# 16 Percent Strength & Percentage Concentrations (In Volume & Weight)

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A medication’s percent strength stands for how much of the active ingredient is present in the preparation, such as clotrimazole cream USP 1%. In a liquid preparation, this is grams per 100 mL or milliliters per 100 mL. In a solid preparation, this is grams per 100 g. So clotrimazole cream USP 1% contains 1 gram of clotrimazole per 100 g of cream. Remember when performing calculations to put mL in the denominator of liquid preparations and g, not mg in the denominator of solid preparations.

As usual, use unit factors to convert between different ratios:

$$\frac{\text{1 g drug}}{\text{100 g cream}} = \frac{\text{(x) mg drug}}{\text{1 g cream}} \;\text{;}$$

$$\frac{\text{1 g drug}}{\text{100 g cream}} \times \frac{\text{1,000 mg}}{\text{1 g}}$$

$$= \text{10 mg clotrimazole}$$

or use proportions:

$$\frac{\text{1 g drug}}{\text{100 g cream}} = \frac{\text{(x) g drug}}{\text{1 g cream}} \;\text{;}$$

$$\frac{\text{1 g drug} \times \text{1 g cream}}{\text{100 g cream}}$$

$$= \text{0.1 g clotrimazole} = \text{10 mg clotrimazole}$$

Let’s look at a liquid preparation. How many grams of drug are in 2 L of a 15% solution? Well, since 2 L is equal to 2,000 mL let’s use a proportion to solve this problem:

$$\frac{\text{15 g drug}}{\text{100 mL sol’n}} = \frac{\text{(x) g drug}}{\text{2,000 mL sol’n}} \;\text{;}$$

$$\frac{\text{15 g drug} \times \text{2,000 mL sol’n}}{\text{100 mL sol’n}}$$

$$= \text{300 g drug}$$

Now let’s look at another way to write these results using percentage concentrations. Percentage concentrations of pharmaceuticals come in 3 types of classifications:

Percent weight-in-weight, also written as % W/W, w/w or wt/wt, stands for g of drug in 100 g of the product.

Percent weight-in-volume, also written as % W/V, w/v or wt/vol, stands for g of drug in 100 mL of the solution.

Percent volume-in-volume, also written as % V/V, v/v or vol/vol, stands for mL of drug in 100 mL of the solution.

Let’s say we have 50 g of active ingredient in 1,600 mL of solution. Then using proportions we can determine that its % W/V is equal to:

$$\frac{\text{50 g}}{\text{1,600 mL}} = \frac{\text{(x) g}}{\text{100 mL}} \;\text{;}$$

$$\frac{\text{50 g} \times \text{100 mL}}{\text{1,600 mL}}$$

$$= \frac{\text{3.125 g}}{\text{100 mL}}$$

$$= \text{3.125% W/V}$$

Similarly, if a 900 mL solution has a 3% V/V, then we can find the amount of active ingredient in it by creating a proportion:

$$\frac{\text{3 mL}}{\text{100 mL}} = \frac{\text{(x) mL}}{\text{900 mL}} \;\text{;}$$

$$\frac{\text{3 mL} \times \text{900 mL}}{\text{100 mL}}$$

$$= \text{27 mL of active ingredient}$$

$$= \frac{\text{27 mL}}{\text{900 mL}}$$