Dilution Calculator
Quickly find any unknown in the dilution equation C₁V₁ = C₂V₂. Perfect for preparing solutions from stock, adjusting concentrations, or performing serial dilutions. Supports concentration units (mol/L, mmol/L) and volume units (L, mL) with automatic conversion.
How to Use the Dilution Equation C₁V₁ = C₂V₂
The dilution formula C₁V₁ = C₂V₂ states that the amount of solute remains constant when diluting a solution. Here: C₁ = initial concentration, V₁ = initial volume, C₂ = final concentration, V₂ = final volume. You can solve for any one variable when the other three are known. This calculator automatically converts between concentration units (mol/L, mmol/L) and volume units (L, mL) so you can mix units freely. It’s ideal for lab work, pharmaceutical preparations, and educational exercises.
Formula
How to Use?
- Select the unknown you want to find: C₁, V₁, C₂, or V₂.
- Enter the three known values, using the dropdowns to select the appropriate units for each.
- The calculator automatically converts everything to base units (mol/L and L) and solves the equation.
- The result is shown with the correct unit (mol/L for concentrations, L for volumes).
Worked Examples
Find final volume when diluting 50 mL of 2.0 M to 0.5 M
Find initial volume needed to make 500 mL of 0.1 M from 2.0 M stock
Find final concentration after diluting 25 mL of 0.5 M to 100 mL
The Dilution Equation Explained
C₁V₁ = C₂V₂ is derived from the fact that the number of moles of solute remains constant during dilution. Rearranging gives formulas for each variable, allowing you to calculate any missing quantity when the other three are known.
Unit Conversions Made Simple
You can enter concentrations in mol/L or mmol/L, and volumes in L or mL. The calculator converts everything to mol/L and L before solving, so you don’t have to worry about mismatched units.
Real‑World Applications
Use this calculator to prepare a specific concentration from a stock solution, determine how much stock is needed for a desired final volume, or find the final concentration after adding solvent.
Table: Example Dilution Calculations
| C₁ | V₁ | C₂ | V₂ | Unknown |
|---|---|---|---|---|
| 2.0 mol/L | 0.1 L | 0.5 mol/L | 0.4 L | V₂ |
| 6.0 mol/L | 0.5 L | 1.5 mol/L | 2.0 L | C₂ |
| 0.5 mol/L | 0.2 L | 0.1 mol/L | 1.0 L | V₁ |
FAQs
What is the difference between C₁V₁ = C₂V₂ and M₁V₁ = M₂V₂?
They are the same equation; M (molarity) is a common symbol for concentration. The formula works for any concentration unit as long as you use the same unit on both sides.
Can I use this for serial dilutions?
Yes – for serial dilutions, you can apply the equation repeatedly. For example, to find the concentration after two steps, you would use the output of the first step as the new C₁ for the second step.
Why is the result for volume given in liters when I entered milliliters?
The calculator converts all volumes to liters for the calculation and returns the result in liters for consistency. If you prefer milliliters, simply multiply by 1000.