SOLVETUTORMATH SOLVER

Instrument MI-04-246 · Health

Lean Body Mass Calculator

A scale tells you how much of you there is. The Boer equation splits that figure, estimating how many kilograms are muscle, bone, organs and water rather than stored fat.

Instrument MI-04-246
Sheet 1 OF 1
Rev A
Verified
Type 04 — Body Composition SER. 2026-04246

Lean body mass

55.2 kg

LBM = 0.407·W + 0.267·H − 19.2

The working Every figure verified twice
  1. lbm = 0.407·70 + 0.267·(1.72·100) − 19.2 = 55.2
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Lean body mass is everything you are built from except stored fat — skeletal muscle, bone, organs, skin and the water they hold. No bathroom scale can weigh it directly, so in 1984 the Dutch physiologist P. Boer fitted a regression of height and weight against measured body fluid volumes in 66 healthy adults. The two coefficients and one constant that fell out of that fit are exactly what this sheet evaluates.

The sexes get genuinely different equations, not one equation with an offset bolted on. The male form leans on the weight term at 0.407 per kilogram and takes 0.267 per centimetre of height; the female form reverses the emphasis, 0.252 per kilogram against 0.473 per centimetre, and subtracts a much larger constant. Feed identical figures to both and they diverge by kilograms, which is why the mode switch sits above the inputs rather than hidden in a footnote.

Reading only two measurements, the estimate knows nothing about how you are put together. A powerlifter and a sedentary office worker of the same height and weight receive the same answer, and one of them is being flattered. Boer is a population regression, excellent for scaling drug doses and fluid volumes across a hospital ward, unreliable as a personal verdict on physique. Calipers, DXA and bioimpedance measure; this one infers.

LBMmen=0.407m+0.267h19.2\mathrm{LBM}_{\text{men}} = 0.407\,m + 0.267\,h - 19.2LBMwomen=0.252m+0.473h48.3\mathrm{LBM}_{\text{women}} = 0.252\,m + 0.473\,h - 48.3
LBM — lean body mass in kilograms · W — body mass in kilograms · H — height in centimetres · the trailing constants, 19.2 and 48.3, are kilograms. Coefficients as published by Boer (1984), fitted on 66 healthy adults. Enter height in whichever unit you measured; the sheet converts to centimetres before substituting.
  • Set the mode to Male or Female. The switch replaces the whole equation, coefficients and constant alike — it does not simply nudge the answer.
  • Enter Body mass in kilograms or pounds. The field converts as you type, so a reading straight off an imperial scale needs no arithmetic first.
  • Enter Height in centimetres, metres or inches. Boer works internally in centimetres and the conversion happens before substitution.
  • Read Lean body mass at the head of the sheet, switching its unit to pounds if that is the number your gym equipment reports.
  • Subtract the reading from your body mass for fat mass — the two always sum to the weight you entered.

Worked example — 70 kg at 172 cm

Take a man of 70 kg standing 172 cm. Height term first: 0.267 × 172 = 45.924. Weight term next: 0.407 × 70 = 28.49. Those add to 74.414, the constant 19.2 comes off, and the needle settles at 55.2 kg of lean tissue — near 79% of him, leaving about 14.8 kg of fat.

Run the identical pair through the female form and the working changes completely: 0.252 × 70 = 17.64, plus 0.473 × 172 = 81.356, less 48.3, giving 50.7 kg. That 4.5 kg gap is the regression encoding a population difference in build, which is why choosing the right mode matters far more than measuring your height to the millimetre.

Questions

What is a normal lean body mass?

There is no single normal figure, because lean tissue scales with frame size — a 155 cm adult and a 190 cm adult cannot share a target. As rough orientation, the Boer estimate usually lands near 75–85% of total weight for men and 65–75% for women. Below that band generally means more stored fat; above it usually means an athletic build. The number is most useful watched over months in one person rather than compared between two.

Why do men and women use different Boer equations?

Because Boer fitted the two groups separately and the fits genuinely differ. In his 1984 data men carried lean tissue more in proportion to weight, women more in proportion to height, so the male form weights the kilograms heavily (0.407) while the female form weights the centimetres heavily (0.473). Averaging them into one equation would misestimate both groups at once, so the sheet keeps them apart.

How accurate is the Boer formula?

Expect a few kilograms of error for any individual — it is a population regression, not a measurement. The fit came from 66 healthy adults of ordinary build, and accuracy degrades at the extremes: heavily muscled, very lean, obese, or fluid-overloaded patients. Clinicians still use it for drug dosing and fluid normalisation, where a reproducible estimate from two known numbers beats a precise reading nobody has. For real body composition, use DXA, air-displacement plethysmography or a skinfold protocol.

How do I get body fat percentage from this?

Subtract the lean figure from total weight to get fat mass, then divide by total weight. At 70 kg with 55.2 kg lean, fat mass is 14.8 kg and the fraction is 14.8 ÷ 70 ≈ 21%. That percentage inherits every bit of the equation's error, so read it as a bracket rather than a reading — a device quoting 21.3% is offering false precision on a number that was estimated from your height.

Is lean body mass better than BMI?

It answers a better question, but from the same evidence. BMI cannot tell muscle from fat; the Boer estimate at least tries to. Both, however, are built from nothing but your height and weight, so this sheet adds no new information about you — it redistributes what those two numbers already imply. The real upgrade is a measurement: a tape at the waist, calipers, or a scan. Two formulas fed identical inputs are still one opinion.

What units does the Boer equation need?

Kilograms and centimetres. The published coefficients only make sense in those units, and the trailing constants, 19.2 and 48.3, are kilograms. Enter pounds or inches if that is how you measured — the sheet converts to kilograms and centimetres before substituting, which means the pound answer it hands back is a conversion of the kilogram result, not a separate imperial formula.

References

Read this first: This instrument computes a screening figure from population formulas — it is not a diagnosis, and it cannot see the whole picture a clinician can. Use it to inform a conversation, not to replace one.