # sex ("m" = male, "f" = female)
is_age_14_or_under = False # True for age 14 or under (also calculates the Peters formula for children)
height_cm = height_in * 2.54 # the formulas use centimeters
weight_kg = weight_lb * 0.45359237 # and kilograms
if sex == "m":
boer = 0.407 * weight_kg + 0.267 * height_cm - 19.2 # Boer (1984)
james = 1.1 * weight_kg - 128 * (weight_kg / height_cm) ** 2 # James (1976)
hume = 0.32810 * weight_kg + 0.33929 * height_cm - 29.5336 # Hume (1966)
else:
boer = 0.252 * weight_kg + 0.473 * height_cm - 48.3
james = 1.07 * weight_kg - 148 * (weight_kg / height_cm) ** 2
hume = 0.29569 * weight_kg + 0.41813 * height_cm - 43.2933
for name, lbm_kg in [("Boer", boer), ("James", james), ("Hume", hume)]:
lbm_lb = lbm_kg / 0.45359237 # back to pounds
ratio = round_half_up(lbm_kg / weight_kg * 100) # share of weight (%)
print(f"{name}: {lbm_lb:.1f} lb ({ratio}% of weight, estimated body fat {100 - ratio}%)")
if is_age_14_or_under:
ecv = 0.0215 * weight_kg ** 0.6469 * height_cm ** 0.7236 # estimated extracellular fluid eECV (L)
peters = 3.8 * ecv # Peters (2011), kg
ratio = round_half_up(peters / weight_kg * 100)
print(f"Peters: {peters / 0.45359237:.1f} lb ({ratio}% of weight, estimated body fat {100 - ratio}%)")
Runs with the standard library only. "**" is the power symbol. Change the height, weight and sex at the top and run it. The code converts to centimeters and kilograms so that the published formulas can be used as they are, then converts the results back to pounds. For age 14 or under, set is_age_14_or_under to True to also show the Peters formula result.
How to write it in LaTeX and other math languages (copy and paste)
Boer formula (1984, the most used in medicine)
Lm = 0.407W + 0.267H − 19.2, Lf = 0.252W + 0.473H − 48.3
L_{m} = 0.407W + 0.267H - 19.2, \quad L_{f} = 0.252W + 0.473H - 48.3
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>L</mi><mi>m</mi></msub>
<mo>=</mo>
<mn>0.407</mn><mi>W</mi>
<mo>+</mo>
<mn>0.267</mn><mi>H</mi>
<mo>−</mo>
<mn>19.2</mn>
<mo>,</mo>
<msub><mi>L</mi><mi>f</mi></msub>
<mo>=</mo>
<mn>0.252</mn><mi>W</mi>
<mo>+</mo>
<mn>0.473</mn><mi>H</mi>
<mo>−</mo>
<mn>48.3</mn>
</mrow>
</math>
L_m = 0.407W + 0.267H - 19.2, L_f = 0.252W + 0.473H - 48.3
{0.407*w + 0.267*h - 19.2, 0.252*w + 0.473*h - 48.3}
Lm := 0.407*w + 0.267*h - 19.2; Lf := 0.252*w + 0.473*h - 48.3;
L_m = 0.407*w + 0.267*h - 19.2; L_f = 0.252*w + 0.473*h - 48.3;
L_m = 0.407W + 0.267H − 19.2, L_f = 0.252W + 0.473H − 48.3
James formula (1976)
Lm = 1.1W − 128(W ÷ H)², Lf = 1.07W − 148(W ÷ H)²
L_{m} = 1.1W - 128\left(\dfrac{W}{H}\right)^{2}, \quad L_{f} = 1.07W - 148\left(\dfrac{W}{H}\right)^{2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>L</mi><mi>m</mi></msub>
<mo>=</mo>
<mn>1.1</mn><mi>W</mi>
<mo>−</mo>
<mn>128</mn>
<msup>
<mrow><mo>(</mo><mfrac><mi>W</mi><mi>H</mi></mfrac><mo>)</mo></mrow>
<mn>2</mn>
</msup>
<mo>,</mo>
<msub><mi>L</mi><mi>f</mi></msub>
<mo>=</mo>
<mn>1.07</mn><mi>W</mi>
<mo>−</mo>
<mn>148</mn>
<msup>
<mrow><mo>(</mo><mfrac><mi>W</mi><mi>H</mi></mfrac><mo>)</mo></mrow>
<mn>2</mn>
</msup>
</mrow>
</math>
L_m = 1.1W - 128(W/H)^2, L_f = 1.07W - 148(W/H)^2
