BMI Metric to Imperial — Where the 703 Comes From

There is no such thing as an imperial BMI. Body mass index is defined in kilograms per square meter, and the American formula — 703 × lb ÷ in² — is the metric definition with the unit conversion folded into a single multiplier. This page is about that multiplier: where it comes from, and how converting on your own produces a different answer.

Deriving 703 from two definitions

Start with the definition, BMI = kg ÷ m², and substitute the imperial units using the values NIST fixes exactly:

• 1 pound = 0.45359237 kg
• 1 inch = 0.0254 m

A weight of W pounds is 0.45359237 × W kilograms. A height of H inches is 0.0254 × H meters, and squaring it gives 0.00064516 × H² square meters. Dividing:

BMI = (0.45359237 ÷ 0.00064516) × W ÷ H² = 703.0696 × W ÷ H²

So 703 is not an empirical constant, a correction factor or anything to do with bodies. It is 0.45359237 divided by 0.0254 squared, rounded down by seven hundredths.

What the rounding costs

Using 703 instead of 703.0696 makes every American BMI about 0.0099 percent low. In practice:

True BMI with 703.0696	Published formula with 703
18.50	18.4982
25.00	24.9975
30.00	29.9970
40.00	39.9960

At BMI 30 the difference is three thousandths of a point. It would take a person sitting within 0.003 of a category boundary for it to matter, and no scale or tape measure resolves anything close to that. The rounding is safe, and 703 is what the NHLBI and every US clinical tool use.

Converting first is not the same as converting inside

Here is the part worth the page. Two routes should give the same BMI, and usually do not:

1. Convert inside the formula. Feed pounds and inches straight into 703 × lb ÷ in².
2. Convert first. Turn pounds into kilograms and inches into meters, round both, then divide.

Take 168 lb and 68.5 in. Route one: 703 × 168 ÷ 4,692.25 = 25.17.

Route two, done the way people actually do it: 168 lb rounds to 76 kg, 68.5 in rounds to 1.74 m, and 76 ÷ 3.0276 = 25.10.

The gap is not the 703. It is the rounding you performed twice on the way. Height is squared, so an error there is roughly doubled in the result — trimming 68.5 inches to 1.74 m instead of 1.7399 m is worth more than the entire 703 approximation, several hundred times over.

The rule that follows is the same one that governs every conversion on this site: convert once, round at the end. If you are going to work in metric, convert with full precision and round the BMI, not the inputs.

The two calculators, and which to use

Use whichever takes the numbers you already have, because they are the same index:

• The BMI calculator takes pounds and inches and applies the 703 internally.
• The metric BMI calculator takes kilograms and meters directly.
• The BMI chart skips the arithmetic and gives the weight range for each height.

If you want to convert your weight and height separately for some other purpose, pounds to kg and feet and inches to meters do those without rounding on the way.

This content is informational. BMI is a screening number, not a diagnosis, and it does not distinguish muscle from fat.