How to Calculate BMI by Hand in Metric and Imperial Units
Body mass index (BMI) is a single number built from two measurements: weight and height. The arithmetic is short enough to do on paper, and doing it once makes it clear what the number really is: weight divided by height multiplied by itself.
This guide walks through the metric and imperial versions, shows where the odd-looking factor 703 comes from, lists the slips that produce wrong answers, and explains how to read the result. It is general information about a screening number, not a diagnosis.
The metric formula
In metric units, BMI is weight in kilograms divided by the square of height in metres.
BMI = weight (kg) ÷ height (m)²Height squared means height × height.
Worked example: a person weighs 68 kg and is 1.70 m tall. Square the height first: 1.70 × 1.70 = 2.89. Then divide: 68 ÷ 2.89 = 23.53, which is written as a BMI of 23.5.
If you only know your height in centimetres, you can skip the conversion by using a shortcut: divide the weight by the height in centimetres squared, then multiply by 10,000. For the same person, 170 × 170 = 28,900, and 68 ÷ 28,900 × 10,000 = 23.5. The 10,000 appears because there are 100 × 100 square centimetres in a square metre.
The imperial formula and the 703
With pounds and inches the same idea needs a conversion factor so the answer matches the metric scale.
BMI = 703 × weight (lb) ÷ height (in)²Convert feet and inches to inches first: 5 ft 6 in = 66 in.
Worked example: a person weighs 150 lb and is 5 ft 6 in tall, which is 66 inches. Height squared is 66 × 66 = 4,356. Multiply the weight by 703: 150 × 703 = 105,450. Divide: 105,450 ÷ 4,356 = 24.21, so the BMI is 24.2.
The 703 is not arbitrary. One pound is 0.45359237 kg and one inch is 0.0254 m, so converting both units gives 0.45359237 ÷ 0.0254² = 703.07, which is rounded to 703. Without it, the number you calculate would be about 703 times too small.
Common slips to avoid
- Forgetting to square the height. Dividing 68 by 1.70 gives 40, which is far outside any realistic BMI.
- Mixing units. Kilograms with inches, or pounds with metres, will give a meaningless result.
- Using centimetres in the metric formula. Height must be in metres unless you use the 10,000 shortcut.
- Rounding too early. Keep at least two decimals while squaring and dividing, and round only the final BMI, usually to one decimal.
- Converting feet and inches badly. 5 ft 6 in is 66 inches (5 × 12 + 6), not 5.6 feet.
If you want to confirm your arithmetic, enter the same figures in the BMI calculator. To convert a height between units first, the height converter handles feet, inches, centimetres and metres.
Reading the result
For adults, the World Health Organization groups BMI into the bands below. They are screening categories for populations, and they do not describe any one person's health.
| BMI | Category |
|---|---|
| Below 18.5 | Underweight |
| 18.5 to 24.9 | Healthy weight (normal range) |
| 25.0 to 29.9 | Overweight |
| 30.0 to 34.9 | Obesity, class I |
| 35.0 to 39.9 | Obesity, class II |
| 40.0 and above | Obesity, class III |
Both examples above, 23.5 and 24.2, fall in the 18.5 to 24.9 band. Some health bodies use lower thresholds for people of Asian descent, and the bands do not apply to children, who are assessed with growth charts instead.
Working backwards from a target BMI
Because BMI is weight divided by height squared, you can rearrange it to find the weight that corresponds to any BMI at a given height.
weight (kg) = BMI × height (m)²For pounds and inches: weight (lb) = BMI × height (in)² ÷ 703.
Worked example: at 1.70 m, height squared is 2.89. A BMI of 18.5 corresponds to 18.5 × 2.89 = 53.5 kg, and a BMI of 25 corresponds to 25 × 2.89 = 72.3 kg. So the 18.5 to 25 range at this height spans roughly 53.5 to 72.3 kg. The article on how a healthy weight range is calculated applies this to a range of heights, and the healthy weight calculator does it for you.
This article is general education and not medical advice. BMI is only a screening number. For questions about your own weight or health, speak to a doctor or other qualified health professional.
- BMI Calculator: Enter your height and weight to see your body mass index, the weight category it falls into and how far you sit from the edges of the healthy range. The guide explains the formula, the categories and what BMI can and cannot tell you.
- Healthy Weight Calculator: Enter your height to see the weight range that corresponds to a body mass index between 18.5 and 25. The guide explains how the range is worked out and where it falls short.
- Height Converter: Enter a height, choose the unit it is in and the unit you want, and the converted value appears instantly. It works for any length from nanometers to miles, with centimeters, meters, feet and inches being the ones people use for body height.
This article is general information, not professional advice. See our Disclaimer and Editorial Policy.
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