PTCB Quiz Prep

How to Calculate Body Surface Area

Updated

Body surface area, written BSA and measured in square metres, is how the most dose-sensitive drugs in the pharmacy are scaled to the patient. Chemotherapy orders are written in milligrams per square metre rather than per kilogram, because surface area tracks metabolism more faithfully than weight does. The formula involves a square root, which makes it look harder than it is: in practice it is one calculator entry followed by a multiplication. Drill it alongside the other calculations on the PTCB math practice test once you have worked the examples below.

Metric: BSA (m2) = square root of [ (height in cm × weight in kg) ÷ 3,600 ]

Imperial: BSA (m2) = square root of [ (height in inches × weight in lb) ÷ 3,131 ]

Two versions of one formula

The equation above is the Mosteller formula, the version used most widely because it is simple enough to run on a basic calculator. It comes in two forms, and the only difference is the number you divide by. Use 3,600 when the height is in centimetres and the weight is in kilograms. Use 3,131 when the height is in inches and the weight is in pounds. Both produce the same answer for the same patient, so pick the one that matches the units in the question rather than converting first.

The one thing you cannot do is mix them. Feeding centimetres and pounds into either version gives a number that means nothing, because each divisor is calibrated to a specific pair of units. If a question gives height in feet and inches, convert to total inches first: 5 feet 6 inches is 66 inches.

The order of operations

Work strictly inside out. Multiply the height by the weight first, then divide that product by the constant, and take the square root of the result last. Taking the root too early, or dividing before multiplying, produces a plausible looking number that is wrong. Then sanity-check the answer: an average adult sits near 1.7 m2, a large adult around 2.0, and a small child well under 1.0. An answer of 17 or 0.17 for an adult means a decimal place has moved.

Worked example: metric units

BSA for a 180 cm, 80 kg adult

Calculate the body surface area of a patient who is 180 cm tall and weighs 80 kg.

  1. Step 1. Multiply height by weight: 180 × 80 = 14,400.
  2. Step 2. Divide by the metric constant: 14,400 ÷ 3,600 = 4.
  3. Step 3. Take the square root: the square root of 4 is 2.
  4. Step 4. Round to two decimal places: 2.00 m2.

Answer: 2.00 m2

The trap: Taking the square root of the height or the weight separately before combining them. The root applies to the whole quantity after the division, not to the individual figures.

Worked example: imperial units

Nothing changes except the divisor, so there is no need to convert to metric first.

BSA for a 68 inch, 154 lb adult

Calculate the body surface area of a patient who is 68 inches tall and weighs 154 lb.

  1. Step 1. Multiply height by weight: 68 × 154 = 10,472.
  2. Step 2. Divide by the imperial constant: 10,472 ÷ 3,131 = 3.3446.
  3. Step 3. Take the square root: the square root of 3.3446 is 1.8288.
  4. Step 4. Round to two decimal places: 1.83 m2.

Answer: 1.83 m2

The trap: Using 3,600 with inches and pounds. The 3,600 divisor belongs to centimetres and kilograms, and mixing them here would give roughly 1.71 m2, which is wrong by enough to matter in a chemotherapy dose.

Worked example: turning BSA into a dose

Calculating the BSA is usually only half the question. The dose comes from multiplying it by the milligrams per square metre the prescriber ordered.

A 75 mg/m2 dose for a 1.6 m2 patient

A chemotherapy agent is ordered at 75 mg/m2. The patient's BSA is 1.6 m2. What is the dose, and how many millilitres are needed from a 20 mg/mL vial?

  1. Step 1. Multiply the BSA by the ordered rate: 1.6 m2 × 75 mg/m2 = 120 mg.
  2. Step 2. The m2 units cancel, leaving milligrams, which confirms the setup is right.
  3. Step 3. Convert to volume with a proportion: 20 mg / 1 mL = 120 mg / x mL.
  4. Step 4. Cross multiply and solve: 20x = 120, so x = 6 mL.

Answer: 120 mg, drawn as 6 mL from the 20 mg/mL vial

The trap: Dividing the BSA into the rate rather than multiplying. A quick unit check catches it: mg/m2 multiplied by m2 leaves mg, which is what the question asked for.

