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BMI Formula Explained With Metric and Imperial Measurements

Master the BMI formula in metric and imperial units — worked examples, unit conversions, practice problems, and common mistakes to avoid.

What is the BMI formula in metric and imperial units?

The BMI formula expresses the same relationship — weight relative to height squared — in two unit systems. Metric: BMI = weight (kg) divided by height (m) squared. Imperial: BMI = 703 × weight (lb) divided by height (in) squared. Both give the same answer for the same person: 75 kg at 1.72 m gives about 25.4, and the equivalent 165 lb at 5 ft 8 in gives about 25.1.

Same body, same number — just two ways of writing the math.

One formula, two unit systems

The BMI formula expresses the same relationship — weight relative to height squared — in two unit systems. You don't get a different answer depending on your country; the formulas are unit conversions of each other. The 703 in the imperial version exists only because pounds and inches don't align decimally the way kilograms and meters do. Learn one concept and you've learned both.

The metric BMI formula

The metric BMI formula is beautifully simple: BMI = weight (kg) / [height (m)]². Worked example: 75 kg, 1.72 m. Square the height: 1.72 × 1.72 = 2.9584. Divide: 75 / 2.9584 = 25.35, so BMI ≈ 25.4. Because the metric system is decimal-based, the BMI formula needs no fudge factors — kilograms per square meter is the whole story. If you measured height in centimeters, divide by 100 first: 172 cm becomes 1.72 m. Never plug centimeters straight into the formula.

The imperial BMI formula

The imperial BMI formula looks messier because pounds and inches do not align decimally: BMI = 703 × weight (lb) / [height (in)]². Worked example: 165 lb, 5 ft 8 in. Convert height to inches: 5 × 12 + 8 = 68 in. Square it: 68 × 68 = 4,624; multiply the weight: 703 × 165 = 115,995; divide: 115,995 / 4,624 = 25.09, so BMI ≈ 25.1. The extra constant is doing the unit bookkeeping for you.

Where does 703 come from?

The 703 is not magic — it is pure unit conversion. One kilogram equals 2.20462 pounds and one meter equals 39.3701 inches; converting kg/m² to lb/in² produces a factor that rounds to 703. It keeps the imperial BMI formula giving the same numbers as the metric one. If you ever forget it, the answer you get without it — a tiny fraction near zero — will remind you instantly.

Side-by-side: the same person, both formulas

Take someone who is 1.75 m (68.9 in) and 80 kg (176.4 lb). Metric: 80 / (1.75 × 1.75) = 80 / 3.0625 = 26.12. Imperial: 703 × 176.4 / (68.9²) = 124,009 / 4,747 = 26.12. Identical. This is the proof that the BMI formula is one idea in two costumes — pick whichever costume matches your scale and tape measure.

Converting measurements between systems

Keep these conversions handy: 1 kg = 2.20462 lb (divide pounds by 2.205 for kilograms); 1 lb = 0.4536 kg; 1 inch = 2.54 cm = 0.0254 m. Worked conversion: 5 ft 4 in and 140 lb. Height: 64 in × 0.0254 = 1.6256 m (or 162.6 cm). Weight: 140 / 2.205 = 63.5 kg. Then BMI = 63.5 / (1.6256²) = 63.5 / 2.6426 = 24.03, so BMI ≈ 24.0, in the healthy range.

Which system should you use?

Use whichever matches your scale and tape measure — converting first and calculating second introduces extra chances to slip. If your scale reads pounds and your wall chart shows feet and inches, use the imperial BMI formula directly. If everything is metric, use the metric version. Accuracy comes from consistent, careful measurement, not from the system you choose.

Common unit mistakes to avoid

Centimeters straight into the metric BMI formula — always convert to meters first, or multiply the result by 10,000. Feet instead of total inches in the imperial formula — 5.8 ft is not 58 inches (it is 5 ft 10 in = 70 in); the decimal notation misleads. Forgetting the 703, which collapses the imperial result to a fraction near zero. Squaring after rounding height — keep full precision until the final division, especially near category boundaries like 24.9/25.0. Mixing shoe-on height with barefoot weight standards — consistent conditions beat "official" conditions you cannot reproduce.

Practice problems with answers

Test yourself with the BMI formula before trusting a calculator. Problem 1 (metric): 68 kg, 1.65 m. Solution: 1.65² = 2.7225; 68 / 2.7225 = 24.98 ≈ 25.0 — right on the boundary between healthy and overweight. Problem 2 (imperial): 200 lb, 6 ft 0 in (72 in). Solution: 72² = 5,184; 703 × 200 = 140,600; 140,600 / 5,184 = 27.12 ≈ 27.1 — overweight range. Problem 3 (conversion): 5 ft 2 in, 120 lb. First convert: 62 in × 0.0254 = 1.5748 m; 120 / 2.205 = 54.4 kg. Then 54.4 / (1.5748²) = 54.4 / 2.4800 = 21.9 — comfortably in the healthy range. If all three answers came out right, you have fully mastered the BMI formula in both systems — unit conversions included.

What the formula assumes

Both versions of the BMI formula assume weight scales with height squared — a good approximation for population screening, though imperfect for very muscular or very tall individuals. The formula also doesn't see body composition; two people with the same BMI can carry very different amounts of fat and muscle. Use the number as a starting point, not a verdict.

Related BMITool tools and guides

Check your body mass index with the BMITool BMI calculator, and read more helpful articles on the BMI formula, body composition, and healthy weight management.

Key takeaway for BMI Formula Explained With Metric and Imperial Measurements

The BMI formula is one idea — weight over height squared — written two ways: kg/m² in metric, 703 × lb/in² in imperial. Both give the same person the same number; the 703 is pure unit conversion, and the biggest pitfalls are centimeter mix-ups and forgotten constants.

Frequently Asked Questions

Why does the imperial BMI formula use 703?

Because pounds and inches don't align decimally like kilograms and meters do. The 703 converts lb/in² to the same scale as kg/m², so both versions of the BMI formula give identical results.

Which BMI formula should I use?

Whichever matches your tools — use the metric BMI formula if your scale reads kilograms, the imperial one if it reads pounds. Converting first and calculating second just adds chances to slip.

Why do I get a wrong answer when I use centimeters?

The metric BMI formula needs height in meters, not centimeters. Divide centimeters by 100 first — or multiply your result by 10,000. Centimeters straight into the formula is the most common unit mistake.

Do I square height before or after converting units?

Convert first, then square. Convert height fully to meters (or inches) with full precision, square it, and divide — especially near category boundaries like 24.9 and 25.0, where rounding early can flip the result.

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