💧 Dilution Calculator (C₁V₁ = C₂V₂)
Work out how to dilute a stock solution: enter three of C₁, V₁, C₂, V₂ and the dilution equation gives the fourth.
Stock volume (V₁)
25 mL
C₁V₁ = C₂V₂, stock concentration × stock volume = final concentration × final volume. 🔒 Computed in your browser.
How the dilution calculator (c₁v₁ = c₂v₂) works
For a dilution, moles of solute are conserved, so C₁V₁ = C₂V₂ (stock concentration × stock volume = final concentration × final volume). Enter any three values and the tool solves for the missing one; the concentration units cancel, so any consistent unit works. The equation holds because diluting adds only solvent, leaving the amount of solute (concentration × volume) unchanged, so you can solve for any one of C₁, V₁, C₂ or V₂.
The everyday bench question, “how much stock do I need for 100 mL of 0.5 M from a 2 M stock?” Solve for V₁ and it answers 25 mL (then top up to 100 mL).
Frequently asked questions
How do I use C₁V₁ = C₂V₂?
Identify your stock concentration (C₁) and the final concentration (C₂) and volume (V₂) you want, then solve for the stock volume V₁ = C₂V₂ / C₁. Add solvent to reach the final volume.
How much stock do I need?
V₁ = (C₂ × V₂) ÷ C₁. For 100 mL of 0.5 M from a 2 M stock: (0.5 × 100) ÷ 2 = 25 mL of stock, diluted to 100 mL.
What units should concentration and volume be in?
Any consistent units, the concentration units cancel and the volume units cancel, so use molarity with mL, or any matching pair.
Does this work for serial dilutions?
Each step of a serial dilution is one C₁V₁ = C₂V₂ calculation; run it repeatedly for each stage.
Why does the dilution equation work?
Diluting adds solvent but not solute, so the number of moles of solute is unchanged: concentration × volume (which equals moles) is the same before and after.
What is the dilution factor?
The ratio of final to initial volume, or equivalently initial to final concentration. Diluting 10 mL of 2 M stock to 100 mL is a 10× dilution (2 M → 0.2 M).
Can I dilute by percentage instead of molarity?
Yes, treat the percentages as the concentrations, since their units cancel. Diluting a 30% solution to 5% in 200 mL needs V₁ = (5 × 200) ÷ 30 = 33.3 mL of the 30% solution, topped up to 200 mL.
How much solvent do I add to dilute a solution?
Find the stock volume V₁ needed, then add solvent up to the final volume V₂, the added solvent is V₂ − V₁. To make 250 mL of 0.2 M from a 1 M stock, use 50 mL of stock and add 200 mL of solvent.
Does C₁V₁ = C₂V₂ work for concentrating a solution?
No, the equation only conserves solute while adding solvent, so it describes dilution (C₂ < C₁). Concentrating means removing solvent by evaporation, which this relationship does not model.