Dilution Calculator (C1V1 = C2V2)
Calculate diluted concentration or volume using the C1V1 = C2V2 equation.
Leave one field blank — the calculator will solve for it.
How It Works
Enter any three of the four values (C1, V1, C2, V2) and leave one field blank. The calculator rearranges C1V1 = C2V2 to solve for the missing variable. C1 is your starting (stock) concentration, V1 is the volume of stock you will take, C2 is your target concentration, and V2 is the final total volume after dilution.
Formula
Worked Examples
- Find C2: 1 M HCl, 10 mL taken, diluted to 100 mL → C2 = (1 × 10) / 100 = 0.1 M
- Find V1: Stock 5 M, want 0.25 M in 200 mL → V1 = (0.25 × 200) / 5 = 10 mL of stock
- Find V2: Stock 12 M HCl, take 8.3 mL, want 1 M → V2 = (12 × 8.3) / 1 = 99.6 mL total
Why C1V1 = C2V2 Works
When you dilute a solution, you add solvent (usually water) but no additional solute. The number of moles of solute in V1 of the stock equals the number of moles in V2 of the diluted solution: moles = C × V. Setting them equal gives C1V1 = C2V2. This principle holds for any concentration unit (M, mM, µM, ppm, g/L) as long as C1 and C2 use the same unit and V1 and V2 use the same unit.
Serial Dilutions
When you need to reduce a concentration by a very large factor (e.g., 1000×), doing it in one step requires using a tiny, hard-to-measure volume of stock. Serial dilutions solve this by performing several smaller dilutions in sequence, each achieving a more manageable dilution factor. For example, three 1:10 dilutions achieve an overall 1:1000 dilution. Apply C1V1 = C2V2 at each step: take 1 mL of stock, dilute to 10 mL (10× dilution); take 1 mL of that, dilute to 10 mL again; repeat once more.
Safety Note for Concentrated Acids
When diluting concentrated strong acids, always add acid to water, never water to acid. Adding water to concentrated H₂SO₄ can cause a violent exothermic reaction. Use a heat-resistant vessel, add the acid slowly with stirring, and allow the solution to cool between additions when making large volumes.
Frequently Asked Questions
What is the dilution equation?
C1V1 = C2V2, where C1 is the initial concentration, V1 is the initial (stock) volume taken, C2 is the final concentration, and V2 is the final total volume. The equation holds because the moles of solute are conserved during dilution.
How do I make a 1 M solution from a 10 M stock?
Use C1V1 = C2V2: 10 × V1 = 1 × 1000 mL (for 1 L final volume), so V1 = 100 mL of stock. Measure 100 mL of the 10 M stock and add water until the total volume reaches 1000 mL.
Does the volume unit matter?
V1 and V2 must use the same unit (both mL, or both L). C1 and C2 must also use the same unit, but that unit can be anything: M, mM, µM, ppm, g/L, etc.
What is the dilution factor?
Dilution factor = V2 / V1 = C1 / C2. For example, taking 10 mL of stock and diluting to 100 mL gives a 10× dilution factor (or 1:10 dilution ratio).
Can I use this for gases or solid concentrations?
C1V1 = C2V2 applies to liquid solutions. For gases, use the ideal gas law (PV = nRT) or mixing laws. For solids dissolved by mass fraction, use a mass balance equation instead.