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Chemistry formula

How to calculate C1V1 = C2V2

C1V1 = C2V2 is the dilution equation for preparing a target concentration from a stock solution.

See the formulaOpen calculator
Direct answer
Formula
C1 * V1 = C2 * V2

Use the table below to match each symbol with the right input. Keep units consistent before you start.

C1V1 = C2V2 formula
Start here when you only need the equation and variable names.
Formula
C1 * V1 = C2 * V2

C1V1 = C2V2 is the dilution equation for preparing a target concentration from a stock solution.

Variable meanings
Check each symbol, meaning, and unit before you calculate.
SymbolNameDescriptionUnit
C1Initial concentrationStock or starting concentration.concentration
V1Initial volumeVolume of stock solution used.volume
C2Final concentrationTarget concentration after dilution.concentration
V2Final volumeTotal volume after adding diluent.volume
When to use this formula
Check that your situation matches the formula before you trust the result.
  • Use it when solute amount is conserved and you know any three of stock concentration, stock volume, final concentration, and final volume.
Step-by-step method
Follow these steps when you are solving it by hand.
  1. 1Convert both concentrations to the same units.
  2. 2Convert both volumes to the same units.
  3. 3Substitute the three known values into C1V1 = C2V2.
  4. 4Rearrange the equation to solve the missing value.
  5. 5If you need diluent volume, subtract stock volume from final volume.
Examples
These sample numbers show the order of operations and units.
Prepare a 0.10 M solution
C1
1.0 M
C2
0.10 M
V2
100 mL
  1. 1.V1 = (C2 * V2) / C1
  2. 2.V1 = (0.10 * 100) / 1.0
  3. 3.V1 = 10 mL
Result
Use 10 mL of stock and add diluent to reach 100 mL total.
Find final concentration
C1
5 mg/mL
V1
2 mL
V2
10 mL
  1. 1.C2 = (C1 * V1) / V2
  2. 2.C2 = (5 * 2) / 10
  3. 3.C2 = 1 mg/mL
Result
The final concentration is 1 mg/mL.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
  • Mixing concentration or volume units before solving the c1v1 = c2v2 formula.
  • Using final volume when the formula needs transferred stock volume, or the reverse.
  • Treating an approximate buffer or dilution equation as valid outside its assumptions.
  • Rounding dilution factors or concentration ratios before the final step.
Open the C1V1 = C2V2 Calculator
Open the calculator for the answer without rewriting the formula.

Enter your values in the related calculator, then compare the output with the hand method above.

Open C1V1 = C2V2 Calculator
FAQs
Short answers for common formula questions.
Can I calculate C1V1 = C2V2 by hand?

Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.

Why does my C1V1 = C2V2 result differ from another calculator?

Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.

When is the C1V1 = C2V2 Calculator better than hand math?

Open the C1V1 = C2V2 Calculator to check several scenarios or skip the hand arithmetic.