Rearrange the BMI equation to find the weight corresponding to a chosen BMI and height. A height-squared diagram explains the unit conversion and the most common algebra mistakes.
Open the reverse bmi calculator · More Health and Fitness videos
The calculation
Weight (kg) = BMI × height (m)²
Worked example
175 cm = 1.75 m. Squaring gives 3.0625 m²; multiplying by a hypothetical BMI of 22 gives 67.375 kg, displayed as about 67.4 kg. Dividing 67.375 by 3.0625 returns 22.
This is the mathematical weight corresponding to a chosen BMI, not a prescribed or ideal weight. BMI is a screening measure and does not directly measure body fat.
Video chapters
- 0:00 — Which weight corresponds to this BMI?
- 0:15 — Undo division by height squared
- 0:32 — Convert centimeters before squaring
- 0:49 — 1.75 × 1.75 = 3.0625
- 1:08 — 22 × 3.0625 = 67.375 kg
- 1:26 — Put the result back into the formula
- 1:44 — A formula result is not a health diagnosis
- 2:04 — Meters → square → multiply by BMI
Read the full transcript
Suppose a height is one hundred seventy-five centimeters and the chosen B M I is twenty-two. What weight corresponds to those two numbers? We can solve that algebraically. The result describes a relationship between height, weight, and B M I. It does not choose a personal goal weight.
B M I equals weight in kilograms divided by height in meters squared. To isolate weight, multiply both sides by height squared. The height-squared factors cancel on the weight side. That leaves weight equal to B M I multiplied by height squared.
The metric equation needs meters. Divide one hundred seventy-five centimeters by one hundred to get one point seven five meters. Make this conversion before squaring. Squaring one hundred seventy-five as though it were meters would make the height-squared value ten thousand times too large.
Squaring means multiplying the height by itself: one point seven five times one point seven five equals three point zero six two five square meters. A drawn square helps show the operation. It is a mathematical picture of height squared, not a person's body surface area.
Now multiply three point zero six two five by the chosen B M I of twenty-two. The corresponding weight is sixty-seven point three seven five kilograms, or about sixty-seven point four kilograms to one decimal place. Keep the unrounded value until the final display.
Check the result by running the original equation. Sixty-seven point three seven five divided by three point zero six two five equals twenty-two. That returns the chosen B M I. A reverse check is useful because an early unit error can still produce a plausible-looking number.
B M I is a screening measure. It does not directly measure body fat or distinguish fat, muscle, and bone. The same calculated B M I can have different meaning in different people. Children and teens require age-specific interpretation. A health assessment uses more information than these two inputs.
Convert height to meters, square it, and multiply by the chosen B M I. Then divide the result by height squared to check your work. At one point seven five meters and a B M I of twenty-two, the corresponding weight is about sixty-seven point four kilograms.