The unit is written in lower-case Latin letters with a slash and a superscript: kg/m², and in running text it is often dropped, saying simply “BMI 23”. Body surface area is written as m², with one decimal place in the clinic and two in drug dosing, and the international abbreviations are BMI and BSA.
Body mass index is neither a pressure nor an area, even though its unit is the same as that of an areal density: it is mass related to the square of height, and by no means kilograms per square metre of skin. The real skin area is given by BSA, about 1.7—2.0 m² in an adult, and nobody would divide weight by it.
On the left a bar of the stadiometer comes down, reaches the crown of the head and reveals the 1.75 mark, while around the turquoise silhouette runs a coral dotted line of the fat layer. The letters kg press on the fraction bar like a load on a scale platform, and it springs; beneath it a dotted square m² breathes, and at the bottom Quetelet’s crowd flickers, over whose bell curve a red marker climbs to the middle and returns.
Quantity data sheet
mass over height squared · skin area sheet 1/1 · rev. 2026-09Body mass index BMI · kg/m² · BSA · m²
SI derived unit · quantity: body mass index, kg/m², and body surface area, m²
The average man who does not exist
The Belgian astronomer Adolphe Quetelet dreamed of finding for society laws like those Kepler found for the planets, and in 1832, going through tables of height and weight of conscripts and prisoners, he noticed that in adults weight grows roughly as the square of height. He needed the ratio of mass to height squared not to judge a particular person but to describe the “average man”, l’homme moyen, an imaginary Belgian around whom the crowd is distributed according to the law of errors.
For a hundred and forty years this number remained a statistical curiosity, until in 1972 the physiologist Ancel Keys compared several weight indices on thousands of men, called the best of them the body mass index and handed it over to epidemiologists. From there it passed into the doctor’s office, insurance tables and phone apps, although Keys himself warned that for an individual the index is a poor guide: it does not know what the weight is made of.
Body surface area lives by the same logic — two simple measurements instead of an inaccessible third — and it was derived in 1916 by Eugene and Delafield Du Bois from paper patterns of nine people. The sheet puts both quantities side by side and shows where they are useful and where they begin to err.
01 · Definition
mass · height · area · compositionBody mass index is a person’s mass in kilograms divided by the square of their height in metres. A person with a mass of 70 kg and a height of 1.75 m has an index of 22.9 kg/m², and by the WHO table falls into the corridor from 18.5 to 24.9, which for adults is called normal weight.
The square comes from observation, not from geometry: if people grew in similar proportions, mass would grow as the cube of height, but tall people are on average slimmer, and Quetelet found the exponent at which the index depends least on height. It later turned out that a power of about 2.5 fits better, and so the index slightly overstates for the tall and understates for the short.
The main limitation of the index is that it does not distinguish fat from muscle, bone and water. For a crowd this does not matter, since errors cancel out, but for a single person it can decide everything: a rugby player and a sedentary person of the same height and weight have the same index, yet the amount of fat differs twofold. Body surface area is arranged differently: it cannot be measured with a tape, and it is calculated from height and mass by a formula fitted on a few measured people.
One number for two different bodies
On the left a person stands on a scale beside a stadiometer: the turquoise core is muscle, bone and water, the coral shell around it is fat, and its thickness is changed by the composition slider. The stadiometer bar comes down to the crown, and the scale display counts up the mass. On the right three hundred blue dots are the adults of today’s world according to the sheet’s model; they fall onto the index scale and gather into a bell curve; the amber line is the crowd of the 1830s as Quetelet saw it, the coloured bands are the WHO categories, the coral needle is your index, and the turquoise triangle is the same person by Trefethen’s formula.
Why the index works for a country and errs for a neighbour
When an epidemiologist compares two countries, each sample holds thousands of rugby players, ballerinas and desk workers, and their deviations on average cancel out, so a shift of the whole crowd to the right almost certainly means added fat. An individual has no such insurance, and so in 2025 a Lancet commission proposed diagnosing obesity only when a high index is confirmed by waist circumference, a fat measurement or signs of disease, leaving the index itself for the screening and statistics it was invented for.
02 · Conversion
WHO · old indices · body areaOne ratio, many old formulas
Enter an index in kg/m², in pounds per square inch or as a fraction of 25, and the sheet will show the WHO category and the Asian cut-offs, convert the index into weight at different heights, compare it with the old “ideal weight” formulas and calculate the body area of a person 1.75 m tall by five formulas.
Rule of thumb: at a height of 1.75 m one unit of index is about three kilograms, and at 1.60 m about two and a half.
