Alligation Calculator
Our mixtures & solutions calculator computes alligation accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Parts of higher = desired - lower | Parts of lower = higher - desired
The alligation cross method calculates mixing ratios by finding the difference between the desired concentration and each source concentration. The difference from the lower concentration gives parts of the higher, and vice versa.
Worked Examples
Example 1: Pharmacy Compounding
Problem:Mix 90% alcohol with 50% alcohol to make 400 mL of 70% alcohol solution.
Solution:Parts of 90% = 70 - 50 = 20\nParts of 50% = 90 - 70 = 20\nRatio = 20:20 = 1:1\nVolume of 90% = (20/40) * 400 = 200 mL\nVolume of 50% = (20/40) * 400 = 200 mL
Result:Mix 200 mL of 90% with 200 mL of 50%
Example 2: Saline Solution
Problem:Mix 10% NaCl with 2% NaCl to prepare a 5% solution. Find the ratio.
Solution:Parts of 10% = 5 - 2 = 3\nParts of 2% = 10 - 5 = 5\nRatio = 3:5
Result:Mix in ratio 3:5 (high:low)
Frequently Asked Questions
What is the alligation method in chemistry and pharmacy?
Alligation is a mathematical method used to determine the proportions in which two solutions of different concentrations must be mixed to obtain a desired intermediate concentration. It is widely used in pharmacy for compounding medications, in chemistry for preparing solutions, and in food science for blending ingredients. The method works by creating a simple cross-multiplication diagram where the desired concentration is placed in the center, and the differences from each source concentration give the mixing ratio.
How does the alligation cross method work?
The alligation cross (or tic-tac-toe method) arranges the higher concentration in the top-left and the lower concentration in the bottom-left, with the desired concentration in the center. You subtract diagonally: desired minus lower gives parts of the higher concentration, and higher minus desired gives parts of the lower concentration. The resulting numbers form the mixing ratio. For example, mixing 70% and 30% solutions to get 50% yields a ratio of (50-30):(70-50) = 20:20 = 1:1.
When should I use alligation versus the dilution equation?
Use alligation when mixing two solutions of different known concentrations to achieve a target concentration. Use the simple dilution equation (C1V1 = C2V2) when diluting a single concentrated solution with pure solvent (effectively 0% concentration). Alligation is more general because it handles mixing any two concentrations, while the dilution equation is a special case of alligation where the lower concentration is zero. Both methods are fundamental tools in pharmaceutical compounding and laboratory preparation.
Can alligation be used for more than two components?
Standard alligation (alligation alternate) handles two components at a time. For three or more components, you can use alligation medial to find the resulting concentration when mixing known quantities, or apply alligation alternate iteratively by grouping components. In practice, multi-component mixing problems are often solved using systems of linear equations rather than the cross method. However, the two-component alligation remains the most commonly used version in pharmacy and chemistry education.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy