Dilution Calculator: C1V1 = C2V2
The dilution equation C1V1 = C2V2 is a fundamental tool in chemistry and biology laboratories. It states that the moles of solute remain constant during dilution: the initial concentration (C1) times the initial volume (V1) equals the final concentration (C2) times the final volume (V2). Use this calculator to find the volume of concentrated stock solution (V1) needed to prepare a target concentration (C2) at a desired final volume (V2). You can also solve for C2 or V2 by entering the other three values.
Dilution formula
C1 * V1 = C2 * V2, therefore V1 = (C2 * V2) / C1
Rearrangements: C2 = (C1 * V1) / V2 and V2 = (C1 * V1) / C2. All concentrations must be in the same units and all volumes in the same units.
Worked example
- Goal: prepare 100 mL of 0.1 M NaCl from a 1 M stock.
- V1 = (C2 * V2) / C1 = (0.1 M * 100 mL) / 1 M = 10 mL.
- Pipette 10 mL of 1 M NaCl into a volumetric flask and make up to 100 mL with distilled water.
- The volume of water to add is V2 - V1 = 100 - 10 = 90 mL.
Frequently asked questions
What does C1V1 = C2V2 mean?
C1V1 = C2V2 is the dilution equation where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume. It states that the number of moles of solute before and after dilution remains the same.
What units should I use?
Concentration units must match (both in mol/L, both in mg/mL, etc.). Volume units must also match (both in mL, both in L, etc.). The calculator accepts any consistent units.
How much solvent do I need to add?
The volume of solvent (water or buffer) to add is V2 minus V1. For example, to dilute 10 mL of 1 M stock to 0.1 M, the final volume V2 = 100 mL, so you add 90 mL of solvent.
Can I use this for serial dilutions?
Yes, but for serial dilutions you apply C1V1 = C2V2 at each step, using the output of one dilution as the input to the next. The dilution factor calculator handles the overall factor automatically.
What can I solve for?
You can solve for any one unknown given the other three. This calculator solves for V1 (volume of stock needed) by default, but the formula can be rearranged for C1, C2, or V2 as needed.
Official sources
- IUPAC Gold Book: Dilution factor definition.
- NIST: NIST Weights and Measures.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.