# health.bsa
Status: needs review and sign-off by a qualified clinician before it is published. Not a medical device; for decision support only; always follow local clinical guidelines.
Body surface area (BSA) in square metres from weight and height, by the two
formulas in common clinical use, each rounded half away from zero to two
decimal places:
- **Mosteller**: BSA (m²) = √( height (cm) × weight (kg) ÷ 3600 )
- **DuBois & DuBois**: A = W^0.425 × H^0.725 × 71.84, with A in cm², W in kg
and H in cm; divided by 10 000 for m² (the familiar 0.007184 × W^0.425 ×
H^0.725)
## Why both
The two disagree by up to a few per cent, more in obesity (150 kg at 165 cm is
2.62 m² by Mosteller and 2.45 m² by DuBois). Chemotherapy verification
standards accept either but insist on consistency: a protocol, a prescriber
and a pharmacist checking the prescription must all use the same formula. So
both are returned, named, and nothing picks one silently.
## Edge cases
- Weight 1 to 650 kg, height 30 to 272 cm; anything else is refused, never
clamped. Height in metres (1.75) is the usual slip. These ranges are guard
rails for a clinician to confirm, not part of either formula.
- DuBois & DuBois derived their formula from nine subjects, one a child;
paediatric protocols often specify Mosteller (or another formula) instead.
- Two decimal places is the precision BSA is prescribed at. Some units round
further (to 0.1 m²) for dose banding; that is the caller's step.
- Powers use `math.pow` (and the square root is `math.pow(x, 0.5)`), not the
platform library, so the three languages agree to the bit (`floats exact`).
## Sources
- Du Bois D, Du Bois EF. *Clinical calorimetry, tenth paper: A formula to
estimate the approximate surface area if height and weight be known.* Arch
Intern Med 1916;17(6):863-871. The equation, the constant 71.84 and the
worked example (150 cm, 60 kg, 1.55 m²) were read from the scanned
original: https://archive.org/details/sim_jama-internal-medicine_1916-06-15_17_6
- Mosteller RD. *Simplified calculation of body-surface area.* N Engl J Med
1987;317(17):1098. doi:10.1056/NEJM198710223171717. The letter itself is
behind a paywall and was not retrieved; the equation and constant 3600 were
confirmed from the NHS Thames Valley Cancer Network, *Verification
standards SOP* (2015), which states "BSA (m²) = ([Height(cm) x
Weight(kg)]/3600)½" citing the letter, and that "the DuBois or Mosteller
formulae are accepted as the standard BSA nomogram for adults":
https://thamesvalleycanceralliance.nhs.uk/wp-content/uploads/2022/03/TVCN-Verification-SOP-November-2015.pdf