Lean body mass formulas compared: Boer, James and Hume

Three equations from three different projects

Boer published his in 1984 to normalise body-fluid volumes, not to assess athletes, and it is the most widely cited of the three in clinical dosing references. James's comes from a 1976 DHSS/MRC government report rather than a journal, which is why this site verifies its coefficients against their reproduction in a 2022 British Journal of Radiology comparison of ten lean-mass equations rather than against the report itself. Hume's, from 1966, is the earliest and was derived against total body water. All three take only height, weight and sex, and all three return an estimate of lean body mass in kilograms.

How far apart they land

At 80 kg and 180 cm for a man, Boer gives 61.42 kg, James 62.72 and Hume 57.79. The 4.93 kg between the extremes is about 8 percent of the lean mass itself, and because fat mass is simply what is left over, it translates into implied body fat of 21.6 percent, 23.2 percent or 27.8 percent depending on which equation ran. A 6.2-point spread in implied body fat, from three equations that were each given identical inputs, is the reason this site prints all three instead of quietly picking one and reporting it to two decimal places.

The spread is not constant

It moves with the body. At 70 kg and 170 cm the three span 4.18 kg; at 60 kg and 160 cm for a woman they span 2.04 kg. James is the only one of the three with a non-linear term - it subtracts 128 times the square of weight over height for men, 148 for women - so it diverges fastest at the extremes of height and weight, while Boer and Hume stay parallel to each other. If you compare two calculators at one body and conclude they agree, that conclusion does not travel to another body.

The blindness all three share

Height, weight and sex are the only inputs any of them has, so two people of identical dimensions receive identical answers regardless of how their mass is actually distributed. That means the disagreement between the equations is a floor on the uncertainty, not the whole of it: all three can agree with each other and still sit some distance from a scan. The 2022 comparison against DXA is the citation for the general point that predictive lean-mass equations disagree; it is not this site's editorial opinion.

The unit error that produces a negative answer

One implementation detail is worth naming because it is the most common way these equations get copied wrong. James's squared term takes weight in kilograms over height in centimetres - not metres, and not BMI. Using metres inflates the subtracted term by a factor of 10,000 and returns a negative lean mass, which is the usual sign that an equation was transcribed rather than tested. If a calculator returns a lean mass you can see is impossible, this is very often why.

Official sources

• Boer, Estimated lean body mass as an index for normalization of body fluid volumes, Am J Physiol 1984
• Br J Radiol 2022 — ten predictive lean-mass equations compared against DXA, and the paper this site verifies the James equation against
• Hume, Prediction of lean body mass from height and weight, J Clin Pathol 1966

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