BSA Worked Examples: Six Body Surface Area Calculations, Shown Step by Step
Six fully worked body surface area examples — Mosteller and Du Bois side by side, a child case, a chemo-dose multiplication, and a cardiac index — with every step of the arithmetic shown.
Body surface area formulas look intimidating until you watch them produce numbers. This post runs six realistic cases through the exact arithmetic a BSA calculator performs: a standard adult by Mosteller, the same adult by Du Bois, a fifteen-kilogram child, a chemotherapy dose multiplication of the kind pharmacists do daily, a heavier adult case, and a cardiac index computation. Every step is written out — products, divisions, square roots — so you can verify each line with a phone calculator. The standing stance applies with extra force here: these are educational estimates, and any real dosing or clinical interpretation belongs to clinicians following protocols.
CHAPTER 01The Two Formulas in One Place
Mosteller: BSA equals the square root of height in centimeters times weight in kilograms, divided by 3600. Du Bois: BSA equals 0.007184 times weight to the power 0.425 times height to the power 0.725. Both take height in centimeters and weight in kilograms and return square meters. Everything below uses those exact forms with intermediate values rounded only for display.
Cardiac index, the one derived quantity used here, is cardiac output in liters per minute divided by BSA. With the two formulas and one division, all six examples are checkable by hand — which is the point. Formulas you can verify are formulas you can trust. The bsa calculator at /bsa-calculator.html runs both formulas side by side, which makes it the natural place to check every example below.
CHAPTER 02Example 1: Standard Adult by Mosteller — 70 kg, 175 cm
Multiply height by weight: 175 times 70 is 12,250. Divide by 3600: 12,250 over 3600 is 3.403. Take the square root: the square root of 3.403 is about 1.845.
So BSA is approximately 1.84 square meters — squarely in the typical adult band of 1.6 to 2.0.
Interpretation: this is the textbook adult case, and it is worth memorizing as an anchor. When any BSA output for a mid-sized adult lands far from 1.8, suspect the inputs before trusting the result.
CHAPTER 03Example 2: The Same Adult by Du Bois
Weight factor: 70 to the power 0.425 — read it as 70 to the 0.4 (about 6.29) times 70 to the 0.025 (about 1.092), which composes to roughly 6.08. Height factor: 175 to the power 0.725 is approximately 42.3.
Multiply: 6.08 times 42.3 is about 257.2. Multiply by 0.007184: 257.2 times 0.007184 is about 1.848.
Interpretation: Du Bois gives about 1.85 square meters against Mosteller's 1.84 — agreement within roughly half a percent. That is the normal relationship between the two formulas for an ordinary adult, and it doubles as your sanity check: if they disagree by more than a couple of percent, recheck the units.
CHAPTER 04Example 3: A Child — 15 kg, 95 cm
Mosteller: 95 times 15 is 1,425. Divided by 3600: 1,425 over 3600 is 0.3958. Square root: about 0.629.
So BSA is approximately 0.63 square meters — about a third of an adult's, for a child about a fifth of an adult's weight. Area does not scale with weight; it scales closer to height times weight, which is why children are not simply small adults in dosing arithmetic.
Interpretation: this is also where the Du Bois formula's known small-child bias shows up, and where pediatric practice leans on formulas like Haycock and on clinical judgment. The number is a fine educational illustration; pediatric dosing is another universe entirely.
CHAPTER 05Example 4: Multiplying a Dose — 50 mg per Square Meter
Take Example 1's BSA of 1.84 square meters and a hypothetical protocol rate of 50 milligrams per square meter. The dose is 50 times 1.84, which is 92 milligrams.
That is the entire multiplication — and that simplicity is exactly why the units matter so much. Enter the BSA as 18.4 (a square-meter slip) and the dose becomes 920 milligrams, a tenfold error that no downstream check will necessarily catch.
Interpretation: the example exists to show the shape of real dose arithmetic, not to suggest you perform it. Actual chemotherapy dosing adds protocol caps, rounding rules, cycle adjustments, and verification steps — pharmacist work, prescribed work, checked work. Understand the multiplication; never perform it.
CHAPTER 06Example 5: A Larger Adult — 85 kg, 160 cm
Mosteller: 160 times 85 is 13,600. Divided by 3600: 13,600 over 3600 is 3.778. Square root: about 1.944.
So BSA is approximately 1.94 square meters.
