Behind every BMI result is a surprisingly simple piece of math. The bmi calculation formula only needs two inputs — height and weight — and produces a single number that’s been used in medicine and public health for decades. If you’ve ever wanted to check a result by hand, or just understand what’s actually happening when you enter your numbers into a calculator, this breaks down the exact bmi calculation formula in both metric and imperial units, with a worked example for each.
The Metric BMI Calculation Formula
In metric units, the bmi calculation formula is:
BMI = weight (kg) ÷ height (m)²
That means you divide your weight in kilograms by your height in meters, squared — not your height in meters multiplied by two, but height times itself.
Worked example: Say someone weighs 70 kg and is 1.75 m tall.
- Square the height: 1.75 × 1.75 = 3.0625
- Divide weight by that number: 70 ÷ 3.0625 = 22.86
Their BMI comes out to roughly 22.9, which falls inside the normal, healthy weight range.
The Imperial BMI Calculation Formula
In pounds and inches, the bmi calculation formula needs one extra step, because pounds and inches aren’t natively metric units:
BMI = (weight in lbs ÷ height in inches²) × 703
The 703 figure is a conversion factor (more precisely 703.0696, rounded for practical use) that converts the pounds-and-inches ratio into the same scale as the metric kg/m² result, so both formulas land on the same final number for the same person.
Worked example: Say someone weighs 154 lbs and is 68 inches (5’8″) tall.
- Square the height: 68 × 68 = 4,624
- Divide weight by that number: 154 ÷ 4,624 = 0.0333
- Multiply by 703: 0.0333 × 703 = 23.4
Their BMI comes out to roughly 23.4 — close to the metric example above, as you’d expect from someone of a similar relative build.
Why Does the 703 Factor Exist?
The imperial bmi calculation formula needs that 703 multiplier purely to bridge unit systems. Kilograms and meters convert cleanly to a kg/m² ratio, but pounds and inches don’t, so the constant does that conversion work in a single step — the CDC’s own formula reference lists this exact calculation as weight (pounds) ÷ height (in)² × 703. Without it, dividing pounds by inches squared would produce a completely different — and meaningless — number. It’s not a rounding shortcut or an approximation of health risk; it’s strictly a unit-conversion constant, mathematically derived from the metric formula.
Step-by-Step: How to Calculate BMI by Hand
Live BMI Calculator
Enter your height and weight below and watch the exact formula from this article run in real time.
The result recalculates instantly from whatever you enter — it’s the live formula, not a fixed example.
If you want to calculate bmi by hand without a calculator app, the process is the same regardless of which unit system you use:
- Get an accurate height and weight. Small errors compound once you square the height figure.
- Convert to the right units if needed. Kilograms and meters for metric; pounds and inches for imperial.
- Square the height figure.
- Divide weight by that squared height number.
- If using imperial units, multiply the result by 703.
- Round to one decimal place for a standard BMI reading.
The whole bmi equation only takes a minute with a basic calculator, and doing it manually once or twice is a good way to understand exactly what an online tool is doing behind the scenes.
Metric vs. Imperial: A Quick Comparison
| Metric | Imperial | |
|---|---|---|
| Formula | kg ÷ m² | (lbs ÷ in²) × 703 |
| Units needed | Kilograms, meters | Pounds, inches |
| Extra constant | None | 703 |
| Common region | Most of the world | United States |
Both versions of the bmi equation metric imperial comparison always produce the same result for the same person — they're just two different unit paths to the identical BMI index number.
People Also Ask
How is BMI calculated?
BMI is calculated by dividing weight by the square of height, using either kg/m² directly (metric) or (lbs/in²) × 703 (imperial) to reach the same result.
What is the 703 in the BMI formula for?
It's a conversion constant that lets the imperial pounds-and-inches version of the formula produce the same result as the metric kg/m² version.
Can I calculate BMI without a calculator?
Yes — the bmi calculation formula only involves squaring a number, dividing, and (for imperial units) one multiplication step, all doable with basic arithmetic or a phone calculator.
Is the BMI formula the same for everyone?
The core math is identical for all adults regardless of age or sex; interpretation of the result (via category cutoffs) is what differs for children and teens, who use age- and sex-specific percentile charts instead of fixed thresholds.
Skip the Manual Math
Working through the bmi calculation formula by hand is a useful exercise, but it's easy to make a small arithmetic slip, especially with the imperial version's extra multiplication step. If you'd rather get an instant, error-free result, skip the math and use our BMI calculator instead — just enter your height and weight and it applies the exact same equation shown above automatically.
The Bottom Line
The bmi calculation formula is straightforward once you see it broken down: square the height, divide the weight by that number, and — for imperial units — multiply by 703. Whether you calculate bmi by hand or let a tool do it instantly, both paths lead to the exact same kg/m² result, which is then compared against the standard weight category ranges to give the final reading.