Alligation Calculator
Use this alligation calculator to mix a low-strength and high-strength solution into a target concentration while also solving the blend ratio and required amounts.
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Run the calculator.
What This Alligation Calculator Helps You Do
The alligation method is a compact way to move from two available concentrations to one required concentration without solving simultaneous equations by hand. That makes it useful for classroom chemistry, dilution planning, and quick bench calculations.
This version goes a step further than a ratio-only tool because it also scales the ratio into real batch amounts, so you can move directly from the target strength to the actual amount of each source you need.
How to Calculate Alligation Calculator
- Enter the two available strengths: Set the lower and higher concentration using the same unit system.
- Set the target concentration: The target must fall strictly between the lower and higher strength.
- Choose the final batch amount: Use any batch unit you want, such as milliliters, liters, or kilograms.
- Read the ratio and amounts: The calculator shows both the alligation ratio and the exact amounts needed from each source.
Alligation Calculator Formula
| Variable | Meaning | Unit |
|---|---|---|
| low | Lower concentration | %, M, ppm, or any consistent strength unit |
| high | Higher concentration | same unit as low |
| target | Desired concentration | same unit as low |
| final amount | Total mixture required | mL, L, kg, or any consistent batch unit |
Use the worked examples below to check how the formula behaves with real values. If the result looks unexpected, verify the unit assumptions and the meaning of each variable before interpreting the answer.
Worked Examples
- Low strength: 15%
- High strength: 22%
- Target: 19%
- Final amount: 100 mL
Result: High : low = 4 : 3, so use 57.14 mL of 22% and 42.86 mL of 15%.
The target sits closer to the stronger solution, so the batch needs more of the 22% source.
- Low strength: 4 M
- High strength: 13 M
- Target: 8 M
- Final amount: 120 mL
Result: High : low = 4 : 5, so use 53.33 mL of 13 M and 66.67 mL of 4 M.
This is the standard Omni-style example for concentration blending.
- Low strength: 30%
- High strength: 55%
- Target: 40%
- Final amount: 250 L
Result: High : low = 2 : 3, so use 100.00 L of 55% and 150.00 L of 30%.
A target near the lower end shifts more of the batch toward the weaker source.
- Low strength: 5%
- High strength: 12%
- Target: 9%
- Final amount: 10 L
Result: High : low = 4 : 3, so use 5.71 L of 12% and 4.29 L of 5%.
Because the target is closer to 12%, the stronger source carries the larger share.
How to Interpret Your Results
| Range | Meaning | Action |
|---|---|---|
| Target near low strength | The weaker source dominates the blend. | Expect a smaller share from the concentrated source. |
| Target near midpoint | The blend ratio is more balanced. | Check the ratio first, then scale it to your batch size. |
| Target near high strength | The stronger source dominates the blend. | Expect a larger share from the concentrated source. |
Frequently Asked Questions
References
Last reviewed: March 2026