Dilution Calculator (C1V1 = C2V2)
Choose the value to solve for and fill in the other three. Concentrations can be in any unit as long as C1 and C2 use the same one.
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Formula
C1 × V1 = C2 × V2(solute is conserved when solvent is added).- Solve for any unknown:
V2 = C1 × V1 ÷ C2,C2 = C1 × V1 ÷ V2,V1 = C2 × V2 ÷ C1,C1 = C2 × V2 ÷ V1. - Solvent to add:
V2 − V1. Dilution factor:C1 ÷ C2.
Worked example
Dilute 25 mL of 12 M stock to 1 M.
V2 = 12 × 25 ÷ 1 = 300 mL- Solvent to add:
300 − 25 = 275 mL - Dilution factor:
12 ÷ 1 = 12
Add the 25 mL of stock to about 250 mL of solvent in a flask, mix, then top up to 300 mL. With strong acids always add the acid to the water.
Frequently asked questions
What is the dilution formula?
C1 × V1 = C2 × V2. The amount of solute does not change when you add solvent, so concentration times volume is the same before and after. For 12 M stock, 25 mL and a 1 M target: V2 = 12 × 25 ÷ 1 = 300 mL.
How much solvent do I add?
Solvent to add = V2 − V1. Taking 25 mL of stock up to 300 mL means adding 275 mL of solvent.
Do the concentration and volume units have to match?
C1 and C2 must use the same unit (both mol/L, or both % and so on), and V1 and V2 must use the same unit. The units cancel, so you do not need to convert.
What is the dilution factor?
It is C1 ÷ C2, which equals V2 ÷ V1. Diluting 12 M to 1 M is a 12-fold dilution, often written 1:12 (one part stock to eleven parts solvent).