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The imperial BMI formula, step by step
Here is the exact math behind your result, using your own numbers.
BMI = 703 × weight (lb) ÷ height (in)²
- Convert your height to inches. Feet × 12, plus the extra inches: 5 ft 7 in = 5 × 12 + 7 = 67 in.
- Square your height. 67 × 67 = 4,489.
- Multiply your weight by 703. 150 × 703 = 105,450.
- Divide. 105,450 ÷ 4,489 = 23.49, which rounds to 23.5.
Why 703?
BMI was defined in kilograms and meters. The 703 converts pounds and inches so you get the same number:
- 1 pound = 0.45359237 kg
- 1 inch = 0.0254 m, so 1 square inch = 0.00064516 m²
- 0.45359237 ÷ 0.00064516 = 703.07
The CDC's formula rounds this to 703. The difference only shows up in the second decimal place, so your rounded BMI is the same either way.
Feet and inches to inches
| Height | Inches | Inches squared |
|---|---|---|
| 5 ft 0 in | 60 | 3,600 |
| 5 ft 4 in | 64 | 4,096 |
| 5 ft 7 in | 67 | 4,489 |
| 5 ft 10 in | 70 | 4,900 |
| 6 ft 1 in | 73 | 5,329 |
| 6 ft 4 in | 76 | 5,776 |
Worked examples
| Height | Weight | Calculation | BMI | Category |
|---|---|---|---|---|
| 5 ft 4 in | 140 lb | 140 × 703 ÷ 4,096 | 24.0 | Healthy weight |
| 5 ft 10 in | 190 lb | 190 × 703 ÷ 4,900 | 27.3 | Overweight |
| 6 ft 1 in | 210 lb | 210 × 703 ÷ 5,329 | 27.7 | Overweight |
Healthy weight for your height in pounds
Reverse the formula: healthy weight = BMI × inches² ÷ 703. Use 18.5 and 24.9 for the bottom and top of the healthy range.1
At 5 ft 7 in: 18.5 × 4,489 ÷ 703 = 118 lb and 24.9 × 4,489 ÷ 703 = 159 lb
Common mistakes
- Using 5.7 for 5 ft 7 in. 5 ft 7 in is 67 inches (or 5.58 feet), not 5.7 feet.
- Squaring feet instead of inches. The formula needs height in inches.
- Forgetting the 703. Pounds ÷ inches² alone gives a tiny number like 0.033.
Frequently asked questions
How do I calculate BMI in pounds?
Multiply your weight in pounds by 703 and divide by your height in inches squared. The calculator above does this and shows every step.
Do I need to convert pounds to kilograms?
No. The 703 does the conversion for you. If you prefer metric, see how to calculate BMI in cm and kg.
What about stones?
Convert stones to pounds first (stones × 14, plus pounds). See BMI in stones and pounds.
Sources
Further reading
This page is for education and is not medical advice. Talk with a healthcare professional about your weight and health.
