Lean Body Mass Calculator

How to use the lean body mass calculator

Set sex, enter weight and height, and the calculator runs three published regression equations over those two numbers. It reports each estimate separately, the band they span, and the fat mass each one implies as the remainder. Both measurement fields carry a unit toggle and convert internally, because all three equations are defined in kilograms and centimetres.

The page opens on a 70 kg man of 175 cm. Boer returns 56.0 kg of lean mass, James returns 56.5 kg and Hume returns 52.8 kg, so the band runs 52.8 to 56.5 kg and the fat mass implied by it runs 13.5 to 17.2 kg, or 19.3 to 24.6 percent of body weight.

The same body with the female coefficients gives 52.1, 51.2 and 50.6 kg, a band of 50.6 to 52.1 kg. The bands differ because the cohorts differed, not because one is more correct, and there is no version of these equations that applies to both.

The spread is not constant either. On this 175 cm frame the three equations sit within 2.4 kg at 60 kg, 3.7 kg at 70 kg, 5.2 kg at 80 kg and 7.2 kg at 120 kg. They agree most closely on the sort of body they were mostly fitted on, and drift apart in both directions from there.

That widening is not noise. James subtracts a term proportional to the square of weight over height, so as body mass climbs that subtraction accelerates while Boer and Hume keep adding in a straight line. The gap between a quadratic and a straight line is the whole story.

What these equations cannot see

Here is the most useful sentence on the page. Take two people who are both 180 cm and both 90 kg. One has trained with weights for a decade. The other has not trained at all. Every equation on this page returns the same band for both of them: 61.1 to 67.0 kg of lean mass.

It has to. The inputs are height and weight. Nothing in Boer, James or Hume takes a measurement of tissue, and no arrangement of two numbers can distinguish a body built one way from a body built another way at the same height and mass.

This is the same limitation body mass index has, and it is worth naming the family resemblance. BMI, ideal weight formulas and these lean mass equations all take height and weight and hand back a population statistic. None of them is a body composition measurement, however precise the decimals look.

If composition is genuinely the question, the methods that answer it take an actual measurement of the body: circumference with a tape, skinfold with callipers, or imaging. The circumference method is the one you can do at home with a tape measure, and it at least reads something about your shape.

Where the three equations came from

None of these was written to tell an individual how much muscle they carry. Knowing what each was actually for explains why they disagree, and why the disagreement is not a defect anyone needs to resolve.

Boer, 1984

Boer published his equation in the American Journal of Physiology in 1984, in a paper about normalising body fluid volumes. He measured blood volume in 66 healthy subjects and extracellular fluid volume in 54, and needed an index that fluid volumes scaled cleanly against. Lean body mass estimated from weight and height was the index that worked.

James, 1976

The James equation comes from the report of the DHSS and MRC group on obesity research, published in 1976. It is the only one of the three with a nonlinear term, subtracting a quantity proportional to the square of weight divided by height, which is what makes it behave so differently at high body mass.

Hume, 1966

Hume published in the Journal of Clinical Pathology in 1966 under the plain title Prediction of lean body mass from height and weight. The paper reports multiple correlation coefficients of 0.96 for the male formula and 0.83 for the female one, which is itself informative: the female equation fitted its data considerably less tightly.

Three purposes, three cohorts, three decades, three answers. Presenting them as a band is not hedging. It is the only presentation that does not quietly assert that one of these teams was right and the other two were wrong.

The formula, worked line by line

All three equations take exactly two inputs, weight in kilograms and height in centimetres, and each carries a separate pair of coefficients for men and women. Two of them are straight lines. One is not, and that difference explains most of what happens at the edges.

Boer and Hume have the same shape: a coefficient on weight, a coefficient on height, and a constant subtracted. Feed them a heavier body and the estimate rises in a straight line forever, which is fine in the middle of the range and increasingly optimistic outside it.

James is built differently. It takes a fixed multiple of weight and then subtracts a term proportional to the square of weight divided by height. As body mass climbs, that subtraction grows faster than the first term, so the curve bends over and eventually turns down.

Boer 1984
  male    LBM = 0.407 x kg + 0.267 x cm - 19.2
  female  LBM = 0.252 x kg + 0.473 x cm - 48.3

James 1976
  male    LBM = 1.10 x kg - 128 x (kg / cm)^2
  female  LBM = 1.07 x kg - 148 x (kg / cm)^2

Hume 1966
  male    LBM = 0.32810 x kg + 0.33929 x cm - 29.5336
  female  LBM = 0.29569 x kg + 0.41813 x cm - 43.2933

fat mass = weight - LBM

Where the equations break outright

Push far enough from the middle and they stop returning possible answers. At 30 kg and 175 cm, a body mass index of about 9.8, Boer and Hume both hand back more lean mass than the whole body has, because their constant height term keeps adding long after the weight term has run out.

The tool drops any equation that returns a negative figure or one larger than total body weight, and says which it dropped. That is the honest handling: an impossible number quietly averaged into a band would make the band look narrower and more confident than it is.

James fails at the other end. Its quadratic term overtakes its linear term at high body mass, so past roughly a body mass index of 45 it starts falling, and eventually goes negative. That is not a claim about heavy bodies. It is an equation being used outside the range it was fitted on.

Questions people ask