What this calculator does
A serial dilution repeats the same dilution step several times, multiplying the factors together. Five tenfold steps from 10⁸ CFU/mL give a total dilution of 100,000 and a final concentration of 1,000 CFU/mL.
The reason to do it in steps rather than one go is measurement accuracy. Diluting 100,000-fold in a single step from a 10 mL final volume would need 0.1 microlitres of stock, which no ordinary pipette can measure. Five steps of ten each use comfortable volumes and the errors, while they do compound, stay small.
The formula
The final concentration is the initial concentration divided by the dilution factor raised to the power of the number of steps. The total dilution factor is that power itself. The logarithm is reported because microbiology and immunology conventionally work in log dilutions.
| Term | Meaning |
|---|---|
| Dilution factor | The factor applied at each step, commonly 10 or 2. |
| Total dilution | The per-step factor raised to the number of steps. |
| Log dilution | The base-10 logarithm of the total, so a 10⁵ dilution is a 5-log dilution. |
| Countable range | The plate count range, typically 30 to 300 colonies, that the dilution series aims to hit. |
The inputs explained
| Field | What to enter |
|---|---|
| Initial concentration (CFU/mL) | Starting concentration, in any unit. |
| Dilution factor per step | Dilution factor at each step. Ten is standard in microbiology, two in immunology titrations. |
| Number of dilution steps | Number of steps performed. |
When to use it
Bacterial plate counting
A dilution series brings an unknown culture into the countable range, typically 30 to 300 colonies per plate.
Antibody titration
Twofold serial dilutions determine the endpoint titre of a serum sample.
Preparing calibration standards
A standard curve is often built from a serial dilution of a single stock.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How far does each number of steps take you?
A range of step counts from the same starting culture.
| Dilution steps | Final concentration | Total dilution factor | Log₁₀ total dilution |
|---|---|---|---|
| 1 steps | 10,000,000 CFU/mL | 10× | 1.000 |
| 3 steps | 100,000 CFU/mL | 1,000× | 3.000 |
| 5 steps | 1,000 CFU/mL | 100,000× | 5.000 |
| 7 steps | 10 CFU/mL | 10,000,000× | 7.000 |
Questions
Why dilute in steps rather than all at once?
Because a single large dilution needs an unmeasurably small stock volume. Diluting 100,000-fold into 10 mL would require 0.1 microlitres. Repeated tenfold steps keep every measured volume in a range an ordinary pipette handles accurately.
Do errors compound through the series?
Yes, multiplicatively. A consistent 2% error at each of five steps compounds to about 10% overall. This is why good technique matters at every step, and why mixing thoroughly between steps is emphasised: an unmixed tube carries its error forward into everything downstream.
What is a 1:10 dilution in this context?
One part stock into nine parts diluent, giving ten parts total and a factor of 10. In microbiology this is usually 1 mL into 9 mL. Note that some fields read 1:10 as one part into ten parts, giving a factor of 11, so stating the volumes avoids ambiguity.
How many steps do I need?
Enough to bring the expected concentration into the countable range, typically 30 to 300 colonies per plate. Since the concentration is unknown, several dilutions are usually plated and whichever lands in range is counted. Plating a spread of dilutions is standard practice rather than a hedge.
For a single dilution step, see the dilution calculator. For the resulting concentration in molar terms, see the molarity calculator.