BMI Formula Explained
Understand the BMI formula step by step, including metric and imperial versions, examples, and common calculation mistakes.
Quick answer
The BMI formula is weight divided by height squared. In metric units, BMI = kg ÷ m². In imperial units, BMI = 703 × lb ÷ in². The formula creates a height-adjusted weight number so people of different heights can be compared more fairly than by weight alone.
Metric formula
BMI = weight (kg) ÷ height² (m²)
If someone weighs 80 kg and is 1.80 m tall, the calculation is 80 ÷ (1.80 × 1.80) = 24.7. The height must be in metres, not centimetres.
Imperial formula
BMI = 703 × weight (lb) ÷ height² (in²)
The number 703 adjusts the formula for pounds and inches. Without this conversion factor, the result would not match the standard BMI scale.
Worked examples
| Weight | Height | Formula | BMI |
|---|---|---|---|
| 70 kg | 1.70 m | 70 ÷ 1.70² | 24.2 |
| 90 kg | 1.80 m | 90 ÷ 1.80² | 27.8 |
| 160 lb | 70 in | 703 × 160 ÷ 70² | 23.0 |
| 200 lb | 72 in | 703 × 200 ÷ 72² | 27.1 |
Why height is squared
Body mass tends to rise with height, but not in a simple one-to-one way. Squaring height makes the formula more stable across different heights. It is still imperfect, but it is more useful than comparing weight alone.
Common calculation mistakes
- Using centimetres instead of metres in the metric formula.
- Forgetting to square height.
- Using pounds with the metric formula.
- Forgetting the 703 conversion factor for imperial units.
- Rounding too early.
- Typing height as 1.8 cm instead of 1.8 m.
Practical takeaway
A calculator removes most arithmetic errors, but understanding the formula helps you spot impossible results. If a BMI result looks extremely high or low, check units first before interpreting the category.
FAQ
Is BMI a diagnosis?
No. BMI is a screening-style number based on height and weight. It can suggest a broad weight category, but it cannot diagnose health, body fat, fitness, or medical risk by itself.
Can BMI be wrong?
Yes. BMI can be misleading for muscular people, older adults, some ethnic groups, people with fluid retention, pregnant people, and anyone whose body composition differs from average assumptions.
Should I use BMI alone?
No. It is better used with waist measurement, body composition, medical history, fitness level, blood pressure, blood markers, and professional context when needed.
What is the metric BMI formula?
BMI = weight in kilograms divided by height in metres squared.
What is the imperial BMI formula?
BMI = 703 × weight in pounds divided by height in inches squared.
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