Body mass index divides weight in kilograms by height in metres squared, and that exponent is the source of its two best-known failures. Bodies grow in three dimensions rather than two, so dividing by a square makes tall people score higher than their build warrants and short people score lower. It also cannot distinguish muscle from fat, because it only ever sees one number for the whole body.
None of this makes BMI useless. It makes it a population screening figure that was designed for population screening, being asked an individual question it was never built to answer.
Where does the formula come from?
From Adolphe Quetelet, a Belgian astronomer and statistician, in the 1830s. He was describing the distribution of body types across a population — l’homme moyen, the average man — and looked for a ratio of weight to height that stayed roughly constant across adults of different sizes. Weight over height squared was the best fit for the data he had.
The name is much newer. Ancel Keys called it the body mass index in 1972, when he compared several weight-for-height measures and concluded that Quetelet’s ratio was the least bad for epidemiological work. Both men were studying groups. Neither proposed it as a diagnosis.
How much does the exponent matter?
Enough to change which category someone falls into. Nick Trefethen, a numerical analyst at Oxford, proposed in 2013 that height should be raised to 2.5 rather than 2, with a scaling constant of 1.3 to keep mid-range results unchanged. The two formulas agree around average height and diverge at the extremes.
| Height and weight | Standard BMI | With exponent 2.5 | Difference |
|---|---|---|---|
| 155 cm, 50 kg | 20.81 | 21.73 | +0.92 |
| 170 cm, 70 kg | 24.22 | 24.15 | −0.07 |
| 180 cm, 80 kg | 24.69 | 23.93 | −0.77 |
| 190 cm, 85 kg | 23.55 | 22.21 | −1.34 |
| 200 cm, 95 kg | 23.75 | 21.83 | −1.92 |
At 190 cm the standard formula reads 1.34 points high; at 155 cm it reads 0.92 points low. A 190 cm adult sitting at 25.5 on the standard scale — technically overweight — is at 24.1 on the adjusted one. Nothing about the person changed.
Why do athletes score badly?
Because muscle is denser than fat and BMI counts only total mass. A well-trained 180 cm athlete at 90 kg scores 27.8 and is classified overweight while carrying a low body fat percentage; a sedentary person of the same height and weight scores identically.
This is not a rounding problem, it is the measurement having no way to see the difference. Any screening figure computed from height and weight alone will have it, which is why body composition is measured by other means entirely when it actually matters.
The same blindness runs the other way. An older adult who has lost muscle can sit comfortably inside the healthy band while carrying more fat than is ideal, and BMI will report nothing at all.
What are the thresholds, and are they universal?
The World Health Organization treats 18.5 to 24.9 as the healthy adult range, below 18.5 as underweight, 25 to 29.9 as overweight, and 30 or above as obese. Translated into weights, that band is narrower than people expect at any given height.
| Height | Healthy weight range |
|---|---|
| 155 cm | 44.45 – 59.82 kg |
| 170 cm | 53.47 – 71.96 kg |
| 180 cm | 59.94 – 80.68 kg |
| 190 cm | 66.79 – 89.89 kg |
The thresholds are not applied identically everywhere. Several health authorities in Asia use lower cut-offs, because the relationship between BMI and metabolic risk differs across populations — which is another way of saying the number is a proxy whose calibration depends on who is being screened.
What measures alongside it?
Waist circumference, most commonly, because it distinguishes where the mass is rather than how much of it there is. A widely used screening rule is to keep the waist below half your height, which for a 170 cm adult means under 85 cm.
That rule has the useful property of being scale-free: it does not need a different threshold for a different height, because the height is already in it. It is also easy to measure badly, and it says nothing about muscle either.
Questions people ask
Does BMI work for children? Not in this form. Children are assessed against age and sex percentile charts, because the healthy ratio changes throughout growth, and an adult threshold applied to a twelve-year-old is meaningless.
Is 24.9 meaningfully different from 25.1? No. The thresholds are conventions drawn across a continuous distribution, and the risk either side of the line is essentially identical. Treat a category boundary as a prompt rather than a verdict.
Should I use the 2.5 exponent instead? It is a better fit at the extremes and it is not the standard, so any figure you produce with it will not match what a clinic reports. Knowing which direction the standard formula errs in for your height is more useful than substituting a different one.
Does it apply during pregnancy? No. Weight gain during pregnancy is assessed against its own guidance, and BMI is used for the pre-pregnancy weight rather than the current one.
Know which way the formula bends for your height and it becomes a usable screening figure again. The BMI calculator shows the healthy weight range alongside the index, the TDEE calculator estimates what you burn, and kilograms to pounds is there if your scale and your doctor disagree about units.