How to Calculate BMI Without a Calculator

Try it: work out each step and check your answer

Here is the exact math behind your result, using your own numbers.

The calculator above starts in "do it by hand" mode. Enter your height and weight, then type the answer to each step and press Check.

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Step 1: square your height without a calculator

Split the number into tens and ones, then use (a + b)² = a² + 2ab + b².

67² = 60² + (2 × 60 × 7) + 7² = 3,600 + 840 + 49 = 4,489

For metric heights, work in centimeters and add the decimal point at the end:

1.75² → 175² = 170² + (2 × 170 × 5) + 5² = 28,900 + 1,700 + 25 = 30,625 → 3.0625

Step 2: multiply by 703 (pounds only)

Break 703 into 700 + 3:

150 × 700 = 105,000, and 150 × 3 = 450, so 150 × 703 = 105,450

Step 3: long division

Divide 105,450 by 4,489:

1. How many times does 4,489 go into 105,450? 4,489 × 23 = 103,247 (since 4,489 × 20 = 89,780 and 4,489 × 3 = 13,467). That's 23, with 105,450 − 103,247 = 2,203 left over.
2. First decimal place. Bring down a zero: 22,030 ÷ 4,489 = 4 (4,489 × 4 = 17,956), leaving 4,074. So far: 23.4.
3. Second decimal place, for rounding. 40,740 ÷ 4,489 = 9 (40,401). So the answer is 23.49...
4. Round to one decimal place. 23.49 rounds to 23.5.

Quick estimates

When you only need to know which category you're in, estimate:

• Metric: divide weight by height in meters, then divide again. 70 ÷ 1.75 = 40, and 40 ÷ 1.75 ≈ 23.
• Pounds: use 700 instead of 703. It's off by less than half a percent, so 150 × 700 ÷ 4,489 = 23.4 instead of 23.5.
• Is it over 25? Multiply 25 by your height squared and divide by 703. At 67 in that's 25 × 4,489 ÷ 703 ≈ 160 lb, so any weight under 160 lb gives a BMI under 25.