C1V1 = C2V2: how to calculate dilutions

Updated October 30, 2026

C1V1 = C2V2 is the most used formula at the bench. It works because diluting a solution does not change how much solute it contains, only the volume it is spread through.

The formula

C1 × V1 = C2 × V2  →  V1 = C2 × V2 ÷ C1

• C1: stock concentration
• V1: volume of stock to use (usually what you want to find)
• C2: final concentration
• V2: final total volume

Make sure C1 and C2 are in the same units. V1 comes out in whatever unit V2 is in.

Worked examples

Molar stock. Make 10 mL of 50 mM Tris from a 1 M stock. Convert 1 M to 1000 mM: V1 = 50 × 10 ÷ 1000 = 0.5 mL of stock plus 9.5 mL water.

X buffer. Make 50 mL of 1X buffer from 10X: V1 = 1 × 50 ÷ 10 = 5 mL plus 45 mL water.

Primer working stock. Make 100 µL of 10 µM primer from a 100 µM stock: V1 = 10 × 100 ÷ 100 = 10 µL plus 90 µL water.

Common mistakes

• Treating V2 as the volume of water to add. V2 is the final volume. The water to add is V2 − V1.
• Mixing units, such as M and mM, or mg/mL and µg/µL written differently.
• Pipetting tiny volumes. If V1 is under about 1 µL, do an intermediate dilution or a serial dilution instead.