Serial Dilutions and CFU Calculations Explained

A culture of bacteria can hold millions or billions of cells per milliliter, far too many to count on a plate. The fix is to dilute the sample until the plate holds a countable number of colonies, then scale the result back up. That scaling is the CFU/mL calculation, and it is one of the most reliably tested pieces of math in an intro microbiology course. This guide follows the cards in Encodr's free Microbiology deck.

What a CFU is

When you spread a diluted sample on agar and incubate it, each viable cell that can grow divides repeatedly and builds a visible colony. You count colonies, but a colony could have started from one cell or from a clump, so the unit is a colony-forming unit, or CFU. Viable plate counts are expressed as CFU per milliliter (CFU/mL).

Because only cells that can form a colony show up, a plate count measures living cells. That is the main contrast with the direct microscopic count, which tallies every visible cell, alive or dead.

The dilution factor

The dilution factor is the reciprocal of the dilution. A 1:10,000 dilution has a dilution factor of 10,000. A 10^-5 dilution has a dilution factor of 10^5, or 100,000.

In a serial dilution you make the dilution in stages, and each tube is made from the one before it. The per-step factors multiply. If one step moves 1 mL of sample into 9 mL of diluent, the sample is now in 10 mL total, so the factor for that step is 10. Five of those steps in a row give 10 x 10 x 10 x 10 x 10 = 10^5.

The mistake to avoid is adding exponents wrongly or dropping one. If you are asked about the plate made from tube 5, the factor to use is 10^5, no matter how many tubes came before it.

The formula

CFU/mL = (colonies counted x dilution factor) / volume plated (mL)

Dividing by the volume plated converts "colonies on this plate" into "colonies per milliliter of the diluted sample", and multiplying by the dilution factor undoes the dilution to give the concentration of the original sample.

The countable range: 30 to 300

Only plates with 30 to 300 colonies are used. A plate with fewer than 30 colonies has a high statistical counting error, because a count that small is noisy. A plate with more than 300 is too dense, with colonies overlapping so that you cannot count them individually. If a question hands you a plate with 12 colonies and asks for CFU/mL, the right answer to the real-world question is that it should not be used.

Worked examples

Example 1. You plate 0.1 mL from a 1:10,000 dilution and count 50 colonies. The dilution factor is 10,000, so CFU/mL = (50 x 10,000) / 0.1 = 5,000,000 = 5 x 10^6 CFU/mL. The 50 colonies fall in the 30 to 300 range, so the plate is usable.

Example 2. You plate 0.1 mL from a 10^-5 dilution and count 145 colonies. The dilution factor is 100,000, so CFU/mL = (145 x 100,000) / 0.1 = 145,000,000 = 1.45 x 10^8 CFU/mL of the original, undiluted sample.

Example 3: choosing the plate. Suppose you plated 0.1 mL from three dilutions. The 10^-4 plate is covered in overlapping colonies, the 10^-5 plate has 145 colonies, and the 10^-6 plate has 12. Only the 10^-5 plate is in the countable range, so it is the one you use, and the answer is the same 1.45 x 10^8 CFU/mL as in example 2.

You can test your own numbers with the serial dilution calculator, which multiplies the steps, applies the formula and flags plates outside the countable range.

Two related counting methods

Direct microscopic count. Count the cells in a counting-chamber square and divide by the square's volume in milliliters. For a Petroff-Hausser chamber square of 8 x 10^-6 mL holding 10 cells: 10 / (8 x 10^-6) = 1.25 x 10^6 cells/mL. No dilution series is needed, but dead cells are counted too.

Most probable number (MPN). The sample is serially diluted into multiple replicate tubes of indicator medium. The pattern of positive tubes, for instance 5, 2, 0 across three dilution levels, is looked up in a standard statistical table. In the course example that pattern reads 49 per 100 mL of original sample.

Dilution series elsewhere in the course

The same idea turns up outside plate counts. In a broth dilution test for antibiotic susceptibility, a twofold dilution series of the drug is prepared, for example 2, 4, 8, 16 and 32 micrograms/mL. The MIC, the minimum inhibitory concentration, is the lowest concentration in the series that shows no visible bacterial growth. If the tubes at 2 and 4 are turbid and 8 is the first clear tube, the MIC is 8 micrograms/mL. For one-off dilutions of a stock solution, the dilution calculator handles C1V1 = C2V2.

How to practice

CFU problems are pattern problems, which is good news: once you have solved five, the sixth is routine. Practice by writing the formula from memory and then solving a new problem without looking, since active recall beats passive review for this kind of procedure. The related growth math is in bacterial growth curve and generation time. For a unit-by-unit plan, see how to study for microbiology.