Body Mass Index Formula
A single equation sits behind every BMI chart and health screening tool–the body mass index formula. Whether you measure in kilograms or pounds, the math follows the same core principle: weight relative to height squared. Knowing the formula lets you calculate your number manually and verify automated results.
What Is the Body Mass Index Formula?
The body mass index formula expresses a person’s weight-to-height ratio in a single value. The metric version works directly with SI units, while the imperial version includes a conversion factor.
Metric (kg/m²):
BMI = weight (kg) / height² (m²)Imperial (lb/in²):
BMI = [weight (lb) / height² (in²)] × 703
The constant 703 comes from converting pounds to kilograms (1 lb = 0.453592 kg) and inches to metres (1 in = 0.0254 m). Dividing 0.453592 by 0.0254² produces approximately 703, so multiplying by 703 gives the same BMI as the metric formula.
To skip the manual arithmetic, enter your details in the BMI calculator above. It applies the same body mass index formula instantly–simply choose your unit system and see your result.
Step-by-Step BMI Calculation Examples
The math becomes clearer with real numbers. Try both metric and imperial examples to see how the formula works.
Metric example
Weight: 70 kg
Height: 1.75 m
- Square the height: 1.75² = 3.0625
- Divide weight by squared height: 70 / 3.0625 = 22.86
BMI = 22.9 (normal weight)
Imperial example
Weight: 154 lb
Height: 68 in
- Square the height: 68² = 4,624
- Divide weight by squared height: 154 / 4,624 ≈ 0.03330
- Multiply by 703: 0.03330 × 703 ≈ 23.4
BMI = 23.4 (normal weight)
BMI Categories and Health Risk Indicators
Once you have a number from the body mass index formula, it falls into standard weight categories. The World Health Organization defines the following ranges for adults:
| BMI range | Weight category |
|---|---|
| Below 18.5 | Underweight |
| 18.5 – 24.9 | Normal weight |
| 25.0 – 29.9 | Overweight |
| 30.0 – 34.9 | Obesity class I |
| 35.0 – 39.9 | Obesity class II |
| 40.0 and above | Obesity class III |
Higher BMI values correlate with increased risk for conditions like type 2 diabetes, cardiovascular disease, and hypertension. That said, the formula is a screening tool, not a diagnostic test.
What Are the Limitations of the BMI Formula?
The body mass index formula compares weight to height, but it doesn’t distinguish between muscle, fat, and bone. This leads to several well-known limitations:
- Athletes and muscular builds: High lean body mass can push BMI into the overweight or obese range despite low body fat.
- Age and sex differences: The same BMI may represent different amounts of body fat in men and women, or in older versus younger adults.
- Ethnic diversity: Some populations have higher body fat percentages at the same BMI, making the standard cut-offs less accurate.
- Children and teens: For ages 2–19, the calculation uses the same formula but must be interpreted with growth‑chart percentiles, not adult categories.
- Pregnancy and medical conditions: BMI is not a reliable indicator during pregnancy or for individuals with certain illnesses that affect body composition.
Additional measurements–waist circumference, waist-to-hip ratio, or direct body fat analysis–often give a fuller picture of health.
This information is for general educational purposes and is not a substitute for individual medical advice. Speak with a healthcare professional before making decisions based on BMI.