Dilution Equation formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| C₁ | Stock concentration | mol/m³ | Concentration of the stock solution |
| V₁ | Stock volume needed | m³ | Volume of stock solution to take |
| C₂ | Final concentration | mol/m³ | Desired final concentration |
| V₂ | Final volume | m³ | Desired final total volume |
What is Dilution Equation?
Dilution Equation: Diluting a solution does not change the amount of solute: the concentration times the volume is the same before and after.
Adding solvent spreads the same number of moles through a larger volume, so C₁V₁ = C₂V₂. This calculator answers the everyday lab question "how much stock do I need?" and also reports the dilution factor and how much solvent to add.
Any concentration unit works (mol/L, mg/mL, %, ×) as long as C₁ and C₂ use the same unit. The same goes for V₁ and V₂.
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
You need 500 mL of 0.1 M HCl from a 2 M stock.
- V₁ = C₂V₂ / C₁ = 0.1 × 500 / 2 = 25 mL of stock.
- Add solvent to reach 500 mL (≈ 475 mL). Dilution factor = 20.
Safety: when diluting concentrated acids, always add acid to water, never water to acid.
Frequently asked questions
Is V₂ the volume of water to add?
No. V₂ is the final total volume. The volume of solvent to add is approximately V₂ − V₁, which the calculator shows as a derived result.
How do I do serial dilutions?
Apply C₁V₁ = C₂V₂ at each step. Ten 1:10 dilutions in series give an overall dilution factor of 10¹⁰.