Body Surface Area (Mosteller) Equation, Derivation & Rearrangements

Core idea

Overview

The Mosteller formula provides a simplified calculation for Body Surface Area (BSA), which is essential for standardizing physiological parameters and determining precise drug dosages. It relates height and weight through a square root function to estimate the total surface area of the human body in square meters.

When to use: This formula is used primarily in oncology and critical care to calculate dosages for medications with narrow therapeutic windows. It is applicable for both adults and children, making it a versatile tool in clinical settings compared to more complex alternatives like the Du Bois formula.

Why it matters: Using BSA instead of weight alone prevents under-dosing in tall, thin patients and over-dosing in shorter, heavier patients. It serves as the basis for calculating indices like the Cardiac Index and allows for accurate comparisons of metabolic functions between individuals of different sizes.

Symbols

Variables

BSA = Body Surface Area, H = Height, W = Weight

B S A

Body Surface Area

m^{2}

H

Height

c m

W

Weight

k g

Walkthrough

Derivation

Formula: Body Surface Area — Mosteller Formula

Estimates total body surface area (BSA) for drug dosing calculations, particularly chemotherapy.

Height in centimetres, weight in kilograms.
Provides a practical approximation suitable for clinical use.

1

Mosteller Formula:

BSA in m². The constant 3600 accounts for unit conversions (cm → m) and an empirical scaling factor.

B S A = \frac{Height (cm) \times Weight (kg)}{3600}

2

Drug Dose Using BSA:

Many chemotherapy agents are prescribed per m² of BSA to normalise for body size and minimise toxicity.

Dose = Dose per m^{2} \times B S A

Note: Normal adult BSA ≈ 1.7–1.9 m². The Du Bois and Haycock formulae are alternatives.

Result

Dose = Dose per m^{2} \times B S A

Source: A-Level Pre-Med / UKMT Pharmacology Notes — Drug Dosing

Free formulas

Rearrangements

Solve for $B S A$

Make BSA the subject

B S A = \frac{e g ^{2} h ^{2} i ^{2} t ^{2} H W}{60}

Exact symbolic rearrangement generated deterministically for BSA.

Difficulty: 4/5

Solve for $H$

Make HT the subject

H = \frac{3600 B S A ^{2}}{g ^{2} h ^{2} i ^{2} t ^{2} W e ^{2}}

Exact symbolic rearrangement generated deterministically for HT.

Difficulty: 3/5

Solve for $W$

Make WT the subject

W = \frac{3600 B S A ^{2}}{g ^{2} h ^{2} i ^{2} t ^{2} H e ^{2}}

Exact symbolic rearrangement generated deterministically for WT.

Difficulty: 3/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph displays a square root relationship where the dependent variable (BSA) increases at a decreasing rate as the independent variable (the product of height and weight) increases. This results in a parabolic curve opening along the horizontal axis, starting from the origin where both height and weight are zero.

Graph type: parabolic

Why it behaves this way

Intuition

Visualize the human body as a complex three-dimensional shape whose total external surface area is estimated by a simple scaling relationship involving its height and weight, much like how the surface area of a simple

BSA

Total external surface area of the human body.

Represents the total area of skin, which is crucial for processes like heat exchange and drug absorption/distribution.

Height

Vertical linear dimension of the individual, typically measured in centimeters.

Taller individuals generally have a larger surface area.

Weight

Mass of the individual, typically measured in kilograms.

Heavier individuals (assuming similar height) generally have a larger surface area.

3600

An empirical scaling constant.

This constant, derived from clinical data, converts the product of height (cm) and weight (kg) into a value that, when square-rooted, yields BSA in square meters.

Signs and relationships

Square root (\sqrt{}): The square root operation is used because body surface area is a two-dimensional quantity (area), and it scales approximately with the square of characteristic linear dimensions, which are implicitly represented by
Product of Height and Weight (Height × Weight): Both height and weight contribute to the overall size and thus the surface area of the body. Their product captures the combined influence of these two primary anthropometric measurements.
Denominator 3600: This constant is an empirical factor that ensures the calculated BSA is in square meters when height is in centimeters and weight is in kilograms, based on the original derivation of the formula.

Free study cues

Insight

Canonical usage

The Mosteller formula is canonically used with height in centimeters (cm) and weight in kilograms (kg) to yield Body Surface Area (BSA) in square meters (m2).

Common confusion

A common mistake is using height in meters or weight in pounds without adjusting the constant 3600, leading to incorrect BSA values. Students may also incorrectly assume the constant 3600 is dimensionless, which would

Unit systems

$H e i g h t$ cm · Must be in centimeters when using the constant 3600 in the Mosteller formula.

$W e i g h t$ kg · Must be in kilograms when using the constant 3600 in the Mosteller formula.

$B S A$ m2 · The resulting Body Surface Area is in square meters.

Ballpark figures

Quantity:
Quantity:
Quantity:

One free problem

Practice Problem

A clinical pharmacist needs to calculate the Body Surface Area (BSA) for an adult male patient who stands 180 cm tall and weighs 80 kg. Using the Mosteller formula, what is the patient's BSA in m²?

Height180 cm

Weight80 kg

Solve for: $B S A$

Hint: Multiply height by weight, divide by 3600, then find the square root of the result.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Height 160cm, weight 60kg. BSA = sqrt(9600/3600) = sqrt(2.66) = 1.63 m².

Study smarter

Tips

Confirm that height (HT) is recorded in centimeters, not meters.
Verify the weight (WT) is in kilograms before starting the calculation.
Always perform the multiplication and division before taking the square root.
Round final BSA results to two decimal places for standard clinical dosing.

Avoid these traps

Common Mistakes

Using weight in lbs or height in inches without adjusting formula constants.
Forgetting the square root step.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

Estimates total body surface area (BSA) for drug dosing calculations, particularly chemotherapy.

This formula is used primarily in oncology and critical care to calculate dosages for medications with narrow therapeutic windows. It is applicable for both adults and children, making it a versatile tool in clinical settings compared to more complex alternatives like the Du Bois formula.

Using BSA instead of weight alone prevents under-dosing in tall, thin patients and over-dosing in shorter, heavier patients. It serves as the basis for calculating indices like the Cardiac Index and allows for accurate comparisons of metabolic functions between individuals of different sizes.

Using weight in lbs or height in inches without adjusting formula constants. Forgetting the square root step.