Lessons · Medicine foundations · an infusion in mL per hour
From micrograms per kilogram per minute to millilitres per hour
Multiply by the weight to get micrograms a minute, by 60 to get micrograms an hour, then divide by the concentration in micrograms per millilitre to get millilitres an hour.
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
This is the calculation that looks hardest on the page and is really three ordinary steps in a fixed order. Written as one long expression it is unreadable and unwriteable under pressure; written as three lines with the unit on each, it is something you can check at a glance.
How to think about it
One line per unit change, and name the unit at the end of each. Micrograms per kilogram per minute, times kilograms, gives micrograms per minute. Times 60 gives micrograms per hour. Divided by micrograms per millilitre gives millilitres per hour. Every step cancels one thing.
Worked example
Rate 5 mcg/kg/min and weight 80 kg: 5 × 80 = 400 mcg/minThe kilograms cancel and a per-minute figure is left.
400 × 60 = 24000 mcg/hSixty minutes to the hour. Minutes out, hours in.
The concentration is given as 1600 mcg/mLMicrograms in every millilitre of the bag.
24000 / 1600 = 15 mL/hMicrograms an hour over micrograms a millilitre. Millilitres an hour.
Your turn
The working has reached 12600 micrograms an hour, and the concentration is 2100 mcg/mL. Write the line that finishes it.
12600 / 2100 = mL/h
Solve one, graded on the server
The trap
Forgetting the sixty. Every step of the arithmetic is right and the answer is sixty times too small, which is the kind of error that reads as a plausible small number rather than as nonsense.