The three equations
All three take only height and weight, which is both their appeal and their limit: two people of identical height and weight get identical answers, however differently they are built.
| Formula | Men | Women |
|---|---|---|
| Boer (1984) | 0.407w + 0.267h − 19.2 | 0.252w + 0.473h − 48.3 |
| James (1976) | 1.1w − 128(w ÷ h)² | 1.07w − 148(w ÷ h)² |
| Hume (1966) | 0.32810w + 0.33929h − 29.5336 | 0.29569w + 0.41813h − 43.2933 |
w = kg, h = cm.
The same person, three answers
An 80 kg, 180 cm man with a measured 18% body fat:
| Method | Lean mass |
|---|---|
| Hume (1966) | 57.8 kg |
| Boer (1984) | 61.4 kg |
| James (1976) | 62.7 kg |
| From measured body fat | 65.6 kg |
The three regressions span 4.9 kg — about 8% — and all three sit below the figure from an actual measurement. That is not a coincidence for this example: they are fitted on population averages, and someone who trains carries more lean mass than the average person of their height and weight.
When each one is the right choice
- Boer is the default here and the most commonly used in clinical dosing contexts. It sits in the middle of the three and behaves sensibly across a wide range of sizes.
- James has a squared term that makes it fall away faster at higher weights, so it under-estimates lean mass in heavier people more sharply than the other two.
- Hume is the oldest, reads lowest in this example, and is still used in some renal and oncology dosing literature.
- A measured body-fat percentage beats all three. Lean mass is simply weight × (1 − body fat), and even a tape measure carrying a ±3 percentage point error usually beats a height-and-weight regression that has never met you.
Why three formulas disagree by five kilograms
All three are regressions: somebody measured lean mass in a group of people by a reference method, then fitted a line through height and weight that predicted it. The coefficients are therefore a description of that group, not of the human body, and the three groups were different.
Boer was fitted on a general clinical population. James is older and derived in a context where it was used for drug dosing. Hume, older still, comes from a different reference method again. None of them knows anything about you beyond your height, your weight and your sex — which is why two people of identical height and weight, one of them a lifter at 12% body fat and the other sedentary at 32%, get exactly the same answer from all three. That is not a bug in the formulas. It is what a regression on height and weight can possibly do, and it is the whole argument for measuring body fat instead.
When a regression is still the right choice
Two situations. The first is when you have no tape measure and no scale that estimates composition, and a rough figure is more useful than none — feeding Katch-McArdle a Boer estimate is better than not using Katch-McArdle at all, provided you know the result inherits the error. The second is when you want a figure that will not move for reasons unrelated to your body: a regression on height and weight is perfectly repeatable, where a tape measurement drifts with how tightly you pulled it and a bioimpedance reading drifts with how much water you drank.
What none of them is good for is comparing yourself to somebody else. Two people can differ by more than the gap between these formulas simply through where they carry their weight, and the regression cannot see any of it.
Which number to write down
Pick one method and stay with it. The absolute figure matters far less than whether the series you are building is internally consistent: Boer every month for a year tells you something real about the direction you are moving, while Boer in January, a smart scale in March and a DEXA scan in June tells you almost nothing at all, because the differences between the methods are larger than the change you are trying to detect.
What lean mass is actually for
Two things, mostly. It is the input to Katch-McArdle, which is the only common BMR equation that responds to body composition. And it is the sensible basis for a protein target once body fat is above about 25%, because fat tissue has essentially no protein requirement and a bodyweight-based target starts over-shooting.
It is also the number to watch while cutting. Losing weight is easy to measure and tells you almost nothing on its own; holding lean mass steady while total weight falls is the actual goal, and it is the reason protein intake and continued lifting matter more than the exact size of the deficit.