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Chemistry formula

How to calculate serial dilution

A serial dilution repeats the same dilution step, so the total dilution factor multiplies with each step.

See the formulaOpen calculator
Direct answer
Formula
final concentration = starting concentration / (dilution factor^steps)

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

Serial dilution formula
Start here when you only need the equation and variable names.
Formula
final concentration = starting concentration / (dilution factor^steps)

A serial dilution repeats the same dilution step, so the total dilution factor multiplies with each step.

Variable meanings
Check each symbol, meaning, and unit before you calculate.
SymbolNameDescriptionUnit
C0Starting concentrationConcentration before the first dilution step.concentration
CnFinal concentrationConcentration after n dilution steps.concentration
DFDilution factorPer-step dilution factor.Depends on inputs
nStepsNumber of repeated dilution steps.Depends on inputs
When to use this formula
Check that your situation matches the formula before you trust the result.
  • Use it for lab dilution series, microbiology counts, assay standards, or any repeated dilution with the same per-step factor.
Step-by-step method
Follow these steps when you are solving it by hand.
  1. 1Find the per-step dilution factor from the ratio or final tube volume divided by transfer volume.
  2. 2Raise the per-step factor to the number of steps.
  3. 3Divide the starting concentration by that total dilution factor.
  4. 4Keep concentration units consistent through the full series.
Examples
These sample numbers show the order of operations and units.
Three tenfold dilutions
C0
100 M
DF
10
n
3
  1. 1.total dilution factor = 10^3 = 1000
  2. 2.final concentration = 100 / 1000
  3. 3.final concentration = 0.1 M
Result
After three tenfold steps, the final concentration is 0.1 M.
Cell count dilution
C0
1,000,000 cells/mL
DF
10
n
4
  1. 1.total dilution factor = 10^4 = 10000
  2. 2.final concentration = 1000000 / 10000
  3. 3.final concentration = 100 cells/mL
Result
The fourth tube is 100 cells/mL.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
  • Mixing concentration or volume units before solving the serial dilution 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 Serial Dilution 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 Serial Dilution Calculator
FAQs
Short answers for common formula questions.
Can I calculate Serial dilution by hand?

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

Why does my Serial dilution 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 Serial Dilution Calculator better than hand math?

Open the Serial Dilution Calculator to check several scenarios or skip the hand arithmetic.