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.

Quick Answer: Alligation sets the high-strength parts equal to target minus low, and the low-strength parts equal to high minus target.

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

  1. Enter the two available strengths: Set the lower and higher concentration using the same unit system.
  2. Set the target concentration: The target must fall strictly between the lower and higher strength.
  3. Choose the final batch amount: Use any batch unit you want, such as milliliters, liters, or kilograms.
  4. Read the ratio and amounts: The calculator shows both the alligation ratio and the exact amounts needed from each source.

Alligation Calculator Formula

High-strength parts = target - low; low-strength parts = high - target; required amount = final amount x part / total parts
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

USA - Mix 15% and 22% into 19%
  • 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.

UK - Prepare 120 mL of an 8 M solution
  • 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.

EU - Blend 30% and 55% into 40%
  • 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.

GCC - Make 10 L at 9% from 5% and 12%
  • 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

Alligation works when you are mixing exactly two known strengths into one target strength that lies between them.

No. Any consistent concentration unit works, including percent, molarity, or ppm, as long as all three strengths use the same unit.

Then the answer is trivial because you only need that source and the other one contributes nothing.

Yes. The alligation ratio is unitless, so you can scale it to any consistent batch amount.
Note: This calculator assumes ideal mixing and consistent concentration units. Real formulations can also depend on density, temperature, and non-ideal solution behavior.

References

Last reviewed: March 2026