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Diluting a concentrated stock solution to a lower working concentration is one of the most routine tasks in any lab, and it all comes down to a single equation: C₁V₁ = C₂V₂. The amount of solute doesn't change when you add solvent — only the volume does.
Pick the value you need, enter the three you know, and the calculator returns the fourth.
How is it calculated?
The dilution equation
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.
| Solve for | Formula |
|---|---|
| Stock volume V₁ | (C₂ × V₂) ÷ C₁ |
| Stock concentration C₁ | (C₂ × V₂) ÷ V₁ |
| Final concentration C₂ | (C₁ × V₁) ÷ V₂ |
| Final volume V₂ | (C₁ × V₁) ÷ C₂ |
How much diluent to add
The most common question is "how much stock and how much water?" Solve for V₁ (the stock you need), then the diluent to add is simply V₂ − V₁. For a 100 mL final volume needing 20 mL of stock, you add 80 mL of solvent.
Keep the units consistent
The two concentrations must share a unit (both M, both %, both mg/mL) and the two volumes must share a unit (both mL, both L). The equation is a ratio, so it doesn't matter which units you pick — only that each pair matches.
Where it helps
Preparing working solutions from a concentrated stock, making serial dilutions, or reconstituting reagents to a spec. To first work out a stock concentration from mass, use a molarity calculator.
Worked example
You have a 10 M HCl stock and need 100 mL of 2 M HCl. Solve for V₁: V₁ = (C₂ × V₂) ÷ C₁ = (2 × 100) ÷ 10 = 20 mL. So you measure 20 mL of the 10 M stock and add 80 mL of water to reach 100 mL total — never the other way around when handling strong acids: add acid to water.
FAQ
What is the C1V1 = C2V2 formula?+
It states that the moles of solute are conserved during dilution: concentration × volume before equals concentration × volume after. Rearranged, it solves for any one of the four values.
How much water should I add to dilute a solution?+
Solve for the stock volume V₁ you need, then the water to add is the final volume minus V₁. For 100 mL needing 20 mL of stock, add 80 mL of water.
Do the units have to match?+
The two concentrations must use the same unit and the two volumes must use the same unit, but you can mix systems between the pairs. The formula is a ratio, so consistent pairs are all that matters.
What is a dilution factor?+
It is the ratio of final volume to stock volume (V₂ ÷ V₁), or equivalently C₁ ÷ C₂. A 1:10 dilution means one part stock to nine parts diluent, a factor of 10.
Can I use this for serial dilutions?+
Yes — apply the calculator once per step, using each step’s result as the stock for the next. Serial dilutions multiply the factors, so three 1:10 steps give a 1:1000 total dilution.