What is the alligation method?

Alligation alternate is a shortcut arithmetic method used in pharmacy and chemistry to find the ratio in which two solutions of different known concentrations must be mixed to produce a desired intermediate concentration. The difference between the target and the lower stock gives the parts of the higher stock, and the difference between the higher stock and the target gives the parts of the lower stock.

Why must the target concentration be between the two stock concentrations?

Mixing two solutions can only produce a concentration that lies between their individual concentrations. If the target is outside that range, no non-negative ratio exists and the calculation is physically impossible.

Can I use percentages, mg/mL, or other units?

Yes. The alligation method is unit-agnostic — it works on any consistent concentration unit (%, mg/mL, g/dL, mEq/L, etc.). Just make sure all three values are in the same unit.

What if one stock is a pure diluent (0%)?

Enter 0 for the lower concentration. The calculator handles this; you are simply diluting the higher stock with a pure solvent.

How do I verify the result?

The result panel shows a verification: (parts_high × C_high + parts_low × C_low) / total_parts = target. If that equals your target, the math is confirmed.

Alligation Calculator

Name: Alligation Calculator
Availability: InStock
Author: Nham Vu

Find the ratio of two solutions at different concentrations needed to reach a target concentration, using the alligation method.

Solution Inputs

Higher concentration (C_high)

Must be greater than the target

Lower concentration (C_low)

Diluent = 0; must be less than target

Target concentration (C_target)

Total batch volume (optional)

Enter the three concentrations on the left and click Calculate.

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Summary

Find the ratio of two solutions at different concentrations needed to reach a target concentration, using the alligation method.

How it works

Enter the concentration of the higher-strength stock solution (must be above target).
Enter the concentration of the lower-strength stock solution or diluent (must be below target).
Enter the desired target concentration.
Optionally enter a total batch volume to see exact volumes to measure.
The calculator applies alligation alternate: parts of each stock = |target − other stock|.

Use cases

Pharmacy compounding: prepare a specific strength cream, ointment, or solution from two stock concentrations.
Intravenous therapy: determine how much concentrated electrolyte solution to mix with saline to reach a target concentration.
Veterinary medicine: dilute a high-strength drug to a safe working concentration for a small animal.
Laboratory settings: prepare buffers or reagents at a precise intermediate concentration from two available stocks.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu