💧 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 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.