1. Danielle DelVillano, Pharm.D.
Pharmaceutical Calculations: Percentage, Ratio Strength, and Other Expressions of Concentration
Danielle DelVillano, Pharm.D.

2. Objectives
Define the expressions percent weight-in-volume, percent volume-in-volume, percent weight-in-weight, ratio strength
Convert percent strength to ratio strength and vice versa
Apply percent strength and ratio strength to pharmaceutical calculations

3. Percentage Definition: rate per hundred Expressed as:
50/100
50%
0.50
Example: express 12.5% as an equivalent decimal fraction
12.5/100, or 0.125

4. Percentage Preparations
Percent weight-in-volume (w/v)
Number of grams of solute in 100 mL solution
% w/v
Percent volume-in-volume (v/v)
Number of mL of a solute in 100 mL solution
Percent weight-in-weight (w/w)
Number of grams of a solute in 100 mL solution
% w/w

5. Important notes When to use which term *Overall idea of this section*
w/v – solutions, suspensions of solids in liquids
v/v – liquids in liquids
w/w – mixtures of solids (creams)
*Overall idea of this section*
Solution = Solute + Solvent

6. Percentage Weight-in-Volume
Number of grams of solute in 100 mL solution
For a 3% solution…
3 g of solute in 100 mL solution

7. Problem 1 (w/v)
How many grams of dextrose are required to prepare 4000 mL of a 5% solution?
(5% solution = 5 g of dextrose in 100 mL)
5 g = x g
100 mL mL
x = 200 g

8. Problem 2 (w/v)
What is the percentage strength of a solution of urea, if 80 mL contains 12 g?
(% strength = x g in 100 mL)
12 g = x g
80 mL mL
x = 15%

9. Percentage Volume-in-Volume
Number of mL of solute in 100 mL solution
For a 5% solution…
5 mL of solute in 100 mL solution

10. Problem 3 (v/v)
How many mL of liquified phenol should be used in compounding of the following prescription?
Liquified phenol 2.5%
Calamine lotion ad 240 mL
2.5 mL = x mL x = 6 mL
100 mL 240 mL

11. Problem 4 (v/v)
What is the percentage strength (v/v) of a solution of 800 g of a liquid with a specific gravity of in enough water to make 4000 mL?
800 g water = 800 mL water 1000 mL = x mL
4000 mL mL
800 mL / = 1000 mL solute x = 25 %

12. Percentage Weight-in-Weight
Number of g of solute in 100 g solution
For a 8% solution…
8 g of solute in 100 g solution
*Important to note*
Unlike w/v, the weight of the solute is INCLUDED in the weight of the solution for these problems

13. Problem 5 (w/w)
How should you prepare 100 mL of a 2% (w/w) solution of a drug substance in a solvent having a specific gravity of 1.25?
100 mL solvent * 1.25 = 125 g solvent
100% solution – 2% solute = 98% solvent
2% = x g
98% 125 g Mix 2.25 g drug with 125 g x = 2.25 g of solvent
Note how the proportion is set up differently in this problem

14. Problem 6 (w/w)
If 5 g of boric acid is added to 100 mL of water, what is the percentage strength (w/w) of the solution?
100 mL water = 100 g water
100 g water (solvent) + 5 g boric acid (solute) =
105 g solution
5 g = x x = 4.76%
105 g 100 mL

15. Ratio Strength
Another way of expressing the percentage strength of a solution
Example: Express 5% as a ratio strength
5 parts per 100, or 5:100
Commonly we express ratio strength as 1:x
So 5:100 would be expressed 1:20
General form: 1 part of solute per x parts of solution

16. Converting between the Strength Expressions
Express 0.02% as a ratio strength
0.02 = 1 part x = 5000
100 x parts Answer: 1:5000
Express 1:4000 as a percentage strength
1 part = x x = 0.025%
4000 parts 100

17. Problem 7 (ratio)
A certain injectable contains 2 mg of drug per milliliter of solution. What is the ratio strength (w/v) of the solution?
2 mg = g
0.002 g = 1 g x = 500 mL
1 mL x mL Answer: 1:500

18. Problem 8 (ratio)
How many milligrams of hexachlorophene should be used in compounding the following prescription?
Hexochlorophane 1:400
Hydrophillic ointment ad 10 g
1 g = x g x = g = 25 mg
400 g g

19. Parts Per Million (PPM) and Parts Per Billion (PPB)
Strengths of very dilute solutions
Example: 1-4 PPM flouride in drinking water
1 PPM – 4 PPM
1: – 4:

20. Problem 9 (PPM)
The concentration of a drug additive in an animal feed is 12.5 ppm. How many milligrams of the drug should be used in preparing 5.2 kg of feed?
12.5 PPM = 12.5:
12.5 g = x g x = g = 65 mg
g g

21. Questions

22. Reference
Ansel, H. C. (2009) Phamaceutical Calculations (13th Ed.). Philadelphia:Lippincott Williams & Wilkins, and Wolters Kluwer Publishers

23. Additional Problems

24. Chapter 6 Problem 7
If a pharmacist dissolved the contents of eight capsules, each containing 300 mg of clindamycin phosphate, into a sufficient amount of an astringent liquid base to prepare 60 mL of topical solution, what would be the percentage strength (w/v) of clindamycin phosphate in the prescription? 4%

25. Chapter 6 Problem 29
A topical solution contains 3% w/v hydroquinone. How many liters of the solution can be prepared from 30 g of hydroquinone?
10 L

26. Chapter 6 Problem 30
What is the percentage strength (v/v) if 225 g of a liquid having a specific gravity of 0.8 is added to enough water to make 1.5 liters of the solution?
18.75%

27. Chapter 6 Problem 38
If 500 g of dextrose are dissolved in 600 mL of water with a resultant final volume of 1 liter, what is the percentage strength of dextrose in the solution on a w/w basis?
45.45%

28. Chapter 6 Problem 57
A sample of white petrolatum contains 10 mg of tocopherol per kilogram as a preservative. Express the amount of tocopherol as a ratio strength.
1:100000

29. Chapter 6 Problem 65
In acute hypersensitivity reactions, 0.5 mL of a 1:1000 (w/v) solution of epinephrine may be administered subcutaneously or intramuscularly. Calculate the milligrams of epinephrine given.
0.5 mg

30. Chapter 6 Problem 70
If a commercially available insulin preparation contains 1 ppm of proinsulin, how many micrograms of proinsulin would be contained in a 10-mL vial of insulin?
10 mcg