Alligation Calculator

What is Alligation?

Alligation is a method used to calculate the proportions of two solutions with different concentrations that must be mixed together to obtain a solution of a desired intermediate concentration. Unlike dilution (which uses a diluent like water), alligation involves mixing two active solutions of different strengths.

This technique is widely used in pharmacy, chemistry, and medicine for preparing solutions, ointments, and mixtures with precise concentrations. The alligation method is particularly valuable when you need to create a specific concentration from available stock solutions.

Alligation Formula

The alligation method uses a simple formula to determine the ratio of two solutions needed:

$$H = C_r - C_l$$ $$L = C_h - C_r$$

where $H$ is the parts of the higher concentration solution, $L$ is the parts of the lower concentration solution, $C_h$ is the higher concentration, $C_l$ is the lower concentration, and $C_r$ is the required (target) concentration. The result is expressed as the ratio $H:L$.

How to Calculate Alligation Volumes

Once you know the alligation ratio, you can calculate the required volumes:

1. Calculate the alligation ratio $H:L$ where $H = C_r - C_l$ and $L = C_h - C_r$.
2. To find volumes from a desired total volume $V_t$: $V_h = \frac{H}{H+L} \times V_t$ and $V_l = \frac{L}{H+L} \times V_t$.
3. To find volumes from a known component volume, scale proportionally using the ratio.

Alligation in Pharmacy

In pharmaceutical practice, alligation is commonly used to prepare ointments, creams, and liquid medications of specific strengths. For example, a pharmacist may need to mix a 20% zinc oxide ointment with a 5% zinc oxide ointment to prepare a 10% ointment. Using the alligation method, the pharmacist can quickly determine that the ratio is 1:2 (one part of 20% to two parts of 5%).

Pair this with the Bleach Dilution Calculator or explore compound naming with the Chemical Name Calculator.