The most common mistake

Two errors account for most wrong answers. The first is mixing unit systems, using centimetres with pounds or inches with kilograms, which quietly invalidates the divisor. The second is applying the square root at the wrong point. Do the multiplication, then the division, then the root, in that order, and finish by checking the answer against the roughly 1.7 m2 adult benchmark before using it in a dose calculation.

Try it

  1. Calculate the BSA of a patient who is 160 cm tall and weighs 90 kg.
  2. Calculate the BSA of a patient who is 70 inches tall and weighs 180 lb.
  3. A drug is ordered at 40 mg/m2 for a patient with a BSA of 1.85 m2. What is the dose?
  4. A patient is 150 cm and 50 kg. Calculate the BSA, then the dose of a drug ordered at 100 mg/m2.
Show answers
  1. 160 × 90 = 14,400. 14,400 ÷ 3,600 = 4. Square root of 4 = 2.00 m2.
  2. 70 × 180 = 12,600. 12,600 ÷ 3,131 = 4.0243. Square root = 2.01 m2.
  3. 1.85 × 40 = 74 mg.
  4. 150 × 50 = 7,500. 7,500 ÷ 3,600 = 2.0833. Square root = 1.44 m2. Dose = 1.44 × 100 = 144 mg.

Frequently asked questions

What is the Mosteller formula for body surface area?

In metric units, BSA in square metres equals the square root of height in centimetres multiplied by weight in kilograms, divided by 3,600. In imperial units, it is the square root of height in inches multiplied by weight in pounds, divided by 3,131. Both give the same answer for the same patient, so use whichever matches the units you were given.

Why are some drugs dosed by body surface area instead of weight?

Body surface area tracks metabolic rate and blood volume more closely than weight alone, which matters most for drugs with a narrow margin between an effective and a toxic dose. Chemotherapy agents are the classic example, which is why oncology orders are written in milligrams per square metre.

What units is BSA measured in?

Square metres, written m2. A typical adult falls somewhere around 1.7 m2, which is a useful sanity check: if your calculated answer is 17 or 0.17 for an average adult, a decimal place has slipped.

Do you need to convert pounds and inches before using the formula?

No, provided you use the matching version. The 3,131 denominator is built for inches and pounds, and the 3,600 denominator is built for centimetres and kilograms. What you must not do is mix them, such as using centimetres with pounds, because the divisor no longer fits.

How many decimal places should a BSA be rounded to?

Two decimal places is the usual convention, so 1.73 m2 rather than 1.7 or 1.732. Round at the end rather than partway through, and follow the pharmacy's own policy where one exists.

Practise this

BSA dosing sits alongside weight-based dosing as the two ways a dose gets scaled to the individual patient, and the final volume step in each example is the same ratio and proportion work. Run a mixed set on the pharmacy math practice test, then head back to the pharmacy math hub for the other formulas.

PTCB Quiz Prep is an independent study resource, not affiliated with the Pharmacy Technician Certification Board. Worked examples are for exam preparation, not clinical dosing advice.

The rest of the pharmacy math series

Each calculation below is worked start to finish with the same method, so once one clicks the others read faster. The full set sits on the pharmacy math guide.

  • Days Supply: how long a dispensed quantity lasts, including the drops, insulin and inhaler cases that trip people up.
  • Conversions: metric, household to metric, temperature, and the Roman numerals that still appear on prescriptions.
  • Concentrations and Dilutions: percentage strength (w/v, w/w, v/v), ratio strength, and the C1 x V1 = C2 x V2 dilution equation.
  • Alligation: the tic-tac-toe method for mixing two strengths to reach a target, and turning parts into quantities.
  • IV Flow Rates: flow rate in mL/hr, drip rate in gtt/min using the drop factor, and infusion time.
  • Ratio and Proportion: the method underneath every other calculation here: match the units, cross multiply, solve for x.
  • Weight-Based Dosing: pounds to kilograms, mg/kg per dose against mg/kg per day, and checking a dose against its maximum.