What this calculator does
Alligation mixing ratio works out finds the ratio and volumes of two concentrations that mix to a target concentration. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaHigher-solution ratio H = target − lower conc.; lower-solution ratio L = higher conc. − target. Volumes: Vh = H/(H+L) × Vr, Vl = L/(H+L) × Vr
The inputs explained
| Field | What to enter |
|---|---|
| Higher concentration (%) | A number, measured in %. Starts at 70. |
| Lower concentration (%) | A number, measured in %. Starts at 20. |
| Target concentration (%) | A number, measured in %. Starts at 40. |
| Total volume needed (mL) | A number, measured in mL. Starts at 500. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with higher concentration
Every other input is held at the calculator’s starting values while higher concentration varies. Select any row to load that scenario into the calculator.
How the answer changes with higher concentration
| Higher concentration (%) | Mixing ratio (higher : lower) | Volume of higher-concentration solution | Volume of lower-concentration solution |
|---|---|---|---|
| 35 | 20.00 : -5.00 | 666.7 mL | -166.7 mL |
| 52.5 | 20.00 : 12.50 | 307.7 mL | 192.3 mL |
| 70 | 20.00 : 30.00 | 200.0 mL | 300.0 mL |
| 105 | 20.00 : 65.00 | 117.6 mL | 382.4 mL |
| 140 | 20.00 : 100.00 | 83.3 mL | 416.7 mL |
| 210 | 20.00 : 170.00 | 52.6 mL | 447.4 mL |