How to calculate BMI by hand (metric and imperial)

BMI has a reputation for being confusing, but the formula itself is two steps: divide, then square. Almost every by-hand mistake comes from a unit slip — squaring centimeters instead of meters, or forgetting the imperial formula needs its own conversion constant — not from the math being genuinely hard. Here is the full calculation, worked both ways.

The metric formula

BMI = weight (kg) ÷ height (m)²

Worked example: a person weighing 70 kg at 1.75 m tall. First square the height: 1.75 × 1.75 = 3.0625. Then divide weight by that: 70 ÷ 3.0625 ≈ 22.86. That falls inside the WHO “normal weight” band of 18.5–24.9, so this person’s BMI reads as healthy by the standard category boundaries.

The most common by-hand error at this step is squaring height in centimeters (175) instead of meters (1.75) — 175² is 30,625, and dividing 70 by that gives 0.0023, a number so far off it’s an obvious red flag, but people transcribing by hand sometimes miss it. Always convert to meters before squaring.

The imperial formula

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

The 703 constant exists purely to convert pounds and inches into the metric formula’s kilograms and meters in one step, so you don’t have to convert units manually first. Worked example: 154 lb at 5’9” (69 inches). Square the height: 69 × 69 = 4,761. Multiply weight by 703: 154 × 703 = 108,262. Divide: 108,262 ÷ 4,761 ≈ 22.74 — close to, but not identical to, what the metric formula on the equivalent metric inputs would give, purely due to the imperial constant’s rounding. For the conversion logic behind pounds and inches themselves, see our ideal weight formulas guide, which covers the related (but distinct) height-weight formulas doctors use.

Side-by-side comparison

Why calculators still round differently

Even two tools both using the “correct” formula can disagree slightly. Some use 703 for the imperial constant, others use 704.5 (a different, also-accepted rounding of the same conversion). Some round your height to the nearest whole inch or centimeter before calculating; others keep full decimal precision. None of this changes which WHO category you land in unless your BMI sits right on a boundary — but it does explain why manually checking a calculator’s output against your own by-hand math might differ by a tenth of a point. For what those category boundaries mean and where they hold up, see is BMI accurate? This guide is educational only, not medical advice.