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The metric BMI formula, step by step
Here is the exact math behind your result, using your own numbers.
The formula is BMI = weight (kg) ÷ height (m)². The only conversion you need is centimeters to meters.
- Convert height to meters. Divide centimeters by 100: 175 cm = 1.75 m.
- Square the height. Multiply it by itself: 1.75 × 1.75 = 3.0625.
- Divide weight by that number. 70 ÷ 3.0625 = 22.86.
- Round to one decimal place. 22.9, which is in the healthy range (18.5 to 24.9).1
A shortcut that skips the meters
If you'd rather keep centimeters, divide your weight by your height twice, then multiply by 10,000:
70 ÷ 175 ÷ 175 × 10,000 = 22.9
It gives the same answer because 10,000 is 100 × 100, the conversion from cm² to m².
Worked examples
| Height | Weight | Height in m, squared | BMI | Category |
|---|---|---|---|---|
| 160 cm | 55 kg | 1.60² = 2.56 | 55 ÷ 2.56 = 21.5 | Healthy weight |
| 175 cm | 70 kg | 1.75² = 3.0625 | 70 ÷ 3.0625 = 22.9 | Healthy weight |
| 188 cm | 95 kg | 1.88² = 3.5344 | 95 ÷ 3.5344 = 26.9 | Overweight |
Healthy weight for your height in kg
Turn the formula around to find the weight range for a healthy BMI: multiply your height in meters squared by 18.5 and by 24.9.
At 175 cm: 18.5 × 3.0625 = 56.7 kg and 24.9 × 3.0625 = 76.3 kg
The calculator above shows this range for your own height.
Common mistakes in metric BMI
- Dividing by centimeters. 70 ÷ 175² = 0.0023. Convert to meters first, or use the × 10,000 shortcut.
- Not squaring the height. 70 ÷ 1.75 = 40, which is far too high.
- Using 703. That factor is only for pounds and inches. In kg and m there's no extra number.
Frequently asked questions
What is the BMI formula in cm and kg?
BMI = weight in kg ÷ (height in cm ÷ 100)². Or, without converting: weight ÷ height ÷ height × 10,000.
Is metric BMI the same as BMI in pounds?
Yes. Both formulas give the same number for the same person. The imperial version just includes a conversion factor of 703. How to calculate BMI in pounds and inches.
What if I know my height in feet but my weight in kg?
Use the unit converter or the calculator's "type it" box, which accepts mixed units like "5'7 68 kg".
Sources
Further reading
This page is for education and is not medical advice. Talk with a healthcare professional about your weight and health.
