Molarity Dilution Calculator (C1V1 = C2V2, Solve for Any Value)
Solve C1V1 = C2V2 for the stock volume, final concentration, final volume or stock concentration — with M to pM and L to µL unit menus, the solvent to add, dilution factor and ratio, moles and grams of solute, a prep table and the worked steps.
How it works
C1 × V1 = C2 × V2 → V1 = C2·V2 ÷ C1 · C2 = C1·V1 ÷ V2 · V2 = C1·V1 ÷ C2 · C1 = C2·V2 ÷ V1 · solvent = V2 − V1 · dilution factor = C1 ÷ C2 = V2 ÷ V1
Diluting a solution adds solvent but leaves the amount of solute unchanged, so concentration × volume is the same before and after: C1V1 = C2V2. C1 and V1 describe the stock you pipette, C2 and V2 the finished solution. Choose which of the four values you need with "Solve for" and enter the other three; each field has its own unit menu (M, mM, µM, nM, pM and L, mL, µL), so you can mix units freely and the calculator converts them before solving. Besides the unknown it reports the solvent to add (V2 − V1), the dilution factor and the stock-to-solvent ratio, and the moles of solute carried over. Add the molar mass under More options to see the grams of solute and the mass concentrations. Two tables show how much stock and solvent the same dilution needs at common final volumes, and the volumes for 2× to 1000× dilutions of your stock. If the stock volume comes out below 1 µL, a note suggests an intermediate dilution so you can pipette it accurately. The equation works for any concentration unit as long as C1 and C2 use the same one (for % or mg/mL solutions see the percent solution and dilution calculators).
Worked example
To make 500 mL of 0.5 M NaCl from a 5 M stock: V1 = 0.5 M × 500 mL ÷ 5 M = 50 mL of stock, topped up with 450 mL of water. The dilution factor is 5 ÷ 0.5 = 10× (1 part stock to 9 parts water), and the final solution holds 0.25 mol of NaCl — 14.61 g at 58.44 g/mol. Going the other way, 2 µL of a 10 mM stock in 1 mL of buffer gives C2 = 10 mM × 0.002 mL ÷ 1 mL = 20 µM.
Sources: LibreTexts Chemistry — Dilution
Frequently asked questions
Do the units have to match?
Not here — every field has a unit menu, and the calculator converts mM, µM, nM, µL and L before solving. If you solve by hand, C1 and C2 must use the same concentration unit and V1 and V2 the same volume unit; V1 then comes out in the unit of V2.
Is V2 the volume of water I add?
No. V2 is the total final volume of the diluted solution. The solvent you add is V2 − V1, which the calculator shows as "Solvent to add".
What is the difference between a dilution factor and a dilution ratio?
A 10× dilution factor means the final volume is ten times the stock volume: 1 part stock plus 9 parts solvent. Some protocols write that as 1:10 (part to total) and others as 1:9 (part to part), so this calculator gives both the factor and the explicit stock : solvent ratio.
My stock volume is less than 1 µL. What should I do?
Volumes that small cannot be pipetted accurately. Dilute the stock 1:10 or 1:100 first and use a larger volume of that intermediate solution — the calculator suggests one automatically — or make a larger final volume.
Add stock to solvent or vice versa?
For strong acids, always add acid to water. Otherwise, add the stock to most of the solvent, mix, then top up to the final volume so the total is exactly V2.
Can I use C1V1 = C2V2 for percent or mg/mL solutions?
Yes, as long as C1 and C2 are in the same unit — the arithmetic is identical. This calculator’s menus are molar; for percent solutions use the percent solution calculator, or enter the numbers as if they were M and read the result in your own unit.
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For educational and lab-planning use. Follow proper safety procedures when handling chemicals.