Alligation Calculator
Determine how much of two stock solutions you need to prepare a mixture at a target strength.
Must fall between the two source strengths.
Volume of strong solution
375 mL
Mix this amount of the stronger stock.
Volume of weak solution
625 mL
Add this amount of the weaker stock.
Use a ratio of 30 : 50 (strong : weak). Scaling this ratio to the desired final volume (1000 mL) gives the volumes above.
How to Use This Calculator
Enter source strengths
Provide the concentrations of the strong and weak stock solutions. Express them in the same unit (percentage, mg/mL, etc.).
Specify the target concentration
Ensure the desired strength lies between the two stock concentrations.
Set the final volume
Enter the total amount of solution you plan to prepare. The calculator scales the alligation ratio accordingly.
Mix the computed volumes
Combine the calculated volumes of the strong and weak solutions, then mix thoroughly to obtain the target strength.
Formula
(C₁ - Cₜ) : (Cₜ - C₂)
The alligation ratio is the difference between each stock concentration (C₁ and C₂) and the target concentration Cₜ. The ratio gives parts of the strong and weak solutions required.
Example
To prepare 500 mL of 40% solution from 70% and 10% stocks: ratio = (70 − 40) : (40 − 10) = 30 : 30 = 1 : 1. Use 250 mL of each stock.
Full Description
The alligation method is a rapid way to compute how much of two stock solutions must be mixed to reach an intermediate concentration. It is widely used in pharmacy compounding, chemical preparation, and food formulation.
By subtracting the desired strength from each stock strength, the method creates a ratio that balances the contributions of the concentrated and dilute components. Scaling the ratio to the desired total volume yields the exact volumes to mix.
While alligation works for two components, more complex mixtures often require algebraic mass-balance equations or dedicated formulation software.
Frequently Asked Questions
Do the concentrations need to be percentages?
No. Any consistent unit works (e.g., mg/mL, g/L). The three concentration values just need the same unit.
What if the target is outside the range?
You cannot obtain a target concentration outside the range defined by the two stocks. Consider using a different stock solution.
Can I scale the result?
Yes. The ratio is independent of volume. Multiply each part by the scaling factor needed for your batch size.
How accurate is the method?
Alligation assumes additive volumes and concentrations. For highly non-ideal mixtures, lab verification is recommended.
Does the order of mixing matter?
No, but for safety add the stronger solution to the weaker one slowly while stirring.