Alligation Calculator
Find how much of a stronger and weaker stock to combine for a target concentration.
01 Set up your calculation
- Enter all three concentrations using the same definition and unit.
- Set a target between the two stock concentrations.
- 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.
Follow the numbers
Combining a 20-unit stock and a 5-unit stock to make 100 mL at 11 units requires 40 mL of the stronger stock and 60 mL of the weaker stock, assuming additive volumes.
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.
Questions from the notebook
Can the lower stock be pure diluent?
Yes. Set its concentration to zero if it contains none of the component being tracked.
What if the target equals one of the stocks?
The other stock’s amount becomes zero.
Can I mix percentages and molarity?
No. Convert all concentrations to the same definition and unit before combining them.
References & reading
- OpenStax, Rice University — Molarity ↗
Defines molarity and derives the dilution balance from conservation of solute.
- OpenStax, Rice University — Other Units for Solution Concentrations ↗
Distinguishes mass, volume, mass-volume percentages and parts per million.
- NIST — Guide to SI conversion factors ↗
Supports physical unit conversions. Input values are converted to the formula’s base units before calculation.
Our explanations are written for ChemistryCalc. Read how we build and check our tools. These calculations are educational estimates where the underlying model requires assumptions.