BMI Formula
How BMI is calculated in metric and imperial units, where the 703 comes from, and every step worked out with your own weight and height. A chart of BMI for every height and weight is on the BMI Chart page.
The BMI formula
BMI (body mass index) is a person's weight divided by the square of their height. In metric units the answer comes out directly in kg/m²; with pounds and inches you multiply by 703 to get the same number.
Metric (kg, m)
\( \displaystyle \text{BMI} = \frac{\text{weight in kg}}{(\text{height in m})^2} \)Imperial (lb, in)
\( \displaystyle \text{BMI} = 703 \times \frac{\text{weight in lb}}{(\text{height in inches})^2} \)Height in centimetres
\( \displaystyle \text{BMI} = 10\,000 \times \frac{\text{weight in kg}}{(\text{height in cm})^2} \)Height in feet and inches
\( \displaystyle \text{BMI} = 703 \times \frac{\text{weight in lb}}{(12 \times \text{feet} + \text{inches})^2} \)The unit of BMI is kg/m², but it is usually written as a plain number such as 22.9.
Work it out with your own numbers
Adult categories (WHO). For ages 2 to 19, BMI is compared with children of the same age and sex instead: use the BMI Calculator for Kids and Teens. To skip the arithmetic, use the BMI Calculator.
Where the 703 comes from
BMI is defined in kilograms and metres. The 703 simply converts pounds and inches into those units. Both conversions are exact by definition:
- 1 pound = 0.45359237 kg
- 1 inch = 0.0254 m
Put a weight in pounds and a height in inches into the metric formula:
\( \displaystyle \begin{aligned} \text{BMI} &= \frac{\text{weight in kg}}{(\text{height in m})^2} \\ &= \frac{\text{lb} \times 0.45359237}{(\text{in} \times 0.0254)^2} \\ &= \frac{\text{lb}}{\text{in}^2} \times \frac{0.45359237}{0.0254^2} \\ &= \frac{\text{lb}}{\text{in}^2} \times \frac{0.45359237}{0.00064516} \\ &= \frac{\text{lb}}{\text{in}^2} \times 703.0696\ldots \;\approx\; 703 \times \frac{\text{lb}}{\text{in}^2} \end{aligned} \)Rounding 703.0696 down to 703 changes a BMI by less than 0.01% (at a BMI of 30, by about 0.003), far below the one decimal place BMI is quoted to. Some sources use 703.07 or 704.5; they all give the same BMI to one decimal for everyday heights and weights.
The same idea gives the centimetre version: 1 m = 100 cm, so dividing by (cm ÷ 100)² is the same as multiplying by 100² = 10 000.
Adult BMI categories
| BMI | Category (WHO) |
|---|---|
| Below 18.5 | Underweight |
| 18.5 to 24.9 | Normal (healthy) weight |
| 25 to 29.9 | Overweight |
| 30 or more | Obesity (class I 30 to 34.9, II 35 to 39.9, III 40 and over) |
Many Asian health bodies use lower cut-offs (overweight from 23, obesity from 27.5); the BMI Calculator has both. See the BMI chart for every height and weight at a glance.
Turning the formula around
Because BMI = weight ÷ height², the weight for any BMI at a given height is:
\( \displaystyle \text{weight in kg} = \text{BMI} \times (\text{height in m})^2 \) \( \displaystyle \text{weight in lb} = \frac{\text{BMI} \times (\text{height in inches})^2}{703} \)That is how the healthy weight range is found: at 1.75 m, BMI 18.5 to 24.9 is 18.5 × 3.0625 = 56.7 kg to 24.9 × 3.0625 = 76.3 kg.
Related numbers
- BMI Prime = BMI ÷ 25, so 1.00 is the top of the normal range.
- Ponderal index = weight in kg ÷ (height in m)³, which depends less on height and is sometimes used for very tall or short people.
- "New BMI" (proposed by Nick Trefethen in 2013) = 1.3 × weight in kg ÷ (height in m)2.5. It is not used by health bodies, but shows that the power of 2 is a choice.
Important notes
The BMI formula is used so widely because it is simple and needs only a scale and a tape measure, which makes it easy to compare people and whole countries. It has limits: it assumes weight grows with the square of height, but in real bodies weight grows a little faster than that, so very tall people tend to get slightly higher BMIs and short people slightly lower ones. BMI also cannot tell muscle from fat or say where the fat is, so athletes can read as overweight, and it is a screening number rather than a diagnosis.
For a full breakdown on the advantages and benefits of the BMI, see What is BMI? and the BMI Calculator.