🧠 The theory: percentages and ratios are just concentrations
Every way of writing strength is really an amount of drug over an amount of preparation. A percentage w/v means grams per 100 mL; a ratio strength 1 in X means 1 gram in X millilitres; parts per million means 1 part in a million. Because they all describe the same thing, you can always rewrite one as another by keeping the amount of drug the same and adjusting the size of the container. Anchoring on 'per 100' or 'per this many mL' is what makes the conversions reliable.
What each expression means
- •% w/v (weight in volume) = grams per 100 mL. A solid dissolved in a liquid, for example glucose 5% w/v.
- •% w/w (weight in weight) = grams per 100 g. A solid in a solid, for example a cream or ointment.
- •% v/v (volume in volume) = millilitres per 100 mL. A liquid in a liquid.
- •1 in X (ratio strength) = 1 gram in X millilitres. Very dilute solutions, for example adrenaline 1 in 1000.
- •parts per million (ppm) = 1 mg per litre. 1% is equal to 10,000 ppm.
Percentage to mg/mL
Worked example
Express 5% w/v as a concentration in mg/mL.
- Step 1 — Write out what the percentage means: 5% w/v is 5 g in 100 mL.
- Step 2 — Convert the grams to milligrams: 5 g = 5000 mg, so it is 5000 mg in 100 mL.
- Step 3 — Divide by 100 to get the amount in 1 mL: 5000 / 100 = 50.
Answer: 50 mg/mL
Worked example
Express 0.9% w/v sodium chloride in mg/mL.
- Step 1 — 0.9% w/v is 0.9 g in 100 mL.
- Step 2 — 0.9 g = 900 mg, so 900 mg in 100 mL.
- Step 3 — Divide by 100: 900 / 100 = 9.
Answer: 9 mg/mL
Worked example
How many grams of glucose are in 500 mL of a 5% w/v solution?
- Step 1 — 5% w/v is 5 g in every 100 mL.
- Step 2 — 500 mL is five lots of 100 mL, so multiply: 5 x 5 = 25.
Answer: 25 g
Ratio strength (1 in X)
Worked example
How many micrograms of adrenaline are in 1 mL of a 1 in 1000 solution?
- Step 1 — A 1 in 1000 solution is 1 g in 1000 mL.
- Step 2 — Divide to find the amount in 1 mL: 1 g / 1000 mL = 0.001 g/mL, which is 1 mg/mL.
- Step 3 — Convert to micrograms: 1 mg = 1000 micrograms.
Answer: 1000 micrograms per mL
Worked example
Express a 1 in 10,000 solution in micrograms per mL.
- Step 1 — 1 in 10,000 is 1 g in 10,000 mL.
- Step 2 — Amount in 1 mL: 1 g / 10,000 = 0.0001 g, which is 0.1 mg.
- Step 3 — Convert: 0.1 mg = 100 micrograms.
Answer: 100 micrograms per mL
Worked example
Express a 1 in 200 solution in mg/mL.
- Step 1 — 1 in 200 is 1 g in 200 mL, which is 1000 mg in 200 mL.
- Step 2 — Divide to get the amount in 1 mL: 1000 / 200 = 5.
Answer: 5 mg/mL
Harder: going the other way
Worked example
Express 50 mg/mL as a percentage w/v.
- Step 1 — A percentage w/v is grams per 100 mL, so scale up from 1 mL to 100 mL: 50 mg/mL x 100 = 5000 mg in 100 mL.
- Step 2 — Convert to grams: 5000 mg = 5 g, so 5 g in 100 mL.
Answer: 5% w/v
Worked example
Express 0.0005% w/v as parts per million.
- Step 1 — Use the fact that 1% equals 10,000 ppm.
- Step 2 — Multiply: 0.0005 x 10,000 = 5.
Answer: 5 ppm
Tip: 1 ppm is also equal to 1 mg in 1 litre.
⚠️ The classic trap
Percentage w/v is grams per 100 mL, not per mL. Forgetting the 100 is the most common error in this topic and gives an answer that is 100 times too big or too small.
Test yourself
Express 10% w/v in mg/mL.
Answer: 10 g in 100 mL = 10,000 mg in 100 mL; divide by 100 = 100 mg/mL
How many grams of drug are in 1 litre of a 5% w/v solution?
Answer: 5 g per 100 mL; 1 litre is 1000 mL = ten lots of 100 mL, so 5 x 10 = 50 g
Express a 1 in 2000 solution in mg/mL.
Answer: 1000 mg in 2000 mL; 1000 / 2000 = 0.5 mg/mL
A 2% w/w cream contains how many mg of drug per gram?
Answer: 2 g in 100 g = 2000 mg in 100 g; divide by 100 = 20 mg per gram