Alligation Calculator
Blend two strengths of the same solute to hit a target strength. Classic alligation alternate for pharmacy compounding.
Recipe
50 of 70% stock + 50 of 30% stock → 100 at 50%
Related tools
Frequently asked questions
StatPearls describes alligation as mixing solutions or solids of different strengths to get an intermediate strength. Mathematically it's a weighted average solved backwards: with stocks at strengths H and L and a target T, the parts needed are (T − L) of the stronger stock and (H − T) of the weaker one. The grid drawing often used to teach it is a memory aid for the same arithmetic.
Yes — same math. Use grams instead of mL. To make 100 g of a 5% ointment from 2.5% and 10% stocks: 10 − 5 = 5 parts of the 2.5%, 5 − 2.5 = 2.5 parts of the 10%, 7.5 parts in total. 5/7.5 × 100 = 67 g of 2.5%, and 2.5/7.5 × 100 = 33 g of 10%.
Yes if both stocks are in the same unit. Two stocks at 10 mg/mL and 50 mg/mL blended to make 25 mg/mL works identically — just use the numbers directly. The 'percentage' framing is convention; the math is the same for any pair of strengths in the same unit.
With three stocks there are many possible mixes that hit the same target, so there's no single answer. One way is to fix the amount of one stock first, then solve the other two as a normal two-stock problem. The tool handles the standard two-stock case only.
For weight-in-weight (w/w) percentages, no: weights add up exactly. For volume-in-volume (v/v) mixes such as alcohol and water, the volumes don't add up exactly, because the mixture shrinks slightly. Measure the final volume, or work by weight, when the exact volume matters.
Help us improve this calculator
What's missing or wrong? What would make this more useful for you? Every suggestion lands in our inbox.
Source: StatPearls: Pharmacy Calculations (alligation method) · Last verified 2026-11. StatPearls: Pharmacy Calculations. This tool provides estimates only and is not legal, tax or financial advice. Always verify your specific situation with the relevant UAE authority or a licensed advisor before taking action.