Lessons · Medicine foundations · body surface area
Body surface area: one square root, in centimetres and kilograms
The Mosteller formula gives body surface area in square metres as the square root of the height in centimetres times the weight in kilograms, divided by 3600.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
Cardiac index, the number a physiology viva asks for after cardiac output, is output per square metre of body surface. Nobody can estimate that area by eye, and the formula that gives it is the one place on this road where a square root shows up. It is worth meeting on a calm afternoon rather than for the first time under a question.
How to think about it
Centimetres and kilograms, in that order, multiplied. Divide by 3600. Take the square root of what is left. Four keystrokes and one habit: do not round until the root has been taken, because rounding under a square root moves the answer more than you expect.
Worked example
BSA = sqrt(height in cm × weight in kg / 3600)The Mosteller formula, as a problem gives it.
170 × 70 = 11900, the product before dividingHeight in centimetres, weight in kilograms. Not metres.
11900 / 3600 = 3.3056, the number under the rootKeep the decimals. This is the value that gets rooted.
sqrt(3.3056) = 1.82 m²One point eight two square metres, to two decimal places.
Your turn
A person is 180 cm tall and weighs 80 kg. The product over 3600 comes to exactly 4. Write the line that finishes the Mosteller formula.
BSA = sqrt(180 × 80 / 3600) = sqrt(4) = m²
Solve one, graded on the server
The trap
Putting the height in metres. The 3600 in the formula is built for centimetres, so a height of 1.8 instead of 180 gives an area about ten times too small, and it is still a plausible-looking decimal.