BMI calculation: where the imperial formula's '703' constant actually comes from
I always wondered why the American BMI formula has that oddly specific '703' multiplied in, until I traced through the unit conversion and realized it's purely there to convert pounds and inches into the metric kg/m² sca
We write the way we argue on the bench: exact factor, one sharp trap, one worked example you can re-check.
I always wondered why the American BMI formula has that oddly specific '703' multiplied in, until I traced through the unit conversion and realized it's purely there to convert pounds and inches into the metric kg/m² scale the formula is actually built on.
I still keep a screenshot of this relationship because memory is where the wrong cousin of a unit sneaks in.
The factor that settles arguments
This is the relationship our converters use. Screenshot it if you have to — just stop re-deriving it from a half-remembered blog post.
BMI (imperial) = 703 × weight(lb) ÷ height(in)² — 703 converts lb/in² into the metric kg/m² scale
Write that line once at the top of your notes. Every later arithmetic step should point back to it instead of inventing a friendlier number mid-stream.
The mistake that keeps showing up
Using the metric BMI formula (weight in kg ÷ height in m, squared) with imperial inputs (pounds and inches) without including the 703 conversion constant — the result comes out numerically nonsensical.
I still write the unit next to every intermediate value. It looks pedantic until it catches the one swap that would have shipped wrong.
- Write down the known value in lb ÷ in² (imperial BMI ratio).
- Confirm the target unit is really BMI (kg/m² scale), not a similar-looking one.
- Apply the factor: BMI (imperial) = 703 × weight(lb) ÷ height(in)² — 703 converts lb/in² into the metric kg/m² scale.
- Round only at the end, to the precision your tool or spec supports.
Worked example
You weigh 150 lb and are 66 inches tall, and want to calculate BMI using pounds and inches directly.
150 lb at 66 in: 703 × 150 ÷ 66² = 703 × 150 ÷ 4,356 = 24.2 BMI.
That's a BMI of 24.2 — the 703 constant is doing the unit conversion work between imperial inputs and the metric kg/m² scale BMI is defined on.
I usually convert once, write the answer with units, then convert back. That two-step habit has saved more weekends than any fancy app.
Quick reference table
| lb ÷ in² (imperial BMI ratio) | Calculation | BMI (kg/m² scale) |
|---|---|---|
| 1 | 1 × — | — |
| 2 | 2 × — | — |
| 5 | 5 × — | — |
| 10 | 10 × — | — |
Use the table for speed once you trust the factor. Do not use it as a substitute for understanding which definition of the unit you are on.
Why the exact number matters
BMI is a widely used (if imperfect) screening metric — getting the formula's unit-conversion constant wrong produces a number that looks plausible but is actually incorrect.
Precision is not about showing off decimals. It is about making sure the shopping list, the machine setting, and the acceptance check are all describing the same physical quantity.
Pocket recap
The imperial BMI formula bakes in a 703 conversion constant specifically so pounds and inches produce the same numeric scale as the metric kg/m² definition — don't drop it when working in imperial units.
Keep the converter link nearby for the next time the same debate shows up in a group chat. Re-typing the factor from memory is how the wrong cousin of a unit sneaks back in.
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FAQ
What is the exact lb ÷ in² (imperial BMI ratio) to BMI (kg/m² scale) factor here?+
BMI (imperial) = 703 × weight(lb) ÷ height(in)² — 703 converts lb/in² into the metric kg/m² scale
Should I round partway through the calculation?+
No — carry full precision through the multiplication and round only the final answer, to the precision your tool, gauge, or spec actually supports.
What's the single biggest mistake people make with this conversion?+
Using the metric BMI formula (weight in kg ÷ height in m, squared) with imperial inputs (pounds and inches) without including the 703 conversion constant — the result comes out numerically nonsensical.
This article was written by The Turbo Unit Converter engineering desk (Applied units & field metrology) and last reviewed on 2026-07-20 against NIST SP 811 and the BIPM SI Brochure. Read our full editorial policy.