Calculator
Dilution calculator (C₁V₁ = C₂V₂)
Dilute a stock solution to a target concentration in a target volume. Enter stock concentration, target concentration, and target volume — the calculator returns the stock volume to add.
Stock volume V₁
10.000 mL
Diluent to add
90.000 mL
Worked example
Diluting a 1 M Tris stock to 100 mM in 500 mL: V₁ = (0.1 × 500) ÷ 1 = 50 mL. Add 50 mL of stock + 450 mL of diluent.
The C1V1 = C2V2 formula
The amount of solute does not change when you dilute, so concentration × volume is the same before and after: C₁ × V₁ = C₂ × V₂. C₁ and V₁ are the stock concentration and the volume of stock you take; C₂ and V₂ are the concentration and total volume you want. Rearranged, V₁ = C₂ × V₂ ÷ C₁.
Serial dilutions
To go from a 1 M stock to 1 mM, dilute 1:10 three times: each step takes 1 part of the previous solution into 10 parts total (e.g. 1 mL into 9 mL), giving 100 mM, 10 mM and then 1 mM. A 10× buffer stock works the same way: 5 mL of 10× stock plus 45 mL of water gives 50 mL of 1×.
Common mistakes
- Adding V₂ of solvent instead of making the total up to V₂.
- Mixing units: C₁ and C₂ must share a unit (both mM, or both %), and so must V₁ and V₂.
- Using C1V1 = C2V2 for reactions or mixing two different solutions — it only describes dilution with pure solvent.
Learn the concept
FAQ
How do I use C₁V₁ = C₂V₂?
Solve for the unknown. To dilute a stock to a target concentration in a target volume, V₁ = (C₂ × V₂) / C₁. Add (V₂ − V₁) of diluent.
Does this calculator handle serial dilutions?
Single-step only. For serial dilutions, apply C₁V₁=C₂V₂ at each step using the previous step's output as the new C₁.
Can I use any units?
Yes, as long as both concentrations share the same unit and both volumes share the same unit. The calculator displays mL by default.