Alligation calculator

Alligation finds the parts of two strengths needed for a target: parts of the higher strength equal the target minus the lower strength, and parts of the lower equal the higher minus the target. The parts sit diagonally opposite the strength they belong to, which is where nearly every error happens.

When to use the alligation calculator

Use when compounding a strength you do not stock from two strengths you do. It is a staple of pharmacy calculation papers and appears constantly in compounding practice.

The alligation formula

Parts of the higher strength = target − lower strength. Parts of the lower strength = higher strength − target. Divide each by the total parts and multiply by the quantity required.

Worked example

Make 500 g of 30% from 70% and 20% stock. Parts of 70% = 30 − 20 = 10. Parts of 20% = 70 − 30 = 40. Total 50 parts, so 10/50 × 500 = 100 g of the 70% and 40/50 × 500 = 400 g of the 20%.

The mistake that costs marks

The parts sit diagonally opposite the strength they belong to, which is where most errors happen: the difference nearest the lower strength gives the parts of the higher one. The target must also lie between the two strengths, because no mixture can reach a concentration outside its own ingredients.

Study aid, not a clinical tool

This calculator exists so you can learn the method and check your working for an examination. It is not medical advice and not clinical decision support, and it must not be used to make a decision about a real patient. Verify any result against your local formulary, the product literature and a qualified pharmacist. Our medical disclaimer sets out the full position.

Calculators you will usually need alongside this

Most questions that reach for one of these reach for another a step later, so these are the three that most often pair with it.

• Dilution calculator (C1V1 = C2V2) — Dilution
• Ratio strength and percentage converter — Ratio strength
• Powder volume and reconstitution calculator — Powder volume

Keep going

Calculations are only half of what examinations test. The other half is knowing why a drug does what it does, which is what decides whether a number you calculated is even the right number to be calculating. Start with Best pharmacy calculators. The drug class pages cover the mechanism behind the number, or browse the rest of the free calculators and try the practice questions.