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Your numbers in the formula
Here is the exact math behind your result, using your own numbers.
Why is height squared?
Taller people weigh more even when they aren't carrying more fat, so weight alone can't be compared between people of different heights. In the 1830s, the Belgian mathematician Adolphe Quetelet found that adult weight rises roughly with the square of height.1 Dividing by height squared cancels most of that effect, so a short person and a tall person with similar builds get similar numbers.
The name "body mass index" came later, in 1972, from the physiologist Ancel Keys, who found it was the simple weight-for-height index that tracked body fat best in large studies.1
The formula in both unit systems
| Units | Formula | Example |
|---|---|---|
| kg and m | weight ÷ height² | 65 ÷ 1.70² = 22.5 |
| kg and cm | weight ÷ height ÷ height × 10,000 | 65 ÷ 170 ÷ 170 × 10,000 = 22.5 |
| lb and in | 703 × weight ÷ height² | 703 × 150 ÷ 67² = 23.5 |
The 703 is the conversion between the two systems. Where 703 comes from.
Rearranging the formula
The same equation answers other questions:
- Weight for a given BMI: weight = BMI × height². At 1.70 m, a BMI of 24.9 is 24.9 × 2.89 = 72.0 kg.
- Height for a given weight and BMI: height = √(weight ÷ BMI).
Frequently asked questions
Is the BMI formula the same for everyone?
Yes. Men, women and children all use the same equation. What changes is how the result is interpreted: children are compared by age and sex, and some guidelines use lower cutoffs for people of Asian descent.
Who invented the BMI formula?
Adolphe Quetelet described the weight-to-height-squared ratio in the 1830s. Ancel Keys named it "body mass index" in 1972.
Can I calculate BMI without the formula?
You can read it from a BMI chart, but the chart is built from the same formula.
Sources
Further reading
This page is for education and is not medical advice. Talk with a healthcare professional about your weight and health.
