health.bsa

def body_surface_area(weight_kg: float, height_cm: float) -> BodySurfaceArea

@dataclass(frozen=True)
class BodySurfaceArea:
    """Both formulas, so a caller uses the one its protocol names and never mixes them."""

    #: m², √(height cm × weight kg ÷ 3600), rounded half away from zero to 2 places
    mosteller: float
    #: m², 71.84 × W^0.425 × H^0.725 cm² ÷ 10000, rounded half away from zero to 2 places
    du_bois: float

from fune.health.bsa import body_surface_area  # health.bsa@^1

import math

from .health_bsa_types import BodySurfaceArea
from .math_pow import pow  ← from math.pow ^1.0.0 · built alongside by fune
from .math_round_float import round_float  ← from math.round-float ^1.0.0 · built alongside by fune


def _check_range(name: str, value: float, low: float, high: float, unit: str) -> None:
    ok = not isinstance(value, bool) and isinstance(value, (int, float)) and math.isfinite(value)
    if not ok or value < low or value > high:
        raise ValueError("%s must be a number from %s to %s %s, received %r" % (name, low, high, unit, value))


def body_surface_area(weight_kg: float, height_cm: float) -> BodySurfaceArea:
    """Body surface area by both published formulas. They differ by up to a
    few per cent, and a dose protocol names one, so both are returned rather
    than a silent default. Powers go through math.pow, never ** or
    math.sqrt, so the three languages agree to the bit before rounding."""
    _check_range("weightKg", weight_kg, 1, 650, "kg")
    # Height in metres (1.75) is the commonest unit slip.
    _check_range("heightCm", height_cm, 30, 272, "cm")
    w = float(weight_kg)
    h = float(height_cm)
    # Mosteller (1987): BSA (m2) = ([height (cm) x weight (kg)] / 3600)^1/2.
    mosteller = pow((h * w) / 3600, 0.5)
    # DuBois & DuBois (1916): A = W^0.425 x H^0.725 x 71.84, A in cm2.
    du_bois = (pow(w, 0.425) * pow(h, 0.725) * 71.84) / 10000
    return BodySurfaceArea(mosteller=round_float(mosteller, 2), du_bois=round_float(du_bois, 2))

Install

fune build

With that line in your source, in a Python project (language python in fune.project), fune build resolves it and its 2 dependencies, pins them in fune.lock, downloads only the Python package of each, and builds the code above into your project’s .fune/build, one readable file per capability with a header linking back here. Or pin a range in fune.project and build in one step:

fune add health.bsa

The manifest, vectors and README with only the Python implementation. Install it without the registry with fune add ./health.bsa-1.0.0-python.fune, or fetch it from a terminal with fune pull health.bsa@1.0.0:python.

The whole function, every language, is one file too: health.bsa-1.0.0.fune, 12,035 bytes, sha256 81cf3f02076ab9cb46048c8c90ba49ad1655d6fda3d2ee260a6db0b00e886756. It installs into a project of any language.

# fune: before health.bsa

# fune: after health.bsa

# fune: replace math.pow in health.bsa
# fune: replace math.round-float in health.bsa

# fune: step health.bsa after <n|label>

More from the author

- **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

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