Free lab tool
Dilution Calculator (C1V1 = C2V2)
Use C1V1 = C2V2 to find the volume of stock solution needed for a dilution: stock concentration times stock volume equals final concentration times final volume. Enter any three values to solve for the fourth, or build a serial dilution table with the dilution factor, number of steps and volume per tube.
Calculator
C1V1 = C2V2 solver
Choose the value to solve for, then fill in the other three.
Stock volume (V1)
Enter your values to see the result.
Serial dilution table
Every tube ends at the same volume. Tube 1 takes its transfer from the stock, and each later tube takes it from the tube before.
10 means 1:10, one part sample in ten parts total.
A whole number from 1 to 20.
Volume in each tube after the transfer.
Add it to label each tube with its concentration.
Enter your values to see the result.
Results are a guide. Check them against your protocol, the reagent data sheet and your instrument manual.
How it works
A dilution adds solvent without adding solute, so the amount of solute is the same before and after. That amount is concentration times volume, which gives the dilution equation. A serial dilution repeats a fixed dilution step tube after tube, so the dilution compounds.
Formula
C1 × V1 = C2 × V2
V1 = (C2 × V2) ÷ C1
diluent = V2 − V1
transfer per tube = V ÷ DF
diluent per tube = V − (V ÷ DF)
total dilution after n tubes = DFⁿ
Where
- C1, V1
- concentration and volume of the stock
- C2, V2
- concentration and volume of the final solution
- DF
- dilution factor per step: 10 means 1 part sample in 10 parts total (1:10)
- V
- volume in each tube after the transfer
Good to know
- Use the same units for C1 and C2, and the same volume unit for V1 and V2 if you work by hand. The calculator converts units for you.
- The equation holds only when diluting with solvent. It cannot give a final concentration higher than the stock.
Worked example
Example: 50 mL of 10 mM from a 1 M stock
- 01
C1 = 1 M = 1,000 mM, C2 = 10 mM, V2 = 50 mL.
- 02
V1 = (10 mM × 50 mL) ÷ 1,000 mM = 0.5 mL.
- 03
Diluent = 50 mL − 0.5 mL = 49.5 mL.
Mix 0.5 mL of stock with 49.5 mL of diluent. For a 10-fold serial dilution in 1 mL tubes, each tube takes 0.1 mL from the previous tube plus 0.9 mL of diluent, and five tubes reach 1:100,000.
Frequently asked questions
What does C1V1 = C2V2 mean?
It is the dilution equation. C1 and V1 are the concentration and volume of the stock, C2 and V2 are those of the final solution. Because diluting adds solvent but not solute, the amount of solute (concentration times volume) stays the same, so C1 × V1 equals C2 × V2.
How do I work out how much diluent to add?
First solve for the stock volume V1 with V1 = (C2 × V2) ÷ C1. The diluent is then the final volume minus the stock volume, V2 − V1. This calculator shows both after you enter three values.
What is a dilution factor?
The dilution factor is the stock concentration divided by the final concentration (C1 ÷ C2), which equals the total volume divided by the sample volume. A 1:10 dilution mixes 1 part sample with 9 parts diluent and has a factor of 10. Some labs write 1:10 to mean 1 part to 10 parts diluent, so check the convention your protocol uses.
How does a serial dilution work?
Each tube is made by transferring a fixed volume from the previous tube into diluent. With a dilution factor DF, the transfer is the tube volume divided by DF, and the total dilution after n tubes is DF to the power n. Ten-fold steps over five tubes give a 1:100,000 dilution.
Why can I not get a higher concentration than my stock?
Adding diluent can only lower the concentration. If the calculated C2 is higher than C1, you need a more concentrated stock, or you need to concentrate the solution, for example by evaporation or freeze drying.
Pipettes for accurate dilutions
Accurate dilutions depend on accurate liquid handling. Al-Shaker supplies Socorex Swiss manual micropipettes, dispensers and repeaters in Jordan and MENA, built for ISO 8655 liquid handling.
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