In children and adolescents the index means nothing by itself, because the body changes proportions every year: they are compared with their peers using WHO percentile tables, and 20 kg/m² may be excess in an eight-year-old and normal in a fifteen-year-old. In the elderly the index is distorted because a person loses a few centimetres of height and muscle is replaced by fat at the same weight.
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04 · Measuring instruments
stadiometer · scale · caliper · DEXATwo simple instruments and two honest ones
Height that changes during the day
The stadiometer seems the simplest instrument on the sheet, but a person’s height in the morning is a centimetre or so greater than in the evening, because during the day the intervertebral discs are compressed under body weight. So in studies height is measured at the same time of day, without shoes, with heels, buttocks and back of the head against the post and the gaze along the Frankfort horizontal plane, and an error of one centimetre shifts the index by a quarter of a unit.
Scales that compare rather than feel
The beam scale of a doctor’s office does not measure force but balances the person with a weight, moving the poise along the beam until its end stands in the middle of the window. Such an instrument does not care where it stands or what gravity is there, and so for centuries they were verified with weights, whereas electronic scales, which measure the deflection of a sensor, have to be checked anew at every move.
A centimetre of fat in the fingers
The caliper pinches a skinfold above the triceps, below the shoulder blade, on the abdomen and on the thigh, and a spring keeps the same pressure on the jaws, so the fold thickness depends almost only on subcutaneous fat. From the sum of folds, by the Durnin or Jackson and Pollock formulas, one gets the body fat fraction, and although this too is an estimate, it sees what the index does not see at all: where the weight lies.
A map of fat, muscle and bone
The DEXA densitometer scans a lying person with X-rays of two energies, which fat, muscle and bone absorb differently, and builds from the scanning arm a map of the three tissues over the whole body. The dose is smaller than for an ordinary chest X-ray, and the result serves as the reference with which the index, the caliper and bioimpedance scales are compared: it was in such a check that it turned out that at an index below 25 there can be as much fat as in obesity.
05 · Writing rules
unit · decimal point · indexThe square stands over the metre, not over the number
The index is written with one digit after the decimal point and the unit kg/m², and body area with two digits and m², because drug doses are calculated from it.
The first line on the right confuses the index with body fat, which is measured in percent, the second loses the superscript and turns m² into “m2”, and the third divides by centimetres and gets a number ten thousand times smaller. A bare 1.85 without a unit and a formula does not allow the dose to be checked, five decimal places ascribe to the index a precision that the stadiometer does not have, and the last line calls weight something that is not weight.
06 · Neighbouring units
kilogram · square metre · kg/m³The index is made of the kilogram and the metre, and next door live the square metre of body area and the Rohrer index in kg/m³, which divides mass by the cube of height and therefore suits children better.
The numerator of the index and the only thing in it that is truly weighed.
The index has the square of height; body area has real skin.
Mass over height cubed; about 13 in an adult, about 27 in a newborn.
07 · Historical section
archive · from the average man to the LancetHow statistics moved to the doctor’s office
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How twenty-nine million people got fat overnight
The bell is the distribution of American adults by index, the coral fill is those called overweight. The dashed boundary slides from the former 27.8 for men to the common threshold of 25 that the NIH introduced in 1998, and the fill grows, although not a single person gained a gram.
A category boundary is a decision of a committee, not a property of the body, and so the number of overweight people changes along with the minutes of a meeting.
Nine people in paper patterns
In 1916 the New York physician Eugene Du Bois was studying metabolism and wanted to compare the heat loss of people of different size, and for that he needed the area of skin. Together with Delafield Du Bois he wrapped the subjects in thin paper and paraffin, cut the resulting shell into flat pieces, transferred them to a sheet and measured them, and then fitted a formula in height and mass that described these measurements. There were nine people in the sample, and not one of them was truly obese.
The formula outlived both its physiology and its sample. In 1928 the mean area of adults, 1.73 m², became the reference body to which kidney filtration is normalised, and in 1958 the paediatrician Donald Pinkel proposed dosing anticancer drugs per square metre, because that way the doses of a child and an adult matched better than per kilogram. Since then an error of the formula of ten percent in a person weighing 150 kg means a dose error of the same ten percent.
So the two quantities of the sheet turned out to be built the same way: they are computed from two well-measured numbers, height and mass, and compared with something hard to measure — body fat fraction and skin area. The accuracy of stadiometer and scale determines only the arithmetic; how truthfully the index or area speaks about a particular body is decided by the sample from which the formula was fitted, and Quetelet’s was an army one, while Du Bois’s was nine people in paper.
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