Lessons · Medicine foundations · a dose in mg per kilogram
A figure written per kilogram is one multiplication
Milligrams per kilogram becomes milligrams by multiplying by the weight in kilograms; a daily figure split into equal parts is then divided by how many parts.
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
It is the most common piece of arithmetic in the whole of paediatrics and the most common place a weight in pounds slips through unconverted. The multiplication is trivial; keeping the units honest on the way in is the actual work.
How to think about it
Convert the weight to kilograms first if it is not already, on its own line. Multiply by the milligrams per kilogram. If the question asks for equal parts, divide the total by the number of parts, and say which of the two numbers you are reporting: the whole amount or one part.
Worked example
The problem gives 15 mg/kg and a weight of 24 kgBoth figures from the question.
15 × 24 = 360 mgMilligrams per kilogram times kilograms. The kilograms cancel.
Split into three equal parts: 360 / 3 = 120 mg eachThe total and one part are different answers; say which you are giving.
A weight given as 66 lb is converted first: 66 / 2.2 = 30 kgNever multiply a per-kilogram figure by pounds.
Your turn
The problem gives 12 mg/kg and a weight of 35 kg. Write the line that gives the total amount in milligrams.
12 × 35 = mg
Solve one, graded on the server
The trap
Multiplying by a weight in pounds. It gives an answer 2.2 times too large, and nothing in the arithmetic complains; only the line where you wrote the unit down would have caught it.