Lessons · Medicine foundations · body mass index
Body mass index: kilograms over metres squared
Body mass index is the weight in kilograms divided by the height in metres, squared.
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
Somebody on a ward round asks for the body mass index, and the chart in your hand gives pounds and feet. The formula is one line; the two conversions in front of it are where the minute actually goes, which is why they get their own lesson before this one.
How to think about it
Get the weight into kilograms and the height into metres first. Square the height, on its own line, before you divide. The unit that comes out is kilograms per square metre, and writing that unit down is what catches the version where you squared the weight.
Worked example
BMI = weight in kg / (height in m)²The formula, with the units in it so they cannot slip.
Height 1.75 m: 1.75 × 1.75 = 3.0625 m²Square the height on its own line. Never square the weight.
70 / 3.0625 = 22.9 kg/m²Weight over the squared height. Rounded to one decimal place.
A height given as 160 cm becomes 1.60 mCentimetres over 100. A BMI worked in centimetres comes out ten thousand times too small and still looks like a number.
Your turn
A person weighs 82 kg and is 1.80 m tall. Write the line that gives the body mass index, to one decimal place.
BMI = 82 / (1.8 × 1.8) = kg/m²
Solve one, graded on the server
The trap
Squaring the weight instead of the height. It is the height that is squared, every time, and the unit kg/m² says so: the metres are downstairs and there are two of them.