How to read percentage and ratio strength
Every concentration problem on this site, and most of the ones on the exam, starts by turning a strength into an amount of drug in a known volume or weight. Percent, ratio strength and mg/mL are three notations for the same thing, and the work is knowing what each one means so you can move between them without a formula.
% w/v = grams of drug per 100 mL • % w/w = grams per 100 g • % v/v = mL per 100 mL • 1:X = 1 g in X mL (or 1 g in X g)
The unit hidden in "percent" is what trips people. 2% w/v is not "2 of something"; it is 2 grams per 100 millilitres, and once you write it that way the arithmetic is a proportion. Ratio strength works the same way: 1:5,000 is 1 gram in 5,000 millilitres. When a question doesn't state w/v or w/w, assume a solid in a liquid is w/v, a liquid in a liquid is v/v, and a solid in a solid is w/w.
Percent to grams
Multiply the percent (as a fraction) by the volume.
Grams of drug in 250 mL of a 2.5% solution:
grams = 2.5% × 250 = 6.25 g
Or set it up as a proportion: 2.5 g is to 100 mL as x is to 250 mL. Same arithmetic. The proportion is slower but it's harder to get the decimal point wrong, which matters more at 0.05%.
Ratio strength to percent
1:X means 1 g in X mL, so the percent is 100 ÷ X.
1:750 as a percent:
percent = 1 ÷ 750 × 100 = 0.1333 → 0.133%
And back the other way: a percent is 1:X where X = 100 ÷ percent.
0.02% as a ratio strength:
X = 100 ÷ 0.02 = 5,000
So 0.02% is 1:5,000.
Anchors worth knowing cold, because they appear in questions without explanation: 1:1,000 is 0.1% (epinephrine for anaphylaxis is 1 mg/mL, which is 1:1,000), 1:10,000 is 0.01%, and 1:100,000 is 0.001%. Each extra zero in the ratio moves the percent one decimal place to the left.
mg/mL to percent
Percent is grams per 100 mL. So take the mg/mL, multiply by 100 to get mg per 100 mL, and divide by 1,000 to turn mg into grams.
12.5 mg/mL × 100 mL = 1,250 mg
1,250 mg ÷ 1,000 = 1.25 g
1.25 g per 100 mL is 1.25% w/v.
Those two steps collapse into one: mg/mL ÷ 10 = %, and % × 10 = mg/mL. 1% lidocaine is 10 mg/mL. 0.9% sodium chloride is 9 mg/mL. 50% dextrose is 500 mg/mL. The shortcut is worth memorizing because it turns up inside every other calculation family: reconstitution, IV rates, weight-based dosing all need a strength as mg/mL at some point.
Worked example: strength of a preparation you made
You dissolve 400 mg of drug in enough water to make 80 mL. What is the percent strength?
400 mg ÷ 80 mL = 5 mg/mL
5 mg/mL ÷ 10 = 0.5%
As a ratio strength that's 100 ÷ 0.5 = 200, i.e. 1:200. Three notations, one preparation.
Where students lose the points
- Percent used as a whole number. 2% × 250 mL is 5 g, not 500. Write the percent as grams per 100 mL and the proportion does the rest.
- Ratio strength read as a fraction of the drug. 1:1,000 is not "one part drug to one thousand parts diluent"; it is 1 g in a total of 1,000 mL. For pharmacy ratio strengths the second number is the whole preparation.
- mg and g in the same line. 1,250 mg per 100 mL is 1.25%, not 1,250%. Convert to grams before calling it a percent.
- Trailing zeros. 0.1333% and 0.13% are different answers. Carry three significant figures on ratio-to-percent conversions that don't terminate.
- w/w treated as w/v. For an ointment, 2% is 2 g per 100 g. The final quantity is a weight, and if the question gives a volume you need a specific gravity to get there.