How to calculate dilutions

Updated February 21, 2017

Chemistry labs and pharmacies often need to dilute concentrated substances into less concentrated forms. Precise calculations will ensure that the dilution contains the proper amount of the concentrated substance. When calculating dilutions, there are two main components of the dilution: the solute and the solvent. The solute, also known as the aliquot, is the concentrated solution. The solvent, also known as the diluent, is the other liquid that is used in the dilution.

Determine how much of the final solution you will need and what its dilution ratio should be. For example, you may require 100mL of a 1:8 dilution.

Divide the total volume of solution required by the second number in the dilution ratio. This second number tells you how many total parts are in the dilution, so the answer will tell you how big each part is. In the above example, 100mL divided by 8 is 12.5mL.

Multiply the above answer by the first number in the dilution ratio to find out how much of the concentrated solute you will need. It is common for the first number to be 1, as in the above case, so you will need 12.5mL of the solute.

Subtract the amount of solute from the total volume of the solution needed to find out how much of the solvent is required. In this case, you will need 100mL minus 12.5mL, or 87.5mL of solvent in the dilution.

Determine the concentration of the starting solution, abbreviated as C1. Most prepared solutions are labelled with their concentration either in weight per unit volume or in molarity, which is the number of moles per litre. For example, you may have a 0.4M solution of acid.

Look up what volume and concentration of the solution you will need. These are abbreviated V2 and C2. For example, you may need 350mL of 0.15M acid solution.

Plug all of the numbers into the formula C1 x V1 = C2 x V2 and solve algebraically to find V1, or the volume of starting solution needed to make the dilution. In this example, you would solve 0.4M x V1 = 0.015M x 350mL to find that V1 is 13.125mL.

Subtract V1 from V2 to find out how much water should be mixed with the portion of the starting solution. In the above example, 350mL minus 13.125mL leaves 336.875mL of water required to mix the dilution.


Always follow safety precautions when working with concentrated solutions of dangerous chemicals. Safety goggles, proper lab attire and education in the handling of the particular chemicals in use will help protect you from burns and other accidents.

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