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Type your weight and height into any BMI calculator and it runs a formula that is almost 200 years old. It comes from Adolphe Quetelet, a Belgian astronomer who turned to measuring people. This post explains who he was, what he actually found, how his index got the name body mass index, how to calculate it correctly, and why the adult cut-offs do not apply to most school students.
Who was Adolphe Quetelet?
According to his MacTutor biography, Quetelet was born in Ghent on 22 February 1796 and died in Brussels on 17 February 1874. He earned a doctorate from Ghent in 1819 with a dissertation on conic sections, then went to Paris in December 1823 to study astronomy. There he learned the theory of probability under Joseph Fourier and Pierre Laplace. In 1832 he became director of the newly opened Brussels Observatory.
Probability became the centre of his work. In popular lectures published in 1828 he wrote, in the English translation MacTutor quotes, that "the theory of probabilities ought to serve as the basis for the study of all the sciences, and particularly of the sciences of observation." He then applied that idea to people: their heights, weights, births, deaths and even crimes.
What was the "average man"?
In 1835 Quetelet published *Sur l'homme et le développement de ses facultés, essai d'une physique sociale* (On man and the development of his faculties: an attempt at social physics). MacTutor describes its central idea: the average man, "l'homme moyen", is the central value around which measurements of a human trait group themselves according to the normal curve. Quetelet was the first to use the normal curve for something other than errors of measurement.
Astronomers already used that bell-shaped curve for repeated measurements of one star. Quetelet applied it to the heights of many different people.
How did weight and height lead to an index?
Quetelet studied how bodies grow. A review by Garabed Eknoyan in Nephrology Dialysis Transplantation (2008) summarises his conclusion: apart from the growth spurts after birth and during puberty, "the weight increases as the square of the height". The ratio of weight to height squared became known as the Quetelet Index.
Why the square? If people of different heights were exact scaled copies of each other, weight would grow with volume, so with height cubed. Quetelet's measurements of real bodies pointed to the square instead. Dividing by height squared therefore gives a number that does not simply rise with height, which is what an index of build needs.
For more than a century this stayed a statistical description. Eknoyan explains that the search for a practical index of relative weight began after life insurers reported higher death rates among overweight policyholders, and came to a head after the Second World War, when the link between weight and heart disease became a subject of research.
Who named it the body mass index?
In 1972 Ancel Keys and colleagues published Indices of relative weight and obesity90027-6) in the Journal of Chronic Diseases. The paper, reprinted in the International Journal of Epidemiology in 2014, compared several indices using data on the weight, height and body fat of men in several European countries, Japan, South Africa and the United States. It assumed that a main reason for such an index is "to remove the dependency of weight on height". Eknoyan records that Keys renamed the Quetelet Index the Body Mass Index.
Worked example: calculating a BMI
Take a sample adult who weighs 68 kg and is 1.70 m tall.
Square the height: 1.70 × 1.70 = 2.89 m².
Divide: 68 ÷ 2.89 = 23.5 kg/m², to one decimal place.
Now a second sample adult with the same weight who is 1.60 m tall: 1.60 × 1.60 = 2.56, and 68 ÷ 2.56 = 26.6 kg/m². The same weight gives a higher index for the shorter person, which is the point of dividing by height.
The WHO fact sheet on obesity and overweight defines overweight in adults as a BMI greater than or equal to 25, and obesity as greater than or equal to 30.
What mistakes do students make with BMI?
Using centimetres. 68 ÷ (170 × 170) gives about 0.0024, which means nothing. Convert to metres first.
Forgetting to square. 68 ÷ 1.70 = 40, a number that looks alarming and is wrong.
Applying adult cut-offs to teenagers. WHO defines overweight for ages 5 to 19 as a BMI-for-age more than 1 standard deviation above the WHO Growth Reference median, and obesity as more than 2 standard deviations above it. A 15-year-old's BMI must be read against a chart for their age and sex.
Assuming one cut-off fits everyone. A WHO expert consultation in The Lancet (2004)15268-3) found that the share of Asian people at high risk of type 2 diabetes and heart disease is substantial at BMIs below 25. It kept the international cut-offs but identified further public health action points at 23.0, 27.5, 32.5 and 37.5 kg/m².
BMI is a screening number, not a diagnosis. If you have questions about your own weight or growth, talk to a doctor rather than a calculator.
Ratios like this test whether you really understand units. If that part feels shaky, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revise the one idea that is blocking you.
What can a student learn from how Quetelet worked?
Quetelet did not set out to invent a health measure. He collected many careful measurements, looked for the pattern that held across them, and stated it as one compact rule. He also pushed for standard methods: Eknoyan notes that in 1853 he organised the first International Statistical Congress, which began work on a uniform naming of causes of death, an ancestor of today's International Classification of Diseases. Data collected the same way everywhere made his patterns possible. To see how later statisticians built on the bell curve, read our post on Francis Galton and regression.
Try it now: calculate the BMI for 55 kg at 1.62 m, then explain in one sentence why the answer would be wrong if you used 162 instead of 1.62.
