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Alligation Calculator
Calculate mixing ratios and volumes for blending two solutions of different concentrations using the alligation method.
Presets
Volume of Solution Aโง
333.33 mL
The amount of the higher concentration (70%) solution needed.
Volume of Solution Bโง
666.67 mL
The amount of the lower concentration (40%) solution needed.
Parts of Aโง
10.00
Alligation parts corresponding to Solution A.
Parts of Bโง
20.00
Alligation parts corresponding to Solution B.
Mixing Ratio (A:B)โง
10.00 : 20.00
The simplified volume ratio for mixing.
Verificationโง
50.0000%
Calculated final concentration from the mixed volumes โ should match desired.
Ratio (A/B)โง
0.5000
Numeric ratio of parts A to parts B.
Alligation Grid
| Higher (70%) | โ 50% โ | 10.00 parts |
| Lower (40%) | 20.00 parts |
Volume Breakdown
A: 333.3 mL
B: 666.7 mL
Common Pharmacy Alligation Examples
| Application | High % | Low % | Target % |
|---|---|---|---|
| Dextrose IV | 50% | 5% | 10% |
| Alcohol dilution | 95% | 0% | 70% |
| Hydrocortisone cream | 2.5% | 0.5% | 1% |
| Saline solution | 23.4% | 0.9% | 3% |
| Betadine prep | 10% | 1% | 5% |
Planning notes, formulas, and examples
About the Alligation Calculator
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, quickly 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.
When This Page Helps
The alligation calculator eliminates arithmetic errors in mixing calculations, which is critical in pharmacy compounding where incorrect concentrations can harm patients. It quickly provides volumes, ratios, and verification so you can compound with confidence.
How to Use the Inputs
- Enter the higher concentration (Solution A) as a percentage.
- Enter the lower concentration (Solution B) as a percentage.
- Enter your desired target concentration between A and B.
- Specify the total volume of mixed solution you need.
- Select the volume unit that matches your workflow.
- Review the parts ratio and calculated volumes for each solution.
- Use the verification value to confirm accuracy.
Formula used
Alligation Alternate: Parts of A = |Desired% โ B%|, Parts of B = |A% โ Desired%|. Volume A = (Parts A / Total Parts) ร Total Volume. Volume B = Total Volume โ Volume A.Example Calculation
Result: 333.33 mL of A + 666.67 mL of B
Parts of A = |50 โ 40| = 10, Parts of B = |70 โ 50| = 20. Ratio is 10:20 or 1:2. Volume A = (10/30) ร 1000 = 333.33 mL, Volume B = (20/30) ร 1000 = 666.67 mL. Verification: (333.33 ร 70 + 666.67 ร 40) / 1000 = 50%.
Tips & Best Practices
- Always double-check that your desired concentration falls between A and B.
- Use the verification output to catch data-entry mistakes before mixing.
- For pharmacy compounding, record the alligation calculation in your compounding log.
- When diluting with pure solvent, set Concentration B to 0%.
- Remember that alligation assumes ideal mixing โ no volume contraction or expansion.
- For critical preparations, weigh ingredients rather than measuring by volume for higher accuracy.
History of the Alligation Method
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 vs. Alligation Medial
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 โ essentially the weighted average. Both are useful, but alternate is the form most commonly needed in practice.
Applications Beyond Pharmacy
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.
Sources & Methodology
Last updated:
Frequently Asked Questions
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 โ w/w%, v/v%, w/v%, or even molarity โ 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.
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