Science & Lab Tools
Alligation Calculator
Calculate the proportions needed to mix solutions of different concentrations to achieve a desired final concentration.
Reviewed by the calculator.uk.com Team · Last reviewed 21 May 2026 · Our methodology
Enter values to see mixing proportions
The Alligation Calculator uses the alligation method, also known as the diagonal method or cross multiplication method, to determine the proportions needed when mixing solutions of different concentrations. This mathematical technique has been used in pharmacy and chemistry for centuries to calculate mixture ratios.
The Alligation Method
The method works by arranging the concentrations in a specific pattern and subtracting diagonally. The higher concentration is placed on top, the lower concentration on bottom, and the desired concentration in the middle. The absolute differences between the desired concentration and each original concentration give the proportions of the mixture.
The calculator performs these steps automatically: 1. Subtracts the desired concentration from the higher concentration to get the proportion of the lower concentration solution 2. Subtracts the lower concentration from the desired concentration to get the proportion of the higher concentration solution 3. Simplifies the ratio by finding the greatest common divisor (GCD) of the two proportions
The calculator provides three key pieces of information to help you mix your solutions accurately:
Higher and Lower Concentration Parts
These numbers represent the relative amounts of each solution needed. For example, if you get 3 parts higher and 2 parts lower, you would mix 3 units of the higher concentration solution with 2 units of the lower concentration solution. The units can be any volume measurement (mL, L, etc.) as long as you use the same unit for both solutions.
Simplified Ratio
This is the same proportion expressed as a simplified ratio. For example, 6:4 would be simplified to 3:2. This ratio can be multiplied by any number to get the desired total volume while maintaining the same concentration.
1. Why can't I enter a desired concentration outside the range of my solutions?
The alligation method only works for creating a mixture with a concentration between your two starting solutions. It's impossible to achieve a concentration higher than your highest concentration or lower than your lowest concentration just by mixing the two solutions.
2. How do I calculate the total volume I need?
Multiply both parts in the ratio by the same factor to achieve your desired total volume. For example, if the ratio is 2:3 and you need 1 liter total, multiply both numbers by 200 to get 400mL of the higher concentration and 600mL of the lower concentration (400 + 600 = 1000mL = 1L).
3. What units should I use for the concentrations?
The calculator uses percentages (%), but the alligation method works with any consistent concentration unit. Just make sure all three concentrations (higher, lower, and desired) use the same unit.
4. How accurate is the alligation method?
The alligation method is mathematically exact for ideal solutions. However, in practice, the accuracy of your final mixture will depend on your measurement precision and whether the solutions mix ideally (some solutions may have volume changes when mixed).
5. What is the scientific source for this calculator?
Alligation is a centuries-old shortcut for finding the mixing ratio of two concentrations to hit a target strength, still taught in pharmacy compounding courses as an alternative to solving the weighted-average equation directly. It reduces to a simple mass-balance identity - the total active ingredient in the mixture must equal what each component contributes - documented in pharmaceutical calculations references such as Ansel's Pharmaceutical Calculations. The method predates modern chemistry and was originally used by apothecaries mixing alloys and tinctures.