Serial Dilution Calculator
Dilution factor for each tube in a series, the total dilution, and CFU per mL from a plate count.
What it does
A serial dilution takes a sample that is far too concentrated to count and steps it down, tube by tube, until a small volume spread on a plate grows a number of colonies a person can actually tally. It is the standard way to count bacteria, yeast and other cells, and the arithmetic behind it is simple multiplication.
Each step has a dilution factor. Transfer 1 mL into 9 mL of diluent and the sample is spread through 10 mL in total, so the concentration falls to one tenth and the factor is 1:10. Transfer 1 mL from that tube into another 9 mL and the concentration falls to one hundredth of the original, so the second tube is 1:100. The factors multiply rather than add, which is why a long series moves so quickly and why the total is best left in exponent form until the end.
The plate comes next. You spread a known small volume, often 0.1 mL, from one tube onto agar, incubate it, and count the colonies that grow. Each colony is assumed to have started from one cell, which is why the result is called colony forming units rather than cells. Dividing the count by the dilution of that tube and by the plated volume gives the concentration in the original sample.
The count itself has a quality test. A plate with fewer than 30 colonies is dominated by chance, since one extra colony moves the estimate by several percent. A plate with more than 300 colonies is crowded enough that colonies merge and the count comes out low. That 30 to 300 window is the countable range, and when a plate falls outside it the usual answer is to plate a different dilution from the same series rather than to trust the number.
The tool gives the per step factor, the total dilution, the dilution at the plated tube, the CFU per mL of the original sample and the countable range check. The series line spells out every tube, which is the quickest way to catch a bookkeeping slip before it reaches a notebook or a report.
How to use
- Enter the volume you move at each step and the volume of diluent already waiting in the receiving tube.
- Set the number of steps in the series, counting the first dilution after the original sample as step one.
- Say which tube the plate came from, using the same numbering: tube 1 is the first dilution.
- Enter the colony count from that plate and the volume you spread on it.
- Read the step factor, the total dilution and the original concentration in CFU per mL.
- Check the countable range line. If the plate falls outside 30 to 300 colonies, count a plate from a different tube and re-enter the numbers.
Formula
- transfer volume
- Volume moved into the next tube, in millilitres
- diluent volume
- Volume of diluent already in the receiving tube, in millilitres
- n
- Number of dilution steps in the series
- colonies
- Colonies counted on the plate
- dilution of the plated tube
- The fraction of original sample present in that tube
The volume plated is part of the denominator because spreading 0.1 mL samples only a tenth of that tube. Written out, CFU per mL = colonies x (1 / dilution) / volume plated, which is the same thing rearranged. A 1:10 dilution is the same as a 0.1 fraction, and a 1:100,000 dilution is 0.00001, so the exponent is the number of tenfold steps.
Worked example
Example: five tenfold steps, plated from tube 4
A series made by moving 1 mL into 9 mL of diluent, five times. The plate is spread with 0.1 mL from tube 4 and grows 150 colonies.
- Each step dilutes by 1 / (1 + 9) = 0.1, so the step factor is 1:10.
- Five steps multiply to 0.1 to the fifth power = 0.00001, which is 1:100,000 for the series.
- Tube 4 is four tenfold steps down, so the plate dilution is 1:10,000.
- CFU per mL = 150 / (0.0001 x 0.1) = 15,000,000.
- The 150 colonies sit inside the 30 to 300 countable range, so the plate is usable.
- The series reads tube 1 at 1:10, tube 2 at 1:100, tube 3 at 1:1,000 and tube 4 at 1:10,000.
Reference table
| Tube | Dilution | Fraction of the original |
|---|---|---|
| 1 | 1:10 | 0.1 |
| 2 | 1:100 | 0.01 |
| 3 | 1:1,000 | 0.001 |
| 4 | 1:10,000 | 0.0001 |
| 5 | 1:100,000 | 0.00001 |
Limits
- The CFU result assumes every colony grew from a single cell, which fails for clumped cells and for organisms that form chains or spores.
- The tool does not correct for pipetting error, which grows with every step and can dominate a long series.
- A countable plate still carries sampling error: 150 colonies has a standard deviation of about 12, so the estimate has a real spread.
- It gives no information about whether the colonies are the organism you wanted, which needs a selective medium or a confirmatory test.
Common mistakes
- Adding the dilution factors, so that five tenfold steps are written as 1:50 instead of 1:100,000.
- Forgetting the plated volume, which turns a 1:10,000 tube into an answer ten times too high when only 0.1 mL was spread.
- Numbering tubes from zero and then plating from the wrong one, which shifts the answer by a factor of ten.
- Mixing the tube before every transfer, since a settled suspension gives a transfer that is not representative.
- Using a plate with more than 300 colonies, where merged colonies make the count falsely low.
Try it yourself
Quick checks. Answers sit tucked under each question.
A series moves 0.5 mL into 4.5 mL of diluent, four times. What is the dilution per step and the total?
1:10 per step and 1:10,000 in total. The step factor is 0.5 / 5 = 0.1, and four steps give 0.1 to the fourth power = 0.0001.
Plating 0.1 mL from tube 3 of that series gives 45 colonies. What is the original concentration?
450,000 CFU/mL. Tube 3 is 1:1,000, so 45 / (0.001 x 0.1) = 45 / 0.0001 = 450,000.
Why is a plate with 500 colonies not used?
Above 300 colonies the plate is too crowded, colonies merge and the count comes out low. The usual fix is to plate a higher dilution from the same series.
Questions
What does 1:10 mean?
One part sample in ten parts total, which is the same as a tenfold dilution. A 1 mL transfer into 9 mL of diluent gives exactly that.
Why must I divide by the volume plated?
Because the colony count is for the volume on the plate, not for a millilitre. Spreading 0.1 mL means the count represents a tenth of a millilitre, so the per mL figure is ten times larger.
What is the countable range and why 30 to 300?
It is the window where the count is statistically usable. Below 30 colonies chance dominates, and above 300 crowding causes merging and undercounting.
Can I use this for a dilution series in a spectrophotometer instead of plates?
The dilution arithmetic is identical. Only the last step changes, since you would read absorbance rather than count colonies.
How many steps should a series have?
Enough to bring the expected concentration into the countable range at one of the tubes. For a dense sample, five or six tenfold steps is common.
Does the diluent volume include the transferred sample?
The tool treats the diluent volume as what is already in the tube, so the total after transfer is transfer plus diluent. That is the usual lab convention: 1 mL into 9 mL gives 10 mL total.
Sources
- American Society for Microbiology: serial dilution protocols
- Biology LibreTexts, Introduction to Microbiology: measurement of bacterial growth and serial dilution