Alligation Calculator

About this calculator

The alligation method (rule of alligation) is a shortcut for finding the ratio in which two ingredients of different strengths must be combined to produce a mixture at a specified target strength, without setting up a full algebraic equation each time. Arranged in the classic cross diagram, the parts of the higher-strength ingredient needed is proportional to (target − lower strength), and the parts of the lower-strength ingredient needed is proportional to (higher strength − target); the ratio of the two ingredient volumes is simply these two differences.

This technique is a staple of pharmacy compounding, where pharmacists dilute or combine two available stock concentrations to prepare a solution or ointment at a concentration that isn’t stocked directly — for example, blending a 10% and a 2% cream to make a 5% cream — and it’s taught explicitly in pharmacy calculations coursework alongside dosage and dilution problems. This calculator takes the two known strengths, the target strength, and the desired total volume, and returns the parts ratio and the exact volume of each solution to combine.