{1.1*w - 128*(w/h)^2, 1.07*w - 148*(w/h)^2}
Lm := 1.1*w - 128*(w/h)^2; Lf := 1.07*w - 148*(w/h)^2;
L_m = 1.1*w - 128*(w/h)^2; L_f = 1.07*w - 148*(w/h)^2;
L_m = 1.1W − 128(W/H)^2, L_f = 1.07W − 148(W/H)^2
Hume formula (1966)
Lm = 0.32810W + 0.33929H − 29.5336, Lf = 0.29569W + 0.41813H − 43.2933
L_{m} = 0.32810W + 0.33929H - 29.5336, \quad L_{f} = 0.29569W + 0.41813H - 43.2933
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>L</mi><mi>m</mi></msub>
<mo>=</mo>
<mn>0.32810</mn><mi>W</mi>
<mo>+</mo>
<mn>0.33929</mn><mi>H</mi>
<mo>−</mo>
<mn>29.5336</mn>
<mo>,</mo>
<msub><mi>L</mi><mi>f</mi></msub>
<mo>=</mo>
<mn>0.29569</mn><mi>W</mi>
<mo>+</mo>
<mn>0.41813</mn><mi>H</mi>
<mo>−</mo>
<mn>43.2933</mn>
</mrow>
</math>
L_m = 0.32810W + 0.33929H - 29.5336, L_f = 0.29569W + 0.41813H - 43.2933
{0.32810*w + 0.33929*h - 29.5336, 0.29569*w + 0.41813*h - 43.2933}
Lm := 0.32810*w + 0.33929*h - 29.5336; Lf := 0.29569*w + 0.41813*h - 43.2933;
L_m = 0.32810*w + 0.33929*h - 29.5336; L_f = 0.29569*w + 0.41813*h - 43.2933;
L_m = 0.32810W + 0.33929H − 29.5336, L_f = 0.29569W + 0.41813H − 43.2933
Peters formula (2011, for age 14 and under)
V = 0.0215 \times W^{0.6469} \times H^{0.7236}, \quad L = 3.8 \times V
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<mn>0.0215</mn>
<mo>×</mo>
<msup><mi>W</mi><mn>0.6469</mn></msup>
<mo>×</mo>
<msup><mi>H</mi><mn>0.7236</mn></msup>
<mo>,</mo>
<mi>L</mi>
<mo>=</mo>
<mn>3.8</mn>
<mo>×</mo>
<mi>V</mi>
</mrow>
</math>
V = 0.0215 xx W^(0.6469) xx H^(0.7236), L = 3.8 xx V
3.8*0.0215*w^0.6469*h^0.7236
v := 0.0215*w^0.6469*h^0.7236; L := 3.8*v;
v = 0.0215*w^0.6469*h^0.7236; L = 3.8*v;
V = 0.0215 W^0.6469 H^0.7236, L = 3.8 V
Share of weight and estimated body fat
R = L ÷ W × 100, F = 100 − R
R = \dfrac{L}{W} \times 100, \quad F = 100 - R
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>R</mi>
<mo>=</mo>
<mfrac><mi>L</mi><mi>W</mi></mfrac>
<mo>×</mo>
<mn>100</mn>
<mo>,</mo>
<mi>F</mi>
<mo>=</mo>
<mn>100</mn>
<mo>−</mo>
<mi>R</mi>
</mrow>
</math>
R = L/W xx 100, F = 100 - R
{100*l/w, 100 - 100*l/w}
R := 100*l/w; F := 100 - R;
R = 100*l/w; F = 100 - R;
R = L/W × 100, F = 100 − R
How to have ChatGPT do the calculation
You are a calculation assistant for health measures. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). For an adult man who is 5 ft 7 in (67 in) tall and weighs 143 lb, convert height to centimeters (1 in = 2.54 cm) and weight to kilograms (1 lb = 0.45359237 kg), then find the lean body mass (LBM) with each of these three formulas (height in cm, weight in kg): 1. Boer formula: 0.407 × weight + 0.267 × height − 19.2 2. James formula: 1.1 × weight − 128 × (weight ÷ height) squared 3. Hume formula: 0.32810 × weight + 0.33929 × height − 29.5336 Give each result in both kilograms and pounds. For each formula, also find the share of weight (% = lean body mass ÷ weight × 100, rounded to a whole number) and the estimated body fat (% = 100 − that share). Show the formulas you used and the numbers from the execution result. Also add a note that this is a statistical estimate, not a medical diagnosis.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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