BMI Formula
Body Mass Index formula for metric and imperial units.
Learn how to calculate BMI with worked examples and interpretation tables.
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The Formula
BMI = weight (kg) / height² (m²)
BMI = 703 × weight (lb) / height² (in²)
BMI = 703 × weight (lb) / height² (in²)
Body Mass Index (BMI) is a simple screening measure that estimates body fat based on weight and height. It was devised in 1832 by the Belgian mathematician Adolphe Quetelet.
BMI does not measure body fat directly. It does not account for muscle mass, bone density, or fat distribution.
Variables
| Symbol | Meaning |
|---|---|
| BMI | Body Mass Index (kg/m²) |
| weight | Body weight in kilograms (or pounds for imperial) |
| height | Height in meters (or inches for imperial) |
| 703 | Conversion factor for imperial units |
BMI Categories (Adults)
| BMI Range | Category |
|---|---|
| Below 18.5 | Underweight |
| 18.5 – 24.9 | Normal weight |
| 25.0 – 29.9 | Overweight |
| 30.0 and above | Obese |
Example 1 — Metric
A person weighs 75 kg and is 1.78 m tall. What is their BMI?
BMI = weight / height²
BMI = 75 / (1.78)²
BMI = 75 / 3.1684
BMI = 23.7 (Normal weight)
Example 2 — Imperial
A person weighs 180 lb and is 5'10" (70 inches) tall. What is their BMI?
BMI = 703 × weight / height²
BMI = 703 × 180 / (70)²
BMI = 126,540 / 4,900
BMI = 25.8 (Overweight)
Limitations
- Athletes with high muscle mass may have a high BMI but low body fat
- Elderly people may have a normal BMI but higher body fat due to muscle loss
- BMI does not distinguish between fat stored around the waist (visceral fat) and fat elsewhere
- Children and teens require age-specific BMI percentile charts
When to Use It
- Quick screening tool for general weight status
- Population-level health studies and statistics
- Starting point for health assessments (not a diagnostic tool on its own)
Key Notes
- Formula: BMI = mass (kg) / height² (m²): A dimensionless index that scales mass to height squared — partially correcting for body size. At fixed BMI, heavier (taller) people have proportionally more body mass, but the index assumes body composition scales with height squared rather than height cubed.
- WHO adult categories: Underweight: <18.5; Normal weight: 18.5–24.9; Overweight: 25–29.9; Obese Class I: 30–34.9; Class II: 35–39.9; Class III (severe): ≥40. These thresholds were established from epidemiological studies linking BMI to cardiovascular and metabolic risk.
- Biological limitations: BMI cannot distinguish fat mass from lean mass. Athletes can have BMI >25 with low body fat; elderly individuals may have "normal" BMI with high fat percentage (sarcopenic obesity). Body fat percentage, waist-to-height ratio, and DEXA scanning are more informative measures.
- Population-specific thresholds: Asian populations show increased metabolic risk (diabetes, hypertension) at lower BMIs. Proposed cutoffs: overweight ≥23; obese ≥27.5. Some countries use these lower thresholds for clinical guidelines in Asian patients.
- Applications: BMI is used in large-scale epidemiological studies (its major advantage is simplicity — just height and weight), clinical screening to trigger further assessment, pediatric growth monitoring (BMI-for-age percentile charts), and as an eligibility criterion for bariatric surgery or weight loss programs.