How do doctors estimate your skin area? Comparing body-surface-area formulas

AA SLAA HLAI SLAI HL Solid Also in: Modelling, Geometry & Voronoi

Research question

How much do the Du Bois and Mosteller formulas for body surface area disagree across the range of human heights and masses, and which agrees better with a geometric model of the body built from cylinders?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Some drug doses are calculated from body surface area, estimated with formulas from 1916 and 1987. Comparing them — and building your own geometric model — is a fascinating mix of power functions, geometry and medicine.

The mathematics you'll need

Power functions of two variables
Percentage differences over a grid of values
Surface areas of cylinders and spheres
Contour or heat-map representations

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

No personal data needed: use a grid of heights and masses and your own body measurements for the geometric model.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain why surface area matters in medicine.
Compare the formulas across a range.
Build a simple cylinder model of the body from your own measurements.
Compare all three.
Reflect on why formulas based on small samples are still used.

Pitfalls that cost marks

Units (cm, kg, m²).
Presenting results as medical advice.
A geometric model with no justification of shapes.

Showing personal engagement

Measure yourself for the geometric model.
Research the original 1916 study's sample and discuss it.
Explain where the formulas disagree most and why that matters for children.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Fit your own power formula to the geometric model's output and compare exponents.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).