This alligation calculator uses the classic alligation method to tell you how to mix two ingredients of different strengths so the blend hits a target strength that sits between them. Alligation is the quick proportion rule taught in pharmacy, chemistry and trades maths: enter the concentration of the strong ingredient, the concentration of the weak ingredient, and the target concentration you want, and the calculator returns the ratio in which to combine them and, if you give a total amount, exactly how much of each to use. It works out the parts by the alligation rule, where the parts of the strong ingredient equal the difference between the target and the weak ingredient, and the parts of the weak ingredient equal the difference between the strong ingredient and the target, then scales those parts to your total. Because the parts come from how far each ingredient sits from the target, an ingredient that is close to the target contributes more of the blend. The same method covers mixing two salt solutions, two alcohol strengths, two alloys, two coffee blends or two priced goods, anything measured as a percentage or a rate. Enter your own three figures to plan a blend, or use the worked example of 20 percent and 5 percent mixed to 12 percent to check the tool before you trust it.
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7 : 8
parts strong to parts weak
Strong ingredient needed46.67
Weak ingredient needed53.33
Blend strength12%
To make 100 at 12%, mix 46.67 of the 20% ingredient with 53.33 of the 5% ingredient, a ratio of 7 to 8.
The target must sit between the two ingredient strengths. Amounts are in whatever unit you use for the total.
How it works
Alligation finds the parts of each ingredient from how far the other ingredient sits from the target. The parts of the strong ingredient equal the target minus the weak strength. The parts of the weak ingredient equal the strong strength minus the target. Add the two to get the total parts. Each ingredient's amount is your total multiplied by its parts divided by the total parts. Checking the blend, the amount-weighted average of the two strengths comes back to the target.
Worked example
You want 100 units of a 12% blend from a 20% strong ingredient and a 5% weak ingredient. The parts of strong are 12 - 5, which is 7. The parts of weak are 20 - 12, which is 8. That is 15 total parts, a ratio of 7 to 8. So you use 100 x 7 / 15, which is 46.67 of the strong, and 100 x 8 / 15, which is 53.33 of the weak. Checking it, (46.67 x 20 + 53.33 x 5) / 100 comes back to 12%, the target.
