HesapHanem

Alligation Calculator

Enter the two strengths, your target, and total volume to find the mix.

How it is calculated

Enter the strengths of two stock solutions (for example in %), the strength you want, and the total volume to prepare. The cross-subtraction gives each solution's share: parts1 = |strength2 − target| and parts2 = |target − strength1|. Each volume is total × parts ÷ (parts1 + parts2). The part counts stay with the solution you entered, so Strength 1 always matches the first volume, whichever of the two is stronger. The target must lie strictly between the two strengths, and the total volume must be above zero; otherwise no result is shown. Volumes use whatever unit you used for the total and are shown to two decimals. The method assumes volumes add up and strengths mix linearly, which suits dilutions but is not exact for every pair of liquids.

Worked example

Make 250 units of a 5% mixture from a 2% and a 10% stock. Parts of the 2% stock: 10 − 5 = 5. Parts of the 10% stock: 5 − 2 = 3. The ratio is 5.00 : 3.00, 8 parts in all. Volume of the 2% stock: 250 × 5 ÷ 8 = 156.25 units. Volume of the 10% stock: 250 × 3 ÷ 8 = 93.75 units. Check: (156.25 × 2 + 93.75 × 10) ÷ 250 = 1,250 ÷ 250 = 5, as wanted.

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Common mistakes

  • Choosing a target outside the two strengths. A 12% mixture cannot be made from 2% and 10% stocks, and a target equal to one of them is rejected too; it must be strictly between.
  • Reading the cross backwards. The weaker solution gets the larger share when the target is closer to the stronger one, which can look wrong at first glance.
  • Mixing up which volume belongs to which solution. Volume 1 goes with Strength 1 and Volume 2 with Strength 2, so keep your own order when measuring out.
  • Entering strengths in different units, such as one in % and one as a ratio like 1:10.
  • Expecting the volumes to add up exactly for liquids that contract on mixing, such as alcohol and water. The tool assumes they do.

About this calculator

The alligation method (rule of alligation) is a shortcut for finding the ratio in which two ingredients of different strengths must be combined to produce a mixture at a specified target strength, without setting up a full algebraic equation each time. Arranged in the classic cross diagram, the parts of the higher-strength ingredient needed is proportional to (target − lower strength), and the parts of the lower-strength ingredient needed is proportional to (higher strength − target); the ratio of the two ingredient volumes is simply these two differences.

This technique is a staple of pharmacy compounding, where pharmacists dilute or combine two available stock concentrations to prepare a solution or ointment at a concentration that isn’t stocked directly — for example, blending a 10% and a 2% cream to make a 5% cream — and it’s taught explicitly in pharmacy calculations coursework alongside dosage and dilution problems.

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Comments (1)

  • Editorial team

    The first volume always belongs to the first strength you type, even when that one is the stronger. Mixing a 95 and a 70 to reach 80 with 500 units in total gives 200.00 of the 95 and 300.00 of the 70, which is easy to read backwards. The method also treats volumes as additive, so for ethanol-water or other non-ideal liquids, a pharmacist should confirm the final preparation. What mixtures are you trying to make?

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