Pick the variable to solve for, fill in the other three, and mix units freely — M, mM, µM for concentration; L, mL, µL for volume. Everything is converted automatically and the substitution is shown step by step.
C₁V₁ = C₂V₂
Why C₁V₁ = C₂V₂ works
Diluting a solution adds solvent but not solute — the dissolved substance's amount in moles never changes. Since moles = concentration × volume, the product C × V before dilution must equal C × V after. That single conservation idea is the whole formula.
Lab-style example
You need 250 mL of 0.1 M HCl from a 1.0 M stock. How much stock do you measure?
Solve for V₁ = C₂V₂ ÷ C₁
V₁ = (0.1 M × 250 mL) ÷ 1.0 M = 25 mL
Measure 25 mL of stock, then add water up to the 250 mL mark.
Answer: 25 mL of stock solution.
Common mistakes with dilutions
⚠ Common mistake: Mixing units across sides — mL on the left and L on the right — is the classic error. Identical units cancel; mismatched units silently scale the answer by 1000. (This calculator converts everything for you.)
⚠ Common mistake: V₂ is the final total volume, not the amount of water added. Adding 25 mL stock + 250 mL water gives V₂ = 275 mL, not 250 mL.
⚠ Common mistake: C₁V₁ = C₂V₂ is for diluting with pure solvent only. Mixing two solutions of different concentrations needs a total-moles calculation instead.
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Frequently asked questions
▸What do C1, V1, C2 and V2 stand for?
C₁ and V₁ are the concentration and volume of the starting (stock) solution; C₂ and V₂ are the concentration and total volume after dilution.
▸Can I use mL on both sides?
Yes — any unit works as long as it matches on both sides. This calculator converts internally to M and L so you can even mix units.
▸What is a serial dilution?
A chain of dilutions where each step dilutes the previous result (often 1:10 each time) — used to reach very low concentrations accurately. Apply C₁V₁ = C₂V₂ once per step.