Dilution Calculator (C1V1 = C2V2)
Enter any three of the stock concentration, stock volume, final concentration and final volume. You get the fourth and the solvent to add.
Fill in three of the four values and leave the one you want to find empty. The answer appears as you type, in the unit shown next to its box. Any concentration unit works if C1 and C2 use the same one.
Worked examples
From a 2 molar stock
C1 2 mol/L, C2 0.5 mol/L, V2 250 mL
V1 = 62.5 mL
0.5 x 250 / 2.
Final strength
10 mL of 6 mol/L made up to 60 mL
1 mol/L
6 x 10 / 60.
About Dilution Calculator (C1V1 = C2V2)
When you dilute a solution, the amount of solute stays the same and only the amount of solvent changes. Since the amount of solute is the concentration multiplied by the volume, the product of concentration and volume before dilution equals the product after: C1 V1 equals C2 V2. This simple relation is used daily in labs, hospitals and kitchens to prepare working solutions from concentrated stocks.
Enter the three values you know. For example, to make 250 millilitres of a 0.5 molar solution from a 2 molar stock, you need 62.5 millilitres of stock, made up to the final volume with solvent, so you add about 187.5 millilitres of solvent. The page also gives the dilution factor. It assumes volumes add up, which is a good approximation for dilute aqueous solutions.
How to use Dilution Calculator (C1V1 = C2V2)
- Enter any three of the stock concentration, stock volume, final concentration and final volume.
- Choose units for the concentrations and volumes.
- Leave the value you want to find empty.
- Read the answer, the solvent to add and the dilution factor.
Common uses
- Making a working solution from a laboratory stock
- Preparing a cleaning solution from a concentrate
- Planning serial dilutions
- Checking the volume of acid needed for a given strength
Frequently asked questions
What does C1V1 = C2V2 mean?
C1 and V1 are the concentration and volume of the stock, and C2 and V2 are those of the diluted solution. The amount of solute is the same on both sides.
How much solvent do I add?
The final volume minus the stock volume. For 62.5 millilitres of stock made up to 250 millilitres, add 187.5 millilitres.
Can I mix units?
Use the same concentration unit for C1 and C2, and the page converts the volumes for you. Percentages and mol/L work equally well if you stick to one.
Why add acid to water and not the other way round?
Diluting a concentrated acid gives out heat. Adding the acid slowly to water spreads the heat. The reverse can boil and spit.