DRV-013

BMI, and where the 703 comes from

Nearly every US site quotes 703 without explaining it. It is a pure unit conversion, and explaining it costs two lines.

The setup

BMI is mass divided by the square of height. In metric units that is kilograms over metres squared and needs no constant at all. The 703 that appears in the imperial form is not an empirical coefficient. It is the conversion between the two unit systems.

The derivation

Step 1: Start from the metric definition

There is nothing to derive here; this is the definition.

BMI = kg / m^2

Step 2: Substitute the unit conversions

A pound is exactly 0.45359237 kg and an inch is exactly 0.0254 m, both by definition rather than by measurement.

0.45359237 kg/lb / (0.0254 m/in)^2 = 0.45359237 / 0.00064516

Step 3: Evaluate

The quotient is 703.07, universally rounded to 703. That is the entire mystery.

BMI = 703 * lb / in^2

bmi = kg / m^2 = 703 * lb / in^2

Checks that prove it is right

A formula you cannot test is a formula you have to trust. These take seconds, and they are what separate a derivation from a formula restatement.

The same person, both unit systems → Identical BMI to two decimal places

If the two forms disagree, the constant is wrong somewhere. The calculator asserts this as a golden case rather than trusting it.

Doubling height at constant mass → BMI falls to a quarter

The inverse-square in height is why BMI systematically overstates adiposity in short people and understates it in tall ones.

Worked example

75 kg at 178 cm.

Metric: 75 ÷ 1.78² = 23.67. Imperial: 165.35 lb ÷ 70.08² × 703 = 23.67. On the standard WHO bands that is healthy. On the thresholds India applies (overweight at 23 rather than 25, obese at 25 rather than 30) the same figure is overweight. Both classifications are correct for their population, and a calculator that only knows the WHO bands is giving an Indian user the wrong answer to the question they actually asked.

Both unit paths computed by the anthropometric engine and asserted to agree.

What it assumes

BMI is a population screening measure. It is not a diagnosis and not a measure of body composition.

Where the formula stops being valid

Stating limits plainly is more useful than pretending there are none, and it is the item competitors most consistently omit.

It does not distinguish fat from muscle, so a trained athlete can register as overweight.
It was developed on European populations. Asian populations carry elevated metabolic risk at lower BMI, which is why India applies lower cut-offs.
It is not valid for children, for whom age-and-sex percentile charts are used instead, nor during pregnancy.