Calculate mixture concentrations, mixing ratios, target amounts, and dilution volumes. Concentrations use % w/v (grams per 100 mL), g/L, mg/mL, mg/L, or approximate ppm for dilute water near 1 kg/L density. Do not enter % w/w or % v/v. The model assumes additive volumes and no chemical reaction.

Mass-per-volume concentrations only: % w/v means grams per 100 mL. ppm assumes dilute water with density about 1 kg/L. Do not enter % w/w or % v/v. Volumes are assumed additive; no reaction, precipitation or volume contraction is modeled.

Display settings

Rounding changes the display only. Very small values use scientific notation.

Alligation Formula

The following formula is used to calculate the Alligation calculation:

C1 × V1 + C2 × V2 = C × V

Variables:

  • C1 is the concentration of the first solution
  • V1 is the volume of the first solution
  • C2 is the concentration of the second solution
  • V2 is the volume of the second solution
  • C is the concentration of the resulting mixture
  • V is the volume of the resulting mixture

To calculate the Alligation calculation, multiply the concentration of the first solution by its volume, then multiply the concentration of the second solution by its volume. Add these two results to obtain the total solute amount in consistent units. Divide that amount by the combined volume to obtain the mixture concentration.

What is a Alligation?

Alligation is a mathematical method used to solve problems related to mixtures and their ingredients. It is a rule that allows one to find the ratio in which two or more ingredients at given prices must be mixed to produce a mixture of a desired price. The method involves the use of a simple diagram known as an alligation chart, where the prices of the cheaper and dearer ingredients are written in the left and right columns, respectively, and the mean price in the middle column. The differences between the mean price and the prices of the ingredients are then calculated and written in the opposite columns. These differences represent the required ratio of the ingredients. Alligation is commonly used in pharmacy to calculate the amount of different substances required to make a particular medicine.

How to Calculate Alligation?

The following steps outline how to calculate the Alligation.

  1. First, determine the quantities or concentrations of the two solutions being mixed.
  2. Next, assign a variable to each quantity or concentration. Let’s call them A and B.
  3. Next, determine the desired concentration of the mixture.
  4. Select Mixing ratio and enter both source concentrations and the target in consistent concentration units.
  5. Check that the target is between the two source concentrations. Equal source concentrations do not determine a unique ratio.
  6. The volume ratio A:B is |target − B| : |A − target|. A target equal to one source requires only that source.
  7. Finally, use the ratio to determine the proportions of A and B needed to achieve the desired concentration.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Concentration of A = 20% w/v

Concentration of B = 40% w/v

Desired concentration = 30% w/v. The required volume ratio A:B is 1:1.