Pharmacy Dilution and Concentration Math
Updated October 27, 2026
Dilution and concentration problems are a step up from basic dosage math, and they show up on the PTCE. Most of them use one formula and two definitions. Here’s what to know, followed by free practice problems with the steps shown.
The dilution formula
C1 × V1 = C2 × V2
C1 and V1 are the concentration and volume of the stock solution; C2 and V2 are the concentration and volume you want. Solve for the missing value.
Example: how much 20% stock is needed to make 500 mL of 5%? 20 × V1 = 5 × 500, so V1 = 125 mL. Add diluent to make 500 mL total.
Percent and ratio strength
- Percent strength (w/v): grams per 100 mL. A 2% solution has 2 g in 100 mL.
- Ratio strength: 1:1,000 means 1 g in 1,000 mL, which is 0.1%.
IV flow rates
- mL per hour: total volume ÷ hours.
- Drops per minute: (volume × drop factor) ÷ minutes.
Free dilution and concentration practice
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How many mL of a 50% dextrose solution are needed to make 250 mL of a 10% solution?Answer: BC1V1 = C2V2: 50 × V1 = 10 × 250, so V1 = 2,500 ÷ 50 = 50 mL.
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How many grams of drug are in 200 mL of a 2% w/v solution?Answer: C2% means 2 g per 100 mL. 200 mL is 2 × 100 mL, so 2 g × 2 = 4 g.
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A ratio strength of 1:1,000 is equal to what percent?Answer: B1:1,000 means 1 g in 1,000 mL, which is 0.1 g in 100 mL, or 0.1%.
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1,000 mL of IV fluid is to run over 10 hours. What is the rate in mL per hour?Answer: CDivide volume by time: 1,000 mL ÷ 10 hours = 100 mL/hr.
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300 mL is to infuse over 2 hours with tubing that delivers 20 drops per mL. What is the drip rate?Answer: B(300 mL × 20 drops/mL) ÷ 120 minutes = 6,000 ÷ 120 = 50 drops per minute.
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How many mL of a 10% stock solution are needed to make 400 mL of a 2.5% solution?Answer: B10 × V1 = 2.5 × 400 = 1,000, so V1 = 100 mL. Add diluent to make 400 mL total.
More basics: pharmacy math practice.
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