Alligations/ Learn
Jason Sparks, Austin Community College

What is Alligations

In the practice of pharmacy, a healthcare practitioner will write a prescription or medication order for a pharmaceutical product that does not exist as a commercially available product. When the prescription is brought to the pharmacy, the requested product must be extemporaneously compounded or prepared on-demand for the specific patient.

To prepare the new product, it may be necessary to combine two or more existing products of a specific strength or concentration to create the new product of a different strength or concentration. For example, 70% alcohol is needed for routine cleaning but only 91% and 50% alcohol are in stock. You can combine 91% and 50% alcohol to make the desired 70% alcohol. To determine how much 91% and 50% alcohol will be needed to make 70% alcohol, we can use a mathematical process known as alligation.

Alligation is a mathematical process used to calculate needed quantities of ingredients when compounding two or more products to obtain a desired concentration. In the example above, we would be using 91% and 50% alcohol in the compound to obtain a desired concentration of 70% alcohol.

Instead of mixing two ingredients of differing strengths, it is often more practical and easier to dilute a known strength to obtain the desired concentration. For example, we could dilute the 91% alcohol with a diluent to obtain the desired concentration of 70% alcohol. The alligation process would also be used to determine the needed quantities of ingredients to obtain the desired concentration.