BMI Formula – Body Mass Index Formula

The complete BMI formula for both metric and imperial units, with variable definitions, derivation, and fully worked examples.

Formula

BMI = \frac{weight (kg)}{height ^{2} (m ^{2} )}

Body Mass Index equals body weight in kilograms divided by height in metres squared. An imperial variant uses a conversion factor of 703.

Variables

Symbol	Name	Description	Unit
BMI	Body Mass Index	The resulting index value	kg/m²
W	Weight	Body weight	kg (or lbs)
H	Height	Body height	m (or inches)
703	Conversion factor	Used only in the imperial variant to preserve kg/m² units	—

How to Use

Obtain weight in kg (metric) or lbs (imperial).
Obtain height in metres (metric) or total inches (imperial).
Metric: square the height in metres, then divide weight by that value.
Imperial: multiply weight in lbs by 703, then divide by height in inches squared.
Compare the result to the WHO BMI category table.

Examples

1. Metric: person weighing 70 kg, 175 cm tall.

Convert height to metres: 175 cm ÷ 100 = 1.75 m, then apply the formula.

BMI = \frac{70}{1.7 5 ^{2}} = \frac{70}{3.0625} \approx 22.9

ℹ22.9 falls in the Normal weight range (18.5–24.9).

2. Imperial: person weighing 200 lbs, 6 ft 0 in tall.

Convert height to total inches: 6 × 12 + 0 = 72 inches, then apply the imperial formula.

BMI = \frac{703 \times 200}{7 2 ^{2}} = \frac{140600}{5184} \approx 27.1

⚠27.1 falls in the Overweight range (25.0–29.9).

3. What weight range is normal for someone 1.70 m tall?

Rearrange the formula to solve for weight: W = BMI × H²

W_{m i n} = 18.5 \times 1.7 0^{2} = 18.5 \times 2.89 = 53.5 kg

W_{m a x} = 24.9 \times 1.7 0^{2} = 24.9 \times 2.89 = 71.9 kg

ℹNormal weight range for a 1.70 m person: 53.5 kg – 71.9 kg.

4. BMI category reference table

Category	BMI Range	Interpretation
Underweight	< 18.5	May indicate nutritional deficiency
Normal weight	18.5 – 24.9	Associated with lowest health risk
Overweight	25.0 – 29.9	Moderately increased risk
Obese — Class I	30.0 – 34.9	High risk
Obese — Class II	35.0 – 39.9	Very high risk
Obese — Class III	≥ 40.0	Extremely high risk