Work out any part of a dilution — the stock volume to use, the final concentration, or how much solvent to add — using the dilution equation C₁V₁ = C₂V₂.
Quick answer: Dilution follows C₁V₁ = C₂V₂, where C is concentration and V is volume. To dilute a 2 M stock to 0.5 M and make 100 mL, you need V₁ = C₂V₂ ÷ C₁ = (0.5 × 100) ÷ 2 = 25 mL of stock, topped up to 100 mL (add 75 mL solvent).
Use the same concentration units for C₁ and C₂ (e.g. both M), and the same volume units for V₁ and V₂ (e.g. both mL).
Diluting a solution lowers its concentration by adding more solvent while the amount of solute stays the same. Because moles of solute are conserved, concentration times volume before equals concentration times volume after — the dilution equation C₁V₁ = C₂V₂. Rearrange it to find whichever value you're missing.
C₁ and V₁ are the concentration and volume of the concentrated stock; C₂ and V₂ are the concentration and volume of the final, diluted solution. The solvent you add is simply V₂ − V₁.
Worked example
You have a 2 M stock and need 100 mL of 0.5 M solution. V₁ = (0.5 × 100) ÷ 2 = 25 mL. Measure 25 mL of stock and add solvent up to the 100 mL mark — that's 75 mL of solvent.
Frequently asked questions
What is the dilution formula?
C₁V₁ = C₂V₂. The concentration times volume of the stock equals the concentration times volume of the diluted solution, because the moles of solute don't change.
How much solvent do I add?
Add V₂ − V₁. Measure the stock volume V₁, then top up with solvent to the final volume V₂, rather than adding a fixed amount.
Do the units have to match?
Yes — use the same units for both concentrations and the same units for both volumes. The equation works for M, %, mg/mL and any consistent pair.
What is a dilution factor?
It's C₁ ÷ C₂ (or V₂ ÷ V₁). A 1:10 dilution means the final concentration is one tenth of the stock.
Written by the CalcPine team · Reviewed for accuracy · Last updated 31 July 2026 · Method: dilution equation C₁V₁ = C₂V₂, solved for the selected variable.
