The BMI formula and its limits

From Quetelet to BMI

The ratio of weight to height squared was first proposed by Adolphe Quetelet in 1832. He was studying how human traits are spread across populations, not measuring individual body fat.

In 1972, Keys and colleagues compared several weight-for-height indices. They concluded that weight divided by height squared was the best of them and proposed the name body mass index.

BMI was then adopted mainly as a population tool. It lets researchers track how common obesity is over time and between countries, which is a different job from describing one person.

The formula

In metric units, divide weight in kilograms by height in meters, squared. With height in centimeters, divide by height twice and multiply by 10,000. For 70 kg and 175 cm, that is 70 ÷ 175 ÷ 175 × 10,000 = 22.9.

In US units, divide weight in pounds by height in inches squared, then multiply by 703. The CDC gives both forms.

Worked example

The calculator needs only ‘Units’, ‘Height’ and ‘Weight’. It also asks for ‘Age’. The calculator applies the adult classes from 18; the CDC uses its adult table from age 20.

The WHO adult classes

The WHO Regional Office for Europe lists these classes for adults. The CDC uses the same cutoffs, with the label healthy weight for the 18.5–24.9 band and overweight for 25–29.9. The example BMI of 22.9 falls in the normal weight band on both scales. Each band is a fixed range, so a result near a cutoff can change class with a small change in weight.

• Below 18.5: underweight
• 18.5–24.9: normal range
• 25.0–29.9: pre-obese (overweight)
• 30.0–34.9: obesity class I
• 35.0–39.9: obesity class II
• 40 and above: obesity class III

What BMI cannot show

The CDC lists several limits. BMI does not measure body fat directly. It is moderately to strongly associated with measures of the amount, location and distribution of fat, but scans such as DEXA are more precise.

BMI does not distinguish between fat, muscle and bone mass. A heavily muscled person can have the same BMI as someone with much more fat. BMI also does not show what type of fat a person has or where it is carried.

Writing in the International Journal of Epidemiology in 2014, Jonathan Wells described BMI as a weak measure of an individual's fat-to-lean ratio. Two people with the same BMI can have very different body compositions.

Why it is still used

BMI needs no equipment beyond a scale and a measuring tape, and anyone can repeat the calculation. The same simple number can be compared across years and across countries, which is how it became a standard population statistic.

Wells sums up the paradox in his title: BMI is not a good index of adiposity, but not a bad index of cardio-metabolic risk. It works better as a statistic for groups than as a portrait of one person.

The calculator shows the number, the class and the matching weight range. Pairing it with a waist-based estimate, such as the U.S. Navy body fat method, adds a second view of the same body.