Chemistry · Dilution
Dilution calculator.
Leave one box empty and solve C1V1 = C2V2. Any concentration unit, any volume unit, as long as each pair matches.
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The dilution equation
When you add solvent to a solution, the amount of solute does not change, only the volume. That gives C1 x V1 = C2 x V2, where C is concentration and V is volume before (1) and after (2) dilution. It works for molarity and for any other concentration unit, as long as C1 and C2 use the same unit.
Worked example. Make 500 mL of 0.1 M solution from a 1 M stock. V1 = C2 x V2 / C1 = 0.1 x 500 / 1 = 50 mL of stock. Add enough solvent to reach 500 mL, which is 450 mL, a dilution factor of 10. Second example: dilute 5 mL of 12 M stock to 0.5 M and the final volume is 12 x 5 / 0.5 = 120 mL.
In practice, pipette the stock into a volumetric flask and fill to the mark rather than adding a fixed volume of diluent, so you do not need to assume the two volumes add up exactly. When diluting concentrated acids or bases, add the stock to the water, not water to the stock, and wear the protective equipment listed on the SDS. If the answer is a final concentration above the stock, the tool says so, since that is a concentration step, not a dilution.
Frequently asked questions
What does C1V1 = C2V2 mean?
The amount of solute is the same before and after dilution: initial concentration x initial volume equals final concentration x final volume.
How much water do I add?
Final volume minus the stock volume you take. The tool shows it as "Add diluent". For accuracy, fill to the final volume mark instead of measuring that diluent by itself.
Can I use mL, L, M, mM or percent?
Yes. Any units work if both concentrations share a unit and both volumes share a unit.
What is the dilution factor?
C1 / C2, or V2 / V1. A factor of 10 means 1 part stock in 10 parts final solution.
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Lab safety and scope
This is arithmetic, not professional advice. Check every result against your own procedure, the safety data sheet (SDS) for each chemical, and your lab supervisor or instructor before you prepare, mix or dispose of anything. Verify values on the reagent bottle, since purity and hydration state change the real molar mass.