C1V1 = C2V2 Dilution Calculator
Use the same concentration unit for C1 and C2 (M, mM, %, mg/mL…).
How the dilution formula works
When you dilute a solution, the amount of solute doesn't change; only the volume does. So concentration × volume before equals concentration × volume after:
C1 × V1 = C2 × V2
C1 is the stock concentration, V1 the volume of stock you take, C2 the concentration you want and V2 the final total volume. Know any three and the calculator solves the fourth. The formula works with any concentration unit (molar, millimolar, % w/v, mg/mL) as long as C1 and C2 use the same one.
Worked example
You need 500 mL of 0.1 M solution from a 2 M stock. V1 = (0.1 × 500) ÷ 2 = 25 mL. Measure 25 mL of stock and add solvent to a total of 500 mL; that's about 475 mL of solvent, but always fill to the final volume in a volumetric flask or graduated cylinder rather than adding a fixed solvent volume, because volumes don't always add perfectly.
Mass from molarity
To make a solution from a solid, use mass (g) = molarity (mol/L) × volume (L) × molecular weight (g/mol). For 500 mL of 0.1 M sodium chloride (58.44 g/mol): 0.1 × 0.5 × 58.44 = 2.922 g. For every direction (mass, molarity or volume) and common presets, use the full molarity calculator. Weighing to that resolution needs a balance that reads at least 0.01 g; for smaller masses or tighter tolerances, an analytical balance reading to 0.0001 g is the right tool. Our precision balances (0.01 g) handle most routine solution prep.
Common mistakes
- Mixing units. Keep C1 and C2 in the same unit, and V1 and V2 in the same unit.
- Using anhydrous molecular weight for a hydrate. Copper sulfate pentahydrate is 249.68 g/mol, not 159.61. Use the MW on your bottle.
- Adding solute to the full volume of solvent. Dissolve, then bring up to the final volume.
- Serial dilutions in one step. For very large dilution factors (1:1000+), do two or more steps for better accuracy; the serial dilution calculator plans each step.
FAQ
Can I use percent concentrations?
Yes. C1V1 = C2V2 works with % as long as both concentrations are the same type (% w/v with % w/v).
What's the dilution factor?
V2 ÷ V1 (or C1 ÷ C2). Diluting 25 mL to 500 mL is a 1:20 dilution.
Does temperature matter?
For precise work, yes: volumetric glassware is calibrated at 20 °C, and solutions expand when warm. Prepare at room temperature.
More tools: molarity calculator, percent solution calculator, and all free lab calculators.
