Sterile Compounding Certification Pharmacy Math Calculations

NEED TO KNOW STERILE COMPOUNDING MATH BASICS

 

CONCENTRATION CALCULATION FORMULAS

Alligation Method

PERCENTAGE CONCENTRATION 

For solids %w/w = gm/100 gm   w = weight

For liquids %v/v = ml/100 ml      v = volume

For a mix of solid and liquid %w/v = gm/100 ml

1% Hydrocortisone (HC) cream contains 1g of HC per 100g of cream.

A 1% solution = 1ml of active ingredient per 100ml of the solution.

A 3% w/v solution = 3g of solid per 100 ml of  the solution.

 RATIO STRENGTH

Ratios…

1.Compare 2 numbers in relation to each other ¼ = 1:4

AND

2. When added together make a whole - 1:2:2 = total of 5 parts

Example

Two solutions are combined in a 2:1 ratio to make a final solution. How many mLs of each solution is needed to make 100 ml of the final solution?

In this case, you would need to solve this question using #2 above. 

1. Total parts = 3 (2+1) 

2. mLs needed for the numerator (top number) = 2/3 x 100 ml = 66.67 mLs

3. mLs needed for the denominator = 1/3 x 100 ml = 33.33 mLs

The total from 2 & 3 above should equal 100 mLs.

 DILUTIONS

To change the strength of a preparation, adding a diluent to it is necessary which would result in the final preparation having a lower percent strength. The most common formula used for liquids and solids is:

V1 x S1 = V2 x S2 (V = Volume and S = Strength (may be entered as whole numbers).

Example: How many mLs of a 0.5% stock solution (SS) is required to make 1.5 L of a 0.05% solution using water as a solvent?

As in proportions, 3 variables must be known to solve for the fourth. Leave percent strength as shown.  So for this example….

V1 = ?    S1 = 0.5%    V2 = 1.5L = 1500ml    S2 = 0.05%

So...........

V1 x S1 = V2 x S2

V1 x 0.5% = 1500ml (1.5 L) x 0.05%

V1 = 1500ml x 0.05%

                 0.5%

V1 = 150 ml of stock solution (SS) required.

From above, you know the diluent or solvent is water so 1500 (total) – 150 (SS) = 1350 ml of water required.

For more math equations such as IV flow rates, dosing calculations and more, sign up for the IV certification program.

**Optional - Obtain access to our AI course assistant to help with your math questions or questions about USP 797 & USP 800.