The dilution equation calculator solves C₁V₁ = C₂V₂ for any of four variables: initial concentration, initial volume, final concentration, or final volume. Works with any consistent concentration units (mol/L, g/L, %, etc.).
Dilution Calculator (C₁V₁ = C₂V₂)
Use any consistent units for concentration and volume. All four fields use the same implied units.
How to Use the Dilution Calculator
C₁V₁ = C₂V₂ expresses conservation of solute moles. Adding solvent increases volume but doesn't change moles of solute, so concentration decreases proportionally.
Example: Diluting a Stock Solution
You have a 10 M HCl stock. How much do you need to make 500 mL of 0.5 M HCl? V₁ = C₂V₂/C₁ = (0.5 × 500) / 10 = 25 mL. Add 25 mL stock to ~475 mL water, then fill to 500 mL. Always add acid to water, never water to acid.
Dilution Factor
Dilution factor = V₂/V₁ = C₁/C₂. A 1:10 dilution (add 1 part sample to 9 parts diluent) has dilution factor = 10. Serial 1:10 dilutions give: 10⁻¹, 10⁻², 10⁻³ concentrations.
Frequently Asked Questions
What is the dilution equation?
C₁V₁ = C₂V₂, where C₁ is the initial concentration, V₁ is the initial volume, C₂ is the final concentration, and V₂ is the final volume. This equation expresses conservation of solute moles — the amount of solute doesn't change when you dilute, only the total volume increases.
How do I dilute a 10 M solution to 2 M?
Using C₁V₁ = C₂V₂: (10 M)(V₁) = (2 M)(1 L). V₁ = 0.2 L = 200 mL. Take 200 mL of the 10 M solution and add water to make the total volume 1 liter. Always add concentrated solution to water (not water to acid) for safety.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
What concentration units does this support?
This calculator works with any consistent concentration units: mol/L (molarity), g/L, mg/mL, percent (%), ppb, ppm. As long as both C₁ and C₂ use the same units, the equation works. Just be consistent throughout the calculation.