Percentages in Preparations
10 minute read
What you will learn
- Distinguish between % w/w, % w/v, % v/v and % v/w
- State the convention used when the type of percentage is not stated
- Calculate the amount of drug in a preparation of known percentage strength
- Convert between ratio strength, percentage and milligrams per millilitre
- Work out how much drug is in a dose or in a container
Key points
- % w/w is grams per 100 g. % w/v is grams per 100 mL. % v/v is millilitres per 100 mL.
- When not stated: 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.
- A ratio strength of '1 in X' means 1 part in X parts. Percentage = 100 ÷ X.
- 1% w/v is 10 mg per mL. 0.1% w/v is 1 mg per mL.
- Amount of drug = percentage × quantity of preparation ÷ 100.
- A w/w strength can be changed to w/v by multiplying by the specific gravity.
Ways of writing strength
The strength of a preparation is the amount of drug in a stated amount of the product. It is most often written as a percentage, but there are different kinds of percentage, and each one means something different.
| Type | Meaning | Used for |
|---|---|---|
| % w/w (weight in weight) | grams of ingredient in 100 g of product | Ointments, creams, powders |
| % w/v (weight in volume) | grams of ingredient in 100 mL of product | Solutions and suspensions of solids |
| % v/v (volume in volume) | millilitres of ingredient in 100 mL of product | Mixtures of liquids, such as alcohol in water |
| % v/w (volume in weight) | millilitres of ingredient in 100 g of product | Liquids in semi-solids (not common) |
When the type is not stated
The usual convention is:
- a solid in a liquid is w/v;
- a liquid in a liquid is v/v;
- a solid in a solid (or semi-solid) is w/w.
So "a 2% solution of sodium bicarbonate" means 2% w/v, and "a 5% ointment" means 5% w/w.
The basic calculation
amount of drug = percentage × quantity of preparation ÷ 100
Example 1. How many grams of drug are in 250 mL of a 2% w/v solution?
- 2 × 250 ÷ 100 = 5 g
Example 2. Make 500 g of a 5% w/w ointment. How much drug and how much base?
- Drug = 5 × 500 ÷ 100 = 25 g
- Base = 500 − 25 = 475 g
Example 3: finding the percentage. 3 g of drug is dissolved in water to make 60 mL. What is the % w/v?
- 3 ÷ 60 × 100 = 5% w/v
Example 4: v/v. How much alcohol is in 200 mL of a 70% v/v solution?
- 70 × 200 ÷ 100 = 140 mL
Example 5: amount in a tube. A 15 g tube holds a 0.5% w/w cream. How many milligrams of drug?
- 0.5 × 15 ÷ 100 = 0.075 g = 75 mg
Example 6: tablets. Make 400 mL of a 0.5% w/v solution from 500 mg tablets. How many tablets?
- Drug needed = 0.5 × 400 ÷ 100 = 2 g = 2 000 mg
- Tablets = 2 000 ÷ 500 = 4 tablets
Milligrams per millilitre
A percentage w/v is easy to turn into milligrams per millilitre:
| Strength | Meaning | mg per mL |
|---|---|---|
| 1% w/v | 1 g in 100 mL | 10 mg/mL |
| 0.1% w/v | 0.1 g in 100 mL | 1 mg/mL |
| 0.01% w/v | 0.01 g in 100 mL | 0.1 mg/mL |
To change % w/v to mg/mL, multiply by 10.
Example 7: dose from a strength. A 2% w/v solution is given in 5 mL doses. How much drug is in one dose?
- 2% w/v = 20 mg/mL
- 5 mL × 20 mg/mL = 100 mg
Ratio strength
A strength can also be written as a ratio, such as 1 in 1000 or 1 : 1000. This means 1 part in 1000 parts:
- for a solid in a liquid: 1 g in 1000 mL;
- for a liquid in a liquid: 1 mL in 1000 mL;
- for a solid in a solid: 1 g in 1000 g.
Converting between ratio strength and percentage
percentage = 100 ÷ X (for a ratio of 1 in X)
X = 100 ÷ percentage
| Ratio strength | Working | Percentage |
|---|---|---|
| 1 in 1 000 | 100 ÷ 1 000 | 0.1% |
| 1 in 200 | 100 ÷ 200 | 0.5% |
| 1 in 2 500 | 100 ÷ 2 500 | 0.04% |
| 1 in 5 000 | 100 ÷ 5 000 | 0.02% |
Percentage to ratio: 0.25% is 1 in how many? X = 100 ÷ 0.25 = 400, so 1 in 400.
Example 8. How many milligrams of drug are in 1 mL of a 1 in 5 000 solution?
- 1 g in 5 000 mL = 1 000 mg in 5 000 mL = 1 000 ÷ 5 000 = 0.2 mg per mL
Weight in weight and weight in volume
A w/w strength is in grams per 100 grams of product. A w/v strength is in grams per 100 millilitres. They are the same only when the product has the same density as water.
To change a w/w strength to w/v for a liquid, multiply by the specific gravity:
% w/v = % w/w × SG
Example. A solution is 10% w/w and has SG 1.05. What is the % w/v?
- 10 × 1.05 = 10.5% w/v
This makes sense: 100 g of this solution is less than 100 mL, so the same 10 g of drug is packed into a smaller volume, giving a higher strength per 100 mL.
Exam focus
- How many grams of drug are in a stated volume or weight of a given percentage strength.
- Converting between ratio strength and percentage, for example 1 in 2500 and 0.04%.
- Calculating the quantity of drug and base for a w/w ointment.
- Common mistake: confusing w/v (per 100 mL) with w/w (per 100 g).
Quick check
Test yourself before you move on. Pick an answer to see the explanation.
1.How many grams of drug are in 250 mL of a 2% w/v solution?
2.A solution has a strength of 1 in 2 500. Expressed as a percentage this is:
3.How much base is needed to make 500 g of a 5% w/w ointment?
4.How many milligrams of drug are in each millilitre of a 1% w/v solution?
5.How many millilitres of alcohol are in 200 mL of a 70% v/v solution?