How serial dilution planning works
Each dilution factor is the final tube volume divided by the transferred sample volume. The cumulative factor is the product of each step factor; the cumulative fraction is its reciprocal.
Terms and units
- Step (tube) factor
- The dilution applied by one transfer: final tube volume ÷ transfer volume. A 1 mL transfer into 9 mL is a factor of 10.
- Transfer volume
- The volume carried from the sample or previous tube into the next: final volume ÷ step factor.
- Diluent volume
- The volume of diluent in the tube before the transfer: final volume − transfer volume.
- Cumulative dilution factor
- The product of every step factor up to that tube — 10, 100, 1,000, 10,000 for a uniform 10-fold series.
- Cumulative dilution fraction
- The reciprocal of the cumulative factor: the portion of the original sample present in that tube. This is the value that enters the CFU formula.
Worked example
For four 1:10 steps with 10 mL final volume per tube, transfer 1 mL into 9 mL diluent at each step. The cumulative dilution factors are 10, 100, 1,000, and 10,000. Mix each tube thoroughly before making the next transfer.
How to use this calculator
Enter values from your own measurement or validated laboratory method. Review the units and assumptions shown with each result before using it in a report.
Assumptions and limitations
These tools perform arithmetic from the values you provide. They do not validate a laboratory method or replace your laboratory's procedures. Biological samples and instruments can introduce uncertainty that a calculation alone cannot account for.
Frequently asked questions
What is a serial dilution used for?
It reduces a concentrated sample step by step until the dilution plated yields countable colonies, while keeping each transfer volume large enough to measure accurately. It is also used to prepare graded concentrations for dose-response work. See serial dilution: definition, principle, and purpose.
What is the difference between a 10-fold and a 2-fold dilution?
A 10-fold step divides the concentration by ten (1 mL into 9 mL); a 2-fold step halves it (equal volumes). Coarse 10-fold series cover a wide range in few tubes; fine 2-fold series give closely spaced concentrations but need many more tubes to reach the same dilution.
How do I find the cumulative dilution factor?
Multiply the step factors: a 10-fold series reaches 10, 100, 1,000, 10,000 after four tubes. For mixed series, multiply whatever factor each step used — 10 × 10 × 5 × 2 = 1,000. Dilution factor vs cumulative dilution shows how both enter the CFU formula.
How many tubes do I need?
Enough that at least one tube falls in the countable window when plated. If the expected concentration and plated volume are known, the required cumulative fraction is roughly (countable colonies × plated volume) ÷ expected CFU/mL. When in doubt, plan one or two extra tubes and plate two adjacent dilutions.
Guides and references
- Serial dilution: definition, principle, and purposeWhy laboratories dilute in steps instead of one large dilution.
- How to plan a 10-fold serial dilutionTransfer and diluent volumes for any final tube volume, with a worked example.
- How to plan a 2-fold serial dilutionHalving steps, cumulative factors, and when finer steps are worth the extra tubes.
- Serial dilution factor vs cumulative dilutionThe two numbers behind most order-of-magnitude errors.
- Calculation methods: serial dilutionThe formulas as implemented by the planner.