Body Surface Area Calculator

Why surface area rather than weight

Body surface area, BSA, is the area of the body’s outer surface in square metres, estimated here by the Mosteller formula, BSA = √(height × weight / 3600), with height in centimetres and weight in kilograms. Several physiological quantities scale with surface area rather than with mass. Basal metabolic rate, cardiac output and glomerular filtration all track it more closely than they track weight, which is a consequence of heat exchange and of how transport surfaces scale with body size. For drugs where the gap between an effective dose and a toxic one is narrow, most visibly cytotoxic chemotherapy, surface area predicts clearance better than weight does.

It is worth knowing that this is contested. Surface area explains only part of the variation in drug clearance between individuals, and for many agents flat or weight based dosing performs just as well in trials. The practice persists largely where the original dose finding studies were conducted that way, so the convention is now embedded in the protocols rather than in the pharmacology.

The four formulas

All take height in centimetres and weight in kilograms and return square metres.

• Mosteller, 1987. BSA = √(height × weight / 3600)
• Du Bois and Du Bois, 1916. BSA = 0.007184 × height^0.725 × weight^0.425
• Haycock, 1978. BSA = 0.024265 × height^0.3964 × weight^0.5378
• Gehan and George, 1970. BSA = 0.0235 × height^0.42246 × weight^0.51456

Mosteller is the usual choice because it can be done on any calculator without a power function. The 3600 in it is not arbitrary: it was chosen so that the result agrees closely with Gehan and George, the formula it simplifies, across the ordinary adult range, which is why a simple square root can stand in for a two exponent fit.

At 170 cm and 70 kg the four give 1.818, 1.810, 1.826 and 1.831 square metres. That is a spread of 0.022, about 1.2 percent, and it will not change a dose. The readout above shows this spread for whatever height and weight you enter, because the agreement is not uniform: it is closest in the middle of the adult range, and it degrades at the extremes. Du Bois in particular was derived from nine subjects, one of them a child, by wrapping them in plaster moulds, and it is known to underestimate in obesity.

Worked reasoning

For a patient of 170 cm and 70 kg by Mosteller:

• 170 × 70 = 11,900
• 11,900 / 3600 = 3.3056
• √3.3056 = 1.818 m²

A property of Mosteller that makes it easy to sanity check: because it is a square root, quadrupling the weight exactly doubles the surface area. If a mental estimate does not have that behaviour, something has gone wrong.

Where 1.73 square metres comes from

Glomerular filtration rate is reported as mL/min per 1.73 m², and that figure was the average adult surface area in the studies which established normal filtration. Indexing to it is what makes an eGFR comparable between a small adult and a large one, since a bigger person has bigger kidneys and a higher absolute filtration rate without being any healthier.

The indexing matters when dosing a renally cleared drug in someone far from average size. An indexed eGFR has to be multiplied back by their actual surface area divided by 1.73 to recover their true clearance in mL/min:

• absolute clearance = indexed eGFR × (actual BSA / 1.73)

Skipping that step underdoses large patients and overdoses small ones. For a 45 kg adult with a surface area of about 1.4 m², an indexed eGFR of 60 corresponds to an absolute clearance of roughly 49 mL/min, which can cross a dose adjustment threshold that the indexed number sits above.

Actual, ideal or adjusted weight

Actual body weight is what all four formulas were derived with and what this calculator uses. Substituting something else is a protocol decision rather than an arithmetic one, and the formula cannot tell you whether to.

Historically many chemotherapy protocols capped surface area at 2.0 or 2.2 m² in obesity, or used an adjusted body weight, on the argument that adipose tissue adds surface area without adding proportionally to drug clearance. Current oncology guidance has largely moved against capping, on the evidence that it underdoses obese patients and worsens outcomes without reducing toxicity. Follow the protocol in front of you rather than the formula, and note which weight it specifies.

Common mistakes

• Entering height in metres. Every formula here wants centimetres. Using 1.7 instead of 170 gives 0.18 m², a tenth of the right answer, and in Mosteller the error is a clean factor of √100.
• Confusing surface area with body mass index. They use the same two measurements and mean different things. BMI is weight over height squared and is a measure of relative weight; surface area scales roughly as height to the power 1.5 and is a measure of absolute size. BMI is shown in the readouts only because the confusion is so common.
• Using an adult formula in a neonate. Du Bois is unreliable in infants, which is precisely what Haycock was developed to fix. Below about 10 kg the choice of formula genuinely changes the answer.
• Carrying too many figures into a dose. Height and weight are measured to about three significant figures at best, and often to two in a busy clinic. A surface area quoted to four decimal places implies a precision the inputs do not support.