Unit Converters
BMI to Weight: Rearrange the Formula
Calculate the weight corresponding to a stated BMI and height, check centimetres versus metres, and distinguish the arithmetic from a health target.
A BMI value alone does not determine weight
Body mass index relates mass to height. The metric formula is BMI = weight in kilograms divided by height in metres squared. Therefore the same BMI corresponds to different weights at different heights. To calculate a weight, both the BMI value and height must be known. The algebraic result answers “what weight gives this BMI at this height?” It does not establish that this weight is suitable for a particular person or that changing weight to reach it is medically indicated.
Rearrange before substituting numbers
Multiply both sides of the BMI equation by height squared. This gives weight in kilograms = BMI × height in metres × height in metres. When the available height is in centimetres, divide it by 100 before squaring. Equivalently, weight = BMI × height in centimetres squared / 10,000. The factor 10,000 appears because the centimetre-to-metre factor is squared along with the height. Dividing by 100 only after squaring would leave the result one hundred times too large.
Follow a complete example
Use an illustrative BMI of 22 and a height of 170 cm. The height in metres is 1.70, its square is 2.89, and the corresponding weight is 22 × 2.89 = 63.58 kg. To check the calculation with the local tool, enter 63.58 for weight and 170 for height. The BMI result should return 22 apart from display rounding. Entering 1.70 in a field labelled centimetres would describe a very different height and is a unit error, not an alternative way to enter the same measurement.
Compare two heights at the same BMI
At 180 cm, the same illustrative BMI of 22 corresponds to 22 × 1.80² = 71.28 kg. The difference from the 170 cm example is 7.70 kg. It is not calculated by adding a fixed amount for every centimetre, because height enters the equation as a square. More generally, keeping BMI constant while multiplying height by a factor k multiplies the corresponding weight by k². This is a property of the index's formula; it is not a biological prediction of an individual's body composition.
Handle rounding and measurement changes
Retain the measured height through the calculation instead of rounding it to a convenient whole metre or broad height category. At a fixed BMI, a small relative error in height has approximately twice that relative effect on the calculated weight. If a height is supplied in feet and inches, convert the entire measurement to centimetres or metres before using the formula. For a weight needed in pounds, calculate kilograms first and divide by 0.45359237. Keep the conversion separate from any choice of a BMI value so that both assumptions remain visible.
Interpret the result in its proper scope
CDC describes BMI as a screening measure and says individual assessment also involves other information. BMI does not directly measure body fat or tell how muscle and fat are distributed. A reverse calculation cannot diagnose a condition or prescribe an ideal weight. Children and adolescents require age- and sex-specific interpretation rather than simply applying adult categories to the number. Use this guide to understand the arithmetic or verify a recorded value. For a personal health decision, discuss the person's measurements and circumstances with an appropriate clinician instead of treating a calculator's inverse result as a treatment goal.
Calculate an interval without turning it into advice
If a mathematical exercise supplies two BMI endpoints, apply the same fixed height to each endpoint independently. At 1.70 m, illustrative index values 21 and 23 correspond to 60.69 and 66.47 kg. This interval is an arithmetic translation of the supplied indices, not an individualized recommended range. Keep the endpoints and height visible in a worksheet so that a reader can distinguish the original assumptions from the calculated masses. Do not silently substitute a category boundary for an index the question actually specifies.
Calculator for the supported step
The BMI Calculator accepts weight in kilograms and height in centimetres. Compute the corresponding weight with the rearranged formula first, then enter that weight and height to verify the original BMI.
Sources and method
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