Math CentralQuandaries & Queries


Question from david:

How do I convert mcg to ml?


Hi David.

You need to recognize that mcg is a unit of mass (or weight) and ml is a unit of volume. To convert between the two, you need to know the density or strength of the substance. A dense substance would have a different conversion factor from a light substance. If you are dealing with a liquid medicine, this might be the dosage strength (how much active medicine is in each ml of the solution).

Something that often confuses people is "what is an mcg"? It means "microgram", which is properly abbreviated as μg. This is 0.000001 grams (10-6 g), a millionth of a gram. The reason that you see mcg instead of the proper term μg is that the μ symbol is a Greek letter that older printers and typewriters in the English-speaking world were incapable of printing, so particularly in English-speaking countries they started using "mc" to mean micro.

Most commonly, people use these small quantities when dealing with medicines.

If in doubt with medication amounts, definitely call your pharmacist or doctor!

Here's an example conversion:

If you have a container of liquid medicine whose dosage strength is 300 mcg/ml and you want to draw a dose that is 500 mcg, then how many ml of the liquid should you take?

This is done just by creating equivalent fractions. In algebra we write this as

and solve for x this way:

So you would take one and two-thirds ml of the liquid.

Stephen La Rocque.

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