Alligation Calculator
Use the alligation alternate method to find the ratio needed to blend two like-for-like strengths into one target concentration. Add an optional total amount when you want real quantities as well as parts.
Edited by Gail Joyce
This calculator page is maintained by the Chemistry Calculators editorial team. The alligation formula, ratio interpretation, and worked examples on this page are reviewed against standard solution-preparation methods and commonly used classroom and pharmacy reference material before major updates.
Alligation Calculator
Enter two source strengths and one target strength to get the alligation ratio. Add an optional total amount if you want actual quantities instead of parts only.
Scope: this page is for two-source alternate alligation only. Use like-for-like values such as all percent, all ppm, or all molarity. It does not convert units and it does not handle multi-source weighted-average mixing.
Quick fills
How to Use the Alligation Calculator
Alligation alternate is a fast cross-difference method for two-source blends. Enter the two source strengths, choose a target that sits between them, and then scale the parts if you need a real batch size.
Enter two like-for-like source strengths
Use the same basis across all values, such as all percent, all ppm, or all molarity. This page does not auto-convert units.
Set a target between them
The target must sit between the higher and lower strengths. If it does not, these two sources alone cannot produce that blend by simple alligation.
Read the alligation parts
The result shows the cross-difference parts for the higher and lower source. Those parts give you the mixing ratio directly.
Scale to a real batch if needed
If you enter a total amount, the calculator converts the ratio into actual source quantities so you can prepare the blend directly.
Table of Contents
Understanding Alligation
Alligation alternate is a classic way to calculate the ratio of two source strengths needed to reach one target strength. Instead of solving the weighted-average equation from scratch, you take the cross-differences between the target and each source.
When alligation is useful
Use it for solution prep, stock blending, pharmacy calculations, and other two-source concentration problems where the target sits between the two inputs.
When not to use it
Do not use it for pH, density-dependent blends, unit conversion, or multi-source weighted-average mixing. This page is only for two-source alternate alligation.
Formula and Equation
For a higher source C₁, lower source C₂, and target Cₜ:
Parts of higher source = |Cₜ - C₂|
Parts of lower source = |C₁ - Cₜ|
Ratio = parts of higher source : parts of lower source
If a total amount is provided:
Amount of higher source = total × higher parts / total parts
Amount of lower source = total × lower parts / total parts
Worked Examples
These examples show how alligation parts turn into a usable ratio and then into actual blend quantities.
Example 1: 10% and 2% to make 5%
Parts of 10% source = |5 - 2| = 3
Parts of 2% source = |10 - 5| = 5
Answer: Ratio = 3:5. For 1000 mL total, use 375 mL of the 10% source and 625 mL of the 2% source.
Example 2: 100% and water to make 70%
Parts of 100% source = |70 - 0| = 70
Parts of water = |100 - 70| = 30
Answer: Ratio = 70:30 = 7:3. For 500 mL total, use 350 mL stock and 150 mL water.
Common Mistakes
Most alligation errors come from using incompatible units, entering the sources in the wrong order, or forgetting that the target must lie between them.
Mixing unlike units
Do not combine percent with molarity, ppm with percent, or mass basis with volume basis unless you convert them first.
Using a target outside the source range
Alligation only works when the target lies between the higher and lower source strengths.
Reversing higher and lower values
Enter the stronger source as the higher value and the weaker source as the lower value so the parts are interpreted correctly.
Treating parts as direct amounts
The parts tell you the ratio only. Use the optional total amount field if you need exact source quantities for prep work.
Frequently Asked Questions (FAQs)
These are the main questions people ask when using a two-source alligation calculator.
What does the alligation ratio mean?
It tells you how many parts of the higher source to mix with how many parts of the lower source to reach the target strength.
Does total amount matter?
Only if you need actual source quantities. If you just need the ratio, the total amount can stay blank.
Can I mix any unit?
You can use any linearly mixed unit, but all values must use the same basis. This page does not convert units for you.
Can I use this for more than two sources?
No. This page is for alternate alligation with two sources only. Multi-source mixing needs a weighted-average or alligation-medial workflow.
How do I verify the result?
Check the weighted average of the actual source amounts. The final value should match the target when the amounts follow the calculated ratio.
References
These references are more useful than generic web summaries when you want the underlying compounding or classroom method behind alligation.
| Resource | Description |
|---|---|
| StatPearls: Pharmacy Calculations | Reference material covering concentration, dosing, and alligation in practical pharmacy calculations. |
| OpenStax Chemistry 2e | Textbook support for concentration, solution prep, and weighted-average reasoning. |
| Ansel, H. C., et al. Pharmaceutical Calculations | Standard compounding and ratio-calculation reference used in pharmacy education. |