BMI Formula — What It Does and Does Not Tell You
Body mass index is one of the simplest formulas anybody uses in daily life, and one of the most over-interpreted. It is a ratio of two measurements and nothing more. Understanding it properly is useful twice over: it is a clean exercise in units and squares for a Class 9 or 10 student, and it stops you drawing conclusions the number cannot support.
The formula
The unit of BMI is kg/m², and that unit should be written down. In imperial units the same quantity is:
The 703 is not a mystery number. It is the conversion factor that turns lb/in² into kg/m²: 1 pound = 0.453592 kg and 1 inch = 0.0254 m, so 0.453592 ÷ (0.0254)² = 0.453592 ÷ 0.00064516 = 703.07. Same formula, different units.
Worked example 1 — metric
A person weighs 62 kg and is 1.70 m tall.
Step 1 — square the height. 1.70² = 1.70 × 1.70 = 2.89 m²
Step 2 — divide. 62 ÷ 2.89 = 21.5 kg/m²
Notice how few significant figures the data supports: a weight given as 62 kg has 2, so quoting 21.4532... would be dishonest precision.
Worked example 2 — a second case
85 kg, height 1.62 m.
1.62² = 2.6244 m²
85 ÷ 2.6244 = 32.4 kg/m²
Worked example 3 — the unit trap
This is the error the formula punishes hardest, because the answer is wrong by a factor of 10 000 and can still look like a number.
Wrong: height entered as 170 centimetres:
170² = 28 900, and 62 ÷ 28 900 = 0.00215 — obviously meaningless.
Right: convert first. 170 cm = 1.70 m, then 62 ÷ 2.89 = 21.5.
If you must work from centimetres in one line: BMI = mass (kg) × 10 000 ÷ [height (cm)]². Check: 62 × 10 000 ÷ 28 900 = 620 000 ÷ 28 900 = 21.5 ✓ — same answer, and the 10 000 is just (100)², the square of the cm-to-m factor.
Worked example 4 — imperial
A person weighs 150 lb and is 5 ft 7 in tall.
Height in inches = (5 × 12) + 7 = 67 in
67² = 4489
BMI = 703 × 150 ÷ 4489 = 105 450 ÷ 4489 = 23.5 kg/m²
Cross-check in metric. 150 lb = 150 × 0.453592 = 68.04 kg; 67 in = 67 × 0.0254 = 1.7018 m; 1.7018² = 2.8961; 68.04 ÷ 2.8961 = 23.5 ✓ The two routes agree, which is the point of the 703.
The standard categories
The widely used international cut-offs for adults are:
| BMI (kg/m²) | Standard label |
|---|---|
| below 18.5 | Underweight |
| 18.5 to 24.9 | Normal range |
| 25.0 to 29.9 | Overweight |
| 30.0 and above | Obese |
An important qualification for readers in India: public-health guidance for Indian and other Asian populations has used lower action points than the international table, because health risk tends to appear at a lower BMI in these populations. Figures around 23 and 27.5 have been used for that purpose. Which cut-offs apply to you is a clinical question — check current national guidance or ask a doctor rather than assuming the international table.
Worked example 5 — working the formula backwards
Rearranging BMI = mass ÷ height² gives mass = BMI × height², which turns a category boundary into a weight. This is a good exercise in rearranging a formula, and it shows how wide the bands actually are.
For a height of 1.70 m, height² = 2.89 m². The international "normal range" band of 18.5 to 24.9 corresponds to:
Lower end: 18.5 × 2.89 = 53.5 kg
Upper end: 24.9 × 2.89 = 72.0 kg
For a height of 1.60 m, height² = 2.56 m²:
18.5 × 2.56 = 47.4 kg and 24.9 × 2.56 = 63.7 kg
Check one: 72.0 ÷ 2.89 = 24.9 ✓
Two observations worth making. First, the band is around 18 to 19 kg wide for an adult — it is not a target weight, and a person can move several kilograms without changing category at all. Second, the same BMI number means a different weight at every height, which is the entire point of dividing by height².
What BMI cannot tell you
The formula uses total mass. It has no way to know what that mass is made of, or where it sits on the body.
- It does not separate muscle from fat. Two people of the same height and weight have identical BMI whether the weight is muscle or fat. A trained athlete can land in the "overweight" band while carrying very little body fat.
- It ignores fat distribution. Waist circumference and waist-to-height ratio carry information BMI does not.
- It is not valid for children and teenagers. Growing bodies are assessed against age-and-sex growth charts and percentiles, not the adult table above.
- It is not appropriate during pregnancy, nor for people with significant fluid retention.
- It behaves oddly at extremes of height, because mass does not really scale as height squared for very short or very tall people.
BMI is a screening number, not a diagnosis. It is used because it is cheap and quick across large populations. A single value from a formula cannot tell an individual whether they are healthy. If your result concerns you, or you are planning a change in diet or exercise, speak to a qualified doctor — not to a calculator, and not to this article.
Common mistakes
- Using centimetres instead of metres. The single biggest source of absurd answers.
- Forgetting to square the height. BMI is not mass ÷ height.
- Mixing systems — kilograms with inches, or pounds with metres. Convert everything to one system first.
- Applying the adult table to a child. It genuinely does not apply.
- Quoting six decimal places. Bathroom-scale data supports two or three significant figures at most.
- Treating a category label as a medical verdict. It is a band on a scale, and the bands themselves differ between guidelines.
Where this maths appears
| Context | Use |
|---|---|
| School maths and science (Class 8–10) | Ratios, squares, unit conversion, data handling projects |
| Biology and health education | Growth, nutrition and population-level screening |
| Statistics practice | Derived variables; the difference between a population measure and an individual one |
| Everyday life | Reading a health report without over-reading it |
Do the conversion and the squaring in one place. The Finance and Everyday section of the calculator suite includes a BMI tool, and the unit converter handles the pounds-and-inches conversions used in example 4.
Open the ABC Chemistry Calculator Suite →Unit errors like the centimetre trap above cost marks in physics and chemistry too. ABC Chemistry runs Class 11–12 chemistry coaching at its Gurugram centre plus online classes across India — abcchemistry.in.