Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

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?

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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

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.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Power functions of two variables; Percentage differences over a grid of values
AA HL	Good fit	Power functions of two variables; Percentage differences over a grid of values
AI SL	Good fit	Power functions of two variables; Percentage differences over a grid of values
AI HL	Good fit	Power functions of two variables; Percentage differences over a grid of values

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: units (cm, kg, m²); and presenting results as medical advice. Say how each one affects your answer.

Use of mathematics (E)

SL: power functions of two variables; percentage differences over a grid of values; surface areas of cylinders and spheres; contour or heat-map representations, each explained in your own words and carried out correctly.

How health & biology explorations reach the top bands in general: Health, biology & medicine IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

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

Extending it for HL

Add an HL technique the question genuinely needs: what an HL health & biology exploration adds.

See a complete IA, marked

Is it cheaper to leave the heating on low overnight? A two-temperature model of my bedroom (AI HL) is a complete health & biology exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL, AA HL, AI SL and AI HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Power functions of two variables, percentage differences over a grid of values, surface areas of cylinders and spheres and contour or heat-map representations.

Where can I get data for this IA?

No personal data needed: use a grid of heights and masses and your own body measurements for the geometric model. Checked sources and tools: Desmos graphing calculator.

Turn this idea into your IA

The planner opens with “How do doctors estimate your skin area? Comparing body-surface-area formulas” filled in: the question, the maths and the data sources.

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