## Percent Strength

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:

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

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

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

## Percentage Concentrations

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:

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

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

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

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