Alligation Medial Calculator
The Alligation Medial Calculator finds the average concentration of a mixture made by combining solutions of different strengths. It is the volume-weighted mean: (c₁v₁ + c₂v₂ + c₃v₃) ÷ (v₁ + v₂ + v₃).
Formula
Average concentration = (c₁×v₁ + c₂×v₂ + c₃×v₃) / (v₁ + v₂ + v₃)
- Alligation medial finds the strength of a mixture when you already know how much of each component you used.
- Multiply each component's concentration by its volume, add these products, then divide by the total volume.
- The result always lies between the highest and lowest input concentrations.
- Leave the third component at zero volume if you are only mixing two solutions.
Example Calculation
Inputs
- Concentration 1: 40 %
- Volume 1: 2 L
- Concentration 2: 20 %
- Volume 2: 3 L
- Concentration 3 (optional): 0 %
- Volume 3 (optional): 0 L
Mixing 2 L at 40% with 3 L at 20%: average = (40×2 + 20×3) ÷ (2+3) = (80 + 60) ÷ 5 = 28%, in a total of 5 L.
Frequently asked questions
What is alligation medial?
It is a method to find the average concentration of a mixture when the quantity and strength of each ingredient are known.
How is it different from alligation alternate?
Medial finds the resulting strength from known amounts; alternate works backwards to find how much of each strength to mix for a target.
Can the average be outside the input range?
No. The weighted average is always between the lowest and highest concentrations you mixed.
What units should I use?
Any consistent units work — concentrations as % (or mg/mL) and volumes in the same unit (e.g. L) throughout.
How do I mix only two solutions?
Set the third concentration and volume to zero, and the calculator uses just the first two components.