Calculate how to dilute a stock solution to a target concentration using C1V1 = C2V2. Enter the stock concentration, the final concentration and the final volume — the tool gives the volume of stock to take and how much diluent to add.
C1V1 = C2V2. Take V1 of stock and add diluent up to the final volume V2.
The C1V1 = C2V2 equation
The number of moles of solute is unchanged by dilution, so:
C1 × V1 = C2 × V2 → V1 = (C2 × V2) / C1
where C1/V1 are the stock concentration and volume, and C2/V2 the final concentration and volume. Take V1 of stock and add diluent up to V2.
Example: to make 10 mL of 100 mM from a 1 M stock: V1 = (0.1 × 10) / 1 = 1 mL stock + 9 mL diluent.
Serial dilutions
For very large dilution factors, do a serial dilution (e.g. several 1:10 steps) rather than pipetting a tiny volume once — it’s far more accurate. Each step uses the same C1V1 = C2V2 logic.
Tips
- If the required stock volume is below ~1 µL, dilute the stock first or use a serial dilution.
- To prepare a solution from solid instead, use the molarity calculator.
- Works for any concentration unit (M, mM, µM, nM) as long as you’re consistent.
Frequently asked questions
What is the dilution formula?
C1V1 = C2V2. Rearranged, the stock volume needed is V1 = (C2 × V2) / C1.
How do I dilute a stock to a lower concentration?
Compute V1 = C2 × V2 / C1, take that volume of stock, and add diluent up to the final volume V2. The tool does this for you.
When should I use a serial dilution?
When the dilution factor is large and a single step would require an impractically small stock volume.
