Reference
BMI Formula.
How Body Mass Index is calculated — metric and imperial formulas, worked examples, and a brief history of the measure.
Metric formula
BMI = weight (kg) / height (m)²
Height must be in metres, not centimetres.
Worked example
- Weight: 70 kg
- Height: 175 cm = 1.75 m
- BMI = 70 / (1.75 × 1.75)
- BMI = 70 / 3.0625
- BMI = 22.9 → Normal weight
Imperial formula
BMI = 703 × weight (lbs) / height (in)²
The factor 703 converts from lb/in² to kg/m².
Worked example
- Weight: 154 lbs
- Height: 5 ft 9 in = 69 in
- BMI = 703 × 154 / (69 × 69)
- BMI = 108,262 / 4,761
- BMI = 22.7 → Normal weight
BMI Prime
BMI Prime = BMI / 25
Normalises BMI so 1.0 = the upper boundary of healthy.
BMI Prime makes comparison easier: a value below 1.0 is healthy; above 1.0 is overweight. It was proposed by Gadzik (2006) as a dimensionless alternative to raw BMI.
Ponderal Index
PI = weight (kg) / height (m)³
Better scaling for extreme heights than BMI.
The Ponderal Index divides mass by the cube of height rather than the square, which better accounts for the fact that body volume scales with the cube of a linear dimension. It is particularly useful for very tall or very short individuals, where BMI systematically overestimates or underestimates adiposity.
History of BMI.
The formula was first proposed by Belgian polymath Adolphe Quetelet around 1832, originally called the Quetelet Index. Quetelet was a statistician, not a physician — he developed the index to describe the statistical properties of human populations, not to diagnose individuals.
The term "Body Mass Index" and its use as a health screening tool were popularised by Ancel Keys in 1972, following his analysis of 7,400 healthy men. Keys specifically noted that BMI was not appropriate for individual clinical diagnosis, only population-level correlation.
The World Health Organization adopted the current category thresholds (18.5 / 25 / 30) in 1995, and they have remained standard ever since, though many researchers advocate for adjusted cutoffs for Asian populations (≥23 for overweight, ≥27.5 for obese).