BMI, Explained: The Math Behind Your Body Mass Index (and the 703 You Keep Seeing)

BMI is one division problem. Weight divided by height squared. That's it — and yet almost everyone gets the units wrong the first time.

The Formula

Metric: BMI = weight (kg) ÷ height (m)²

Imperial: BMI = 703 × weight (lb) ÷ height (in)²

The 703 is not a fudge factor. It converts pounds per square inch into kilograms per square metre (0.4536 ÷ 0.0254² ≈ 703.07). Both formulas give the same answer for the same person, because 703 is just the unit-conversion constant that makes imperial units behave like metric ones.

Worked Examples

Metric: 70 kg, 1.75 m → 1.75 × 1.75 = 3.0625 → 70 ÷ 3.0625 = 22.9 (healthy).

Imperial: 150 lb, 5 ft 7 in (67 in) → 150 × 703 = 105,450 → 67² = 4,489 → 105,450 ÷ 4,489 = 23.5 (healthy).

What the Number Means

The CDC categories for adults 20 and older: below 18.5 underweight, 18.5–24.9 healthy weight, 25.0–29.9 overweight, 30.0 and above obesity. The same bands apply to men and women at every adult age. They are screening bands, not a health verdict — but they are the bands every doctor, insurer, and health app is using when they quote your BMI.

Your Healthy Weight Range

Run the formula backward: weight = BMI × height². At 5 ft 9 in, BMI 18.5 is 125 lb and BMI 24.9 is 169 lb — a healthy range of 125–169 lb. Try the free BMI calculator to find your own range instantly.

5 Mistakes to Avoid

1. Forgetting to square your height.
2. Using centimetres instead of metres.
3. Using 703 with kilograms.
4. Entering 5 ft 9 in as 5.9 feet — it is 69 inches.
5. Rounding in the middle of the calculation.

The Trap

BMI is a screening tool, not a diagnosis. It does not distinguish muscle from fat — a muscular athlete can score 25.5 while carrying very little body fat. It also ignores where fat is carried: waist circumference matters too (elevated risk above 40 inches for men, 35 inches for women). And for ages 2–19, the CDC uses BMI-for-age percentiles, not these adult cutoffs.

Bottom Line

BMI is one division problem, and doing it by hand once is worth it: the formula stops being a mystery. For the full step-by-step guide, see how to calculate BMI — or skip the arithmetic and use the free BMI calculator.