C1V1 = C2V2
When you dilute a solution the amount of solute stays the same, so concentration × volume is the same before and after. C1 and V1 are the stock concentration and the volume of stock you use; C2 and V2 are the concentration and volume you want.
To make 10 mL of 1 M from a 5 M stock: V1 = C2 × V2 ÷ C1 = 1 × 10 ÷ 5 = 2 mL of stock, topped up with 8 mL of water or buffer to 10 mL.
C1 and C2 must be in the same units, and so must V1 and V2.
Dilution factors
A 1:10 dilution is 1 part stock in 10 parts total, such as 100 µL of stock plus 900 µL of diluent. Note that "1:10" sometimes means 1 part plus 10 parts, so check which is meant in a protocol.
Serial dilutions
For very large dilutions, dilute step by step. Six 1:10 steps take a sample from 108 to 102 cells per mL, a dilution of 106, with volumes that are easy to pipette. Mix each tube well before taking the next transfer, and change tips between tubes.
Calculators
The Dilution Calculator solves C1V1 = C2V2 for any of the four values and converts units for you. The Serial Dilution Calculator lists the concentration in each tube and how much to transfer and add.
More worked examples
- 10× buffer to 1×: for 500 mL, V1 = 1 × 500 ÷ 10 = 50 mL of 10× buffer, made up to 500 mL.
- 70% ethanol from 95%: for 100 mL, V1 = 70 × 100 ÷ 95 = 73.7 mL of 95% ethanol, made up to 100 mL.
Ethanol and water shrink a little when mixed, so 73.7 mL plus 26.3 mL of water gives slightly less than 100 mL. Fill up to the mark on a cylinder or flask instead of adding a fixed volume of water.
Common mistakes
- Adding V2 instead of making up to V2. V2 is the final total volume. Adding 10 mL of water to 2 mL of stock gives 12 mL at a different concentration.
- Volumes too small to pipette. Below about 1 µL, pipetting is inaccurate. Make an intermediate dilution first.
- Mixed units. A stock in mg/mL and a target in µg/mL differ by a factor of 1,000. Convert one before using the formula.