How to use the alligation mixture calculator
- Choose whether the values are prices per unit or strengths in percent.
- Enter the value of item A and item B, and the value you want the blend to reach. It must fall between the two.
- Optionally enter the total amount of blend, in any unit, to split it between A and B.
- Read the ratio, the share of each item, and the check that the blend comes out at your target.
Formula
parts of A = |value of B - target|
parts of B = |target - value of A|
amount of A = total x parts of A / (parts of A + parts of B)
This is the alligation cross. Each item gets the distance of the other item from the target. The ratio is then reduced to the smallest whole numbers, and the check recomputes the weighted average of the two amounts.
Blending $8 and $12 coffee to $9.50
Blending coffee at $8 and $12 per pound to a price of $9.50 gives parts of A = 12 - 9.5 = 2.5 and parts of B = 9.5 - 8 = 1.5. The ratio of 2.5 to 1.5 is the same as 5 to 3.
For 40 pounds, A is 40 x 5 / 8 = 25 pounds and B is 15 pounds, and the check gives (25 x 8 + 15 x 12) / 40 = $9.50. With strengths, mixing a 5 percent solution and a 25 percent solution to reach 10 percent takes 15 parts of the weaker to 5 parts of the stronger, which is 3 to 1.
When alligation works
Alligation is a quick way to find a blend ratio. It works when the blended value is a weighted average of the two values, which is true for prices per unit and for strengths by weight or volume, when the amounts simply add together.
It does not work when mixing changes the volume, or when values combine in other ways. Some liquids shrink slightly on mixing, and some values such as speeds do not average by weight. For exact work in a lab or pharmacy, follow the proper procedures and checks.
Related tools
To dilute a single solution, use the Solution Dilution Calculator. For other ratios use the Ratio Calculator, and for salt mixes see the Brine Calculator.
Assumptions and limits
- The target must lie between the two values, or equal one of them.
- The blend value is a weighted average, so quantities simply add.
- Changes in volume on mixing are not modeled.
- Percent strengths must be between 0 and 100.
Frequently asked questions
What is alligation?
It is a method for finding the ratio in which two items of different value are mixed to reach a target value. You subtract each value from the target and the differences give the parts.
How do I mix two prices to get a target price?
Take the difference between the second price and the target for the first item, and the difference between the target and the first price for the second. $8 and $12 to $9.50 gives 2.5 to 1.5.
Can I use it for solution strengths?
Yes, if the amounts are measured the same way, by weight or volume. Choose strengths in percent and enter the percents of each solution.
What if my target is outside the two values?
It cannot be reached by blending, because a blend always lands between the two. The page asks for a target between them.