How Is BMI Calculated?
Instant Answer
BMI = weight (kg) ÷ height (m)². In imperial: BMI = weight (lbs) × 703 ÷ height (inches)². Example: 75 kg (165 lbs), 175 cm (5'9"): BMI = 75 ÷ 1.75² = 75 ÷ 3.0625 = 24.5. The formula was created by Adolphe Quetelet in 1832 and adopted by the WHO as a population screening tool.
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BMI = weight (kg) ÷ height (m)². In imperial: BMI = weight (lbs) × 703 ÷ height 💪 — calculated at snapbodycalc.com
The BMI Formula Explained
BMI (Body Mass Index) uses one of the simplest formulas in medicine. Metric formula: BMI = weight (kg) ÷ height (m)². You square your height in meters and divide your weight by that number. Imperial formula: BMI = weight (lbs) × 703 ÷ height (inches)². The 703 factor converts from imperial to metric units. The formula produces a single number that represents your weight-to-height ratio. This number is then compared against WHO classification ranges: below 18.5 = underweight, 18.5–24.9 = normal, 25.0–29.9 = overweight, 30.0+ = obese. The beauty of the formula is its simplicity — you need only a scale and a tape measure. The limitation is equally simple: it can't tell what your weight is made of.
Step-by-Step Calculation Examples
Example 1 — Metric: A person weighing 70 kg (154 lbs) at 170 cm (5'7"). Step 1: Convert height to meters: 170 cm = 1.70 m. Step 2: Square the height: 1.70 × 1.70 = 2.89. Step 3: Divide weight by squared height: 70 ÷ 2.89 = 24.2. Result: BMI = 24.2 (normal weight). Example 2 — Imperial: A person weighing 180 lbs (81.6 kg) at 5'10" (70 inches / 178 cm). Step 1: Multiply weight by 703: 180 × 703 = 126,540. Step 2: Square the height in inches: 70 × 70 = 4,900. Step 3: Divide: 126,540 ÷ 4,900 = 25.8. Result: BMI = 25.8 (overweight). Example 3: A person weighing 55 kg (121 lbs) at 165 cm (5'5"): 55 ÷ (1.65)² = 55 ÷ 2.7225 = 20.2 (normal weight).
Why Height Is Squared (The Math Behind It)
You might wonder why height is squared rather than simply dividing weight by height. The answer lies in how bodies scale. If you simply divided weight by height, taller people would always appear 'heavier' relative to shorter people, because weight scales roughly with the cube of height (volume increases in three dimensions) while height is one-dimensional. Squaring height provides a better approximation of the relationship between weight and height for the human body's proportions. However, this is still imperfect — Quetelet originally developed this formula in 1832 using data from Belgian and Scottish populations, and it tends to overestimate BMI in tall people and underestimate in short people. Some researchers have proposed BMI = weight ÷ height^2.5 as a correction, but the standard formula persists due to its simplicity and widespread adoption.
Quick Reference BMI Table
Here's what specific weights produce at common heights. At 160 cm (5'3"): 50 kg (110 lbs) = BMI 19.5, 55 kg (121 lbs) = BMI 21.5, 60 kg (132 lbs) = BMI 23.4, 65 kg (143 lbs) = BMI 25.4. At 170 cm (5'7"): 55 kg (121 lbs) = BMI 19.0, 65 kg (143 lbs) = BMI 22.5, 75 kg (165 lbs) = BMI 26.0, 85 kg (187 lbs) = BMI 29.4. At 175 cm (5'9"): 60 kg (132 lbs) = BMI 19.6, 70 kg (154 lbs) = BMI 22.9, 80 kg (176 lbs) = BMI 26.1, 90 kg (198 lbs) = BMI 29.4. At 180 cm (5'11"): 65 kg (143 lbs) = BMI 20.1, 75 kg (165 lbs) = BMI 23.1, 85 kg (187 lbs) = BMI 26.2, 95 kg (209 lbs) = BMI 29.3. At 185 cm (6'1"): 70 kg (154 lbs) = BMI 20.5, 80 kg (176 lbs) = BMI 23.4, 90 kg (198 lbs) = BMI 26.3, 100 kg (220 lbs) = BMI 29.2.
History of the BMI Formula
Belgian mathematician Adolphe Quetelet created the formula in 1832, calling it the 'Quetelet Index.' He wasn't a physician — he was a statistician studying 'l'homme moyen' (the average man) using data from military conscripts. The formula wasn't designed to assess individual health; it was a tool for studying population-level weight distributions. It wasn't until 1972 that American researcher Ancel Keys renamed it 'Body Mass Index' and proposed it as a practical (if imperfect) measure of obesity. The WHO adopted it in the 1990s as the global standard for weight classification. This history matters because it explains BMI's limitations: a formula designed for 19th-century Belgian populations wasn't built to handle the diversity of modern human body types, ethnicities, and fitness levels.
Limitations of the BMI Calculation
The BMI formula has well-documented blind spots. It doesn't measure body composition — a bodybuilder and a couch potato can have identical BMIs. It doesn't account for age — older adults lose muscle and gain fat without weight change, making the same BMI riskier. It doesn't adjust for ethnicity — Asian populations face elevated health risks at lower BMIs (WHO recommends different cutoffs: overweight at 23 instead of 25 for Asian populations). It doesn't capture fat distribution — visceral fat (around organs) is far more dangerous than subcutaneous fat, but BMI treats all weight equally. Despite these limitations, BMI remains the most widely used screening tool because of its simplicity. For a more complete picture, combine it with body fat percentage, waist circumference, and waist-to-hip ratio — all available in our free calculator suite.