Alligation Calculator

01 Set up your calculation

1. Enter all three concentrations using the same definition and unit.
2. Set a target between the two stock concentrations.
3. Choose a volume basis for concentration per volume, or a mass basis for mass percentages (0–100), and enter the total amount.

02 The relationship

For the assumptions behind these results, read the explanation below. You can also explore Solution Dilution and Mixing Ratio.

03 A weighted-average balance

Alligation finds the relative shares that make a desired weighted average. The concentration gaps on either side of the target determine how much of the opposing stock is needed. A target closer to the stronger stock requires a larger share of that stock.

The calculation conserves the tracked component. It assumes that mixing does not cause a reaction, precipitation, loss, or another change in the amount being tracked. The target cannot fall outside the two starting concentrations under this model.

04 Match the amount basis to concentration

Choose the volume basis for concentration per volume when stock volumes may reasonably be treated as additive. Choose the mass basis when entering weight percentages from 0 to 100. That mode reports the component quantities as masses, avoiding an incorrect conversion of a mass recipe into milliliters.

Some liquids contract or expand significantly on mixing. In that situation, use a preparation method based on measured final volume and suitable density data. An alligation ratio alone cannot correct for a nonadditive volume.