Serial Dilution Calculator
The concentration at every step of a serial dilution — with the total dilution reached and the volumes for each tube.
Each step multiplies the dilution: n steps at a factor of f give a total dilution of fⁿ.
How the serial dilution calculator works
Each step multiplies the dilution: n steps at a factor of f give a total dilution of fⁿ. Ten 10-fold steps reach 10¹⁰, which is how a bacterial culture gets to a countable plate.
Serial dilution exists because a single 10,000,000-fold dilution would need a microlitre into ten litres. Splitting it into steps keeps every transfer a pipettable volume, at the cost of compounding any error at each one.
Formula: Cₙ = C₀ / fⁿ
Worked examples
| Inputs | Final concentration | Note |
|---|---|---|
| Six 10-fold steps | 0.000001 | 10⁻⁶ of the original |
| Ten 2-fold steps | 0.0009765625 | 1/1024 |
| Three 100-fold steps | 0.000001 | a millionth |
FAQFrequently asked questions
Why dilute serially instead of all at once?
Because a 10⁶-fold dilution in one step would mean a microlitre into a litre. Serial steps keep every transfer a volume you can pipette accurately.
How many steps do I need?
log(total dilution) ÷ log(step factor). A 10⁶ dilution takes six 10-fold steps or three 100-fold ones.
Does error accumulate?
Yes, and multiplicatively. A 2% error at each of six steps compounds to about 13%. Fewer, larger steps are more accurate if you can pipette them.
What volumes should I use?
For a 10-fold step with 0.9 mL of diluent, transfer 0.1 mL. Mix thoroughly before each transfer — incomplete mixing is the biggest source of error.
Where is this used?
Bacterial plate counts, immunoassay standard curves, and any titration of a potent compound down to a working range.
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- Royal Society of Chemistry — the UK chemistry professional body
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.