Lessons · Pharmacy · a dose from a percent strength

A dose out of a percent strength

A percent strength written w/v is grams in 100 mL, and turning it into milligrams per millilitre is a multiplication by 10.

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

Injectables, irrigations and many topical liquids carry a percent on the label and nothing else. The order is in milligrams. Between the two there is one conversion, and it is worth knowing cold.

How to think about it

Write the percent as grams in 100 mL. Turn the grams into milligrams. Divide by the 100 mL. That is milligrams per millilitre, and the short way is to multiply the percent by 10. Then multiply by the volume to get the milligrams in it.

Worked example

2% w/v = 2 g in 100 mL

Percent weight in volume is grams per hundred millilitres.

2 g = 2,000 mg, and 2,000 mg / 100 mL = 20 mg/mL

Milligrams per millilitre before anything else happens.

5 mL x 20 mg/mL = 100 mg

The milligrams sitting in that volume.

The short way: percent x 10 = mg/mL, so 2 x 10 = 20 mg/mL

Same answer, one line, and it falls straight out of the two lines above.

Your turn

A solution is 5% w/v. Write its strength in milligrams per millilitre.

5 x 10 =  mg/mL

The trap

Reading 2% as 2 mg/mL. It is 20 mg/mL, ten times more, and the mistake is invisible in the answer because both are ordinary-looking numbers.

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