Interpretation: a heavier but shorter person lands near the same area as Example 1's taller, lighter adult — 1.94 versus 1.84. This is BSA's character in one comparison: it measures the interface, not the mass, and it compresses differences that weight-based thinking would exaggerate.
CHAPTER 07Example 6: Cardiac Index — 5.0 L/min over 1.84 m²
Cardiac output of 5.0 liters per minute, divided by BSA of 1.84 square meters: 5.0 over 1.84 is about 2.72 liters per minute per square meter.
The typical adult range for cardiac index runs roughly 2.5 to 4.0, so 2.72 sits comfortably inside it — a normal resting heart, scaled to body size.
Interpretation: this is BSA's normalizing job in one line — raw output becomes per-size output, and suddenly a small person and a large person can be compared on equal terms. The same pattern underlies GFR reporting per 1.73 square meters. Run all six cases yourself at /bsa-calculator.html; watching the tool reproduce your hand math is the best possible check on both.
CHAPTER 08Cross-Checks and Cautions
Three habits catch nearly every BSA error. Cross-formula agreement: Du Bois and Mosteller should land within about two percent for typical adults — compute both and compare. Anchor sense: a mid-sized adult should land near 1.8, a ten-year-old near 1.1 to 1.3, a newborn near 0.25; wild departures mean unit slips. And unit discipline: centimeters and kilograms, always — pounds and feet must be converted before entering, not after.
The caution is permanent: these are educational estimates of areas nobody measures exactly, and the two most consequential uses — dosing and cardiac index — are clinical acts surrounded by protocol. Use the worked examples to understand what the number is and where it comes from; leave the application to the people with the chart, the protocol, and the license.
A closing note on where these numbers come from: every BSA formula is a regression fitted on measured groups, which means each carries population-level error that is invisible in its decimals. Du Bois was fitted on nine adults in 1916; Mosteller on larger but still finite samples. The practical consequence is the rounding discipline used throughout this post — two decimals in square meters, no more. Numbers that pretend to more precision than their data support are not more accurate; they are merely better dressed, and in dose arithmetic, better-dressed numbers get trusted exactly as if they were right.
🔑 Key takeaways
- Mosteller in one line: square root of (height times weight over 3600) — Example 1's 70 kg, 175 cm adult computes to about 1.84 m².
- Du Bois lands within about half a percent of Mosteller for the same adult (1.85 versus 1.84) — agreement is your input sanity check.
- Example 3's 15 kg child computes to about 0.63 m²: area scales closer to height times weight than to weight alone, which is why children are not small adults in dosing.
- Example 4 shows the whole dose arithmetic — 50 mg/m² times 1.84 m² equals 92 mg — and why a units slip becomes a tenfold error.
- Example 5's larger-but-shorter adult (1.94 m²) nearly matches Example 1's taller adult: BSA measures interface, not mass.
- Cardiac index is output divided by BSA — 5.0 over 1.84 gives 2.72 L/min/m², inside the typical 2.5 to 4.0 band.
- Verify with cross-formula agreement and size anchors, keep centimeters and kilograms straight, and leave all clinical application to protocols and clinicians.
❓ Frequently asked questions
Why do Mosteller and Du Bois give slightly different answers?
They were fitted on different populations with different mathematics, so small differences — a percent or two for typical adults — are by design. Larger gaps indicate input problems, usually units, not a formula failure.
Which formula do hospitals use?
It depends on the protocol: oncology traditionally names Du Bois, quick bedside estimates use Mosteller, and pediatrics often uses Haycock. The protocol's named formula governs; the rest are estimates for context.
Can I use pounds and feet with a conversion in my head?
Convert carefully with fixed factors — 2.205 pounds per kilogram and 2.54 centimeters per inch — before entering anything. Mental approximations shift BSA by amounts that matter in any downstream arithmetic.
Is a BSA of 2.2 too high?
BSA is a size description, not a health grade, so there is no 'too high' in itself. In dosing contexts, protocols sometimes cap BSA around 2.0 to 2.2 for certain drugs — a treatment rule, not a judgment of the body.
Why does my child's BSA look so small compared with mine?
Because area scales with height times weight rather than weight alone, a child at a fifth of adult weight has roughly a third of adult area. That asymmetry is exactly why pediatric dosing is its own discipline.
Can this calculator tell me if my chemo dose is right?
No. Doses come from protocols that specify the rate, formula, caps, and rounding, verified by pharmacists. A calculator can show the arithmetic transparently; only the care team can tell you what applies to you.
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