Calculate mixing ratios and volumes for blending two solutions of different concentrations using the alligation method.
The alligation method is a time-tested technique used in pharmacy, chemistry, and food science to determine the correct proportions for mixing two solutions of different concentrations to obtain a desired intermediate concentration. This algebraic shortcut has been relied upon by pharmacists for centuries and remains a core competency tested on pharmacy licensing exams worldwide.
Alligation alternate works by arranging the higher and lower concentrations diagonally with the desired concentration in the center, then cross-subtracting to find the number of parts of each solution required. The beauty of the method lies in its simplicity: no matter how complex the concentration arithmetic might seem, the cross-subtraction always yields the correct mixing ratio.
This calculator automates the alligation process, instantly computing the required volumes of each solution given your total desired quantity. Whether you're compounding a prescription cream at a specific concentration, diluting stock solutions in a research lab, or blending ingredients in food manufacturing, the alligation calculator handles the math so you can focus on technique and safety. The tool also verifies the result and shows a visual breakdown of the mixing proportions.
The alligation calculator eliminates arithmetic errors in mixing calculations, which is critical in pharmacy compounding where incorrect concentrations can harm patients. It instantly provides volumes, ratios, and verification so you can compound with confidence. This alligation calculator helps you compare outcomes quickly and reduce avoidable mistakes when making day-to-day care decisions. Use the estimate as a planning baseline and confirm final decisions with a qualified professional when risk is high.
Alligation Alternate: Parts of A = |Desired% − B%|, Parts of B = |A% − Desired%|. Volume A = (Parts A / Total Parts) × Total Volume. Volume B = Total Volume − Volume A.
Result: 333.33 mL of A + 666.67 mL of B
Parts of A = |50 − 40| = 10, Parts of B = |70 − 50| = 20. Ratio is 10:20 or 1:2. Volume A = (10/30) × 1000 = 333.33 mL, Volume B = (20/30) × 1000 = 666.67 mL. Verification: (333.33 × 70 + 666.67 × 40) / 1000 = 50%.
The alligation technique dates back to ancient commerce, where merchants needed to blend goods of different qualities (such as gold alloys or grain mixtures) to achieve a target quality at a fair price. The word itself derives from the Latin "alligatio," meaning "binding together." By the 18th century, alligation had become a standard tool in pharmaceutical education, appearing in every compounding textbook.
Alligation alternate is the method implemented in this calculator: it determines the ratio for mixing two components to reach a target concentration. Alligation medial, by contrast, calculates the resulting concentration from mixing known quantities of multiple solutions — essentially the weighted average. Both are useful, but alternate is the form most commonly needed in practice.
While pharmacy is the most common context, alligation finds use in food science (blending juices or dairy products to target sugar or fat content), environmental engineering (mixing waste streams), agriculture (fertilizer blending), and even bartending (cocktail dilution calculations). Any scenario where two miscible liquids of different concentrations must be combined benefits from this straightforward technique.
Alligation is a mathematical technique for calculating the ratio in which two solutions of different concentrations must be mixed to produce a solution of a desired intermediate concentration. This keeps planning practical and lowers the chance of preventable errors.
The alligation alternate method works for exactly two solutions. For three or more, you would use alligation medial or solve a system of linear equations.
Yes. Alligation works with any consistent concentration unit — w/w%, v/v%, w/v%, or even molarity — as long as both solutions and the target use the same unit.
The desired concentration must lie between A and B. Solution A is defined as the higher concentration so the cross-subtraction produces positive parts.
Absolutely. Alligation remains a required competency on the NAPLEX and FPGEC exams and is used daily in compounding pharmacies worldwide.
Yes. Alligation is commonly used to dilute high-proof alcohol (e.g., 95% ethanol) with water (0%) to a target percentage such as 70% for disinfection.