BMI (Imperial Units)
Overview
United States clinical practice computes body mass index without converting to metric, using BMI = w_lbs ÷ h_in² × 703. The multiplier is not arbitrary: one kilogram is 2.20462 pounds and one metre is 39.3701 inches, so converting the metric definition term by term gives 39.3701² ÷ 2.20462 ≈ 703.07, rounded to 703. An adult weighing 160 lb at 68 inches computes 160 ÷ 4,624 × 703, close to 24.3 kg/m² — the same value the metric formula returns for 72.6 kg and 1.727 m. The rounding introduces an error under 0.01 percent, far below measurement noise. Because height is squared, an error of one inch shifts the result by roughly 0.7 index points for a typical adult, which is why clinical height is measured with a stadiometer rather than self-reported.
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| $w$ | Body weight | lb | Total body mass in pounds. |
| $h$ | Height | in | Standing height in inches. |
| $703$ | Conversion factor | dimensionless | Converts lb/in² to kg/m²; derived, not arbitrary. |
Computing BMI Without Converting Units
United States clinical practice calculates body mass index directly from pounds and inches:
$$BMI = \frac{w_{lbs}}{h_{in}^2} \times 703$$
An adult weighing 160 lb at 68 inches computes $160/4624 \times 703 \approx 24.3$ kg/m². The result is in metric units despite the imperial inputs, because the factor performs the conversion.
Where 703 Comes From
One kilogram is 2.20462 pounds and one metre is 39.3701 inches. Substituting into the metric definition:
$$\frac{w_{lb}/2.20462}{(h_{in}/39.3701)^2} = \frac{w_{lb}}{h_{in}^2} \times \frac{39.3701^2}{2.20462} = \frac{w_{lb}}{h_{in}^2} \times 703.07$$
The rounding to 703 introduces an error of about 0.01 percent — roughly 0.0024 index points for a BMI of 24 — which is far below measurement noise.
Sensitivity to Height
Because height is squared, measurement error in height dominates. For a typical adult, an error of one inch shifts the index by roughly 0.7 points, enough to cross a category boundary near the thresholds. Clinical protocols therefore require a stadiometer reading without shoes rather than a self-reported figure, which studies consistently find is overstated by an inch or more.
Categories
| BMI | WHO category |
|---|---|
| < 18.5 | Underweight |
| 18.5 – 24.9 | Normal weight |
| 25.0 – 29.9 | Overweight |
| ≥ 30.0 | Obese |
Derivation & History
Adolphe Quetelet proposed the weight-over-height-squared index in 1832 while developing his statistical portrait of the homme moyen, the average man; he was studying population distributions rather than individual health. Ancel Keys revived the ratio in 1972, comparing it against several alternatives in a seven-country cohort and naming it the body mass index. The imperial variant is not a separate formula but the same expression with unit conversion folded into a single constant, a device that predates pocket calculators and survives because it removes a conversion step from bedside arithmetic.
Worked Examples
5 ft 10 in, 185 lb
- Square the height: 70² = 4,900
- Divide: 185 ÷ 4,900 = 0.037755
- Apply the factor: 0.037755 × 703 = 26.54
Result: BMI 26.5, in the overweight band
Cross-check against the metric formula
- 1.778² = 3.161
- 83.9 ÷ 3.161 = 26.54
Result: Identical 26.5, confirming the factor
Edge Cases & Limitations
Height in feet and inches: Convert fully to inches first. Treating 5 ft 10 in as 5.10 understates height by more than four inches.
Muscular build: The index does not distinguish lean from fat mass, so trained athletes commonly register as overweight without excess adiposity.
Children and adolescents: Fixed adult cut-offs do not apply; paediatric assessment uses age- and sex-specific percentile charts.
Asian populations: Several health authorities apply lower thresholds, with overweight beginning at 23 and obesity at 27.5 kg/m².
Very short or tall stature: The squared denominator systematically overstates the index for short adults and understates it for tall ones.
Real-World Applications
United States primary care records BMI at routine visits, and insurers use it in underwriting. Bariatric surgery eligibility is defined by BMI thresholds, military and public-safety recruitment screens against it, and epidemiological studies use it as the standard adiposity proxy in population data.