Body surface area calculator

How to calculate body surface area (BSA)

Multiply height in centimeters by weight in kilograms, divide by 3,600 and take the square root. That is the Mosteller formula (1987). For 175 cm and 70 kg, 175 × 70 ÷ 3,600 = 3.4028, and √3.4028 = 1.84 m², close to the average adult's 1.8 m².

Mosteller, DuBois and Haycock formulas

With weight W in kilograms and height H in centimeters:

• Mosteller (1987): BSA = √(H × W ÷ 3,600)
• DuBois (1916): BSA = 0.007184 × W^0.425 × H^0.725
• Haycock (1978): BSA = 0.024265 × W^0.5378 × H^0.3964

The power formulas need a calculator with an x^y key. For the same 70 kg, 175 cm adult:

1. DuBois: 70^0.425 = 6.0837 and 175^0.725 = 42.287, so BSA = 0.007184 × 6.0837 × 42.287 = 1.848 m².
2. Haycock: 70^0.5378 = 9.8241 and 175^0.3964 = 7.7471, so BSA = 0.024265 × 9.8241 × 7.7471 = 1.847 m².
3. Mosteller, for comparison, gives 1.845 m² before rounding to 1.84.

The three differ in where they came from:

• DuBois and DuBois fitted their equation to only 9 people.
• Mosteller's 1987 letter offered a simpler alternative to DuBois that works on a pocket calculator.
• Haycock and colleagues measured 81 subjects from premature infants to adults. They found DuBois increasingly underestimated surface area below 0.7 m², by 7.96 % in newborns.

BSA chart: the three formulas compared

Each row gives weight in kilograms and height in centimeters, with BSA rounded to two decimals. Spread is the largest estimate minus the smallest, as a percentage of Mosteller, worked from unrounded values.

For the three average-build adults in the first rows, the formulas agree within 0.5 %. They drift apart in obesity: at 120 kg and 170 cm they run from 2.28 to 2.44 m², a 6.9 % spread.

The weight exponents explain the order. DuBois raises weight to the power 0.425, Mosteller to 0.5 and Haycock to 0.5378, so at a fixed height Haycock climbs fastest as weight rises and DuBois slowest.

Small children show the DuBois shortfall Haycock described. For a 3.5 kg, 50 cm newborn, DuBois gives 0.209 m² against 0.220 m² for Mosteller and 0.224 m² for Haycock.

What body surface area is used for

Many chemotherapy drugs are dosed in milligrams per square meter, so a 75 mg/m² dose for a 1.84 m² adult is 138 mg. Cardiac output divided by BSA gives the cardiac index.

Kidney function is reported per 1.73 m², a reference adult's surface area. A person with a BSA of 2.1 m² filters about 21 % more in absolute terms than their reported eGFR.

An adult comparison study found the formulas diverge across body-size groups, including obesity. Dosing protocols state which formula their doses assume.

A BSA figure does not set a dose on its own. The protocol names the formula, and the treating team accounts for organ function, the indication and dose limits.

Common BSA mistakes

• Putting pounds and inches into the formulas. The constants assume kilograms and centimeters. 200 lb and 6 ft are 90.718474 kg and 182.88 cm, which give a Mosteller BSA of 2.15 m².
• Taking the square root of height alone. The root covers the whole product of height and weight divided by 3,600.
• Swapping formulas. Use the formula the protocol names, not whichever result is smallest, and keep the same one when comparing results over time.

For weight relative to height, use the BMI calculator. The eGFR calculator reports kidney filtration per 1.73 m², and the dosage by weight calculator handles doses given per kilogram.