Laboratory Techniques · Biology and introductory microbiology
Serial dilution questions become much easier when you keep three quantities separate: the dilution fraction, the volume examined and the number counted. This guide uses simulated data to explain colony-forming units per millilitre, with worked examples and a self-check quiz.
Dilution fraction versus dilution factor
A dilution reduces concentration by adding diluent. Define the fraction for one step as the transferred sample volume divided by the final total volume. In a calculation involving 1 mL sample plus 9 mL diluent, the final volume is 10 mL and the fraction is 1/10 = 10⁻¹.
Some textbooks call the reciprocal, 10, the “dilution factor”; others use that phrase for the fraction. Avoid ambiguity by writing the fraction explicitly. In this article, d always means the cumulative dilution fraction relative to the original sample.
Cumulative dilution fraction = d₁ × d₂ × d₃ …
Original concentration = diluted concentration / cumulative fraction
Serial dilution means each diluted mixture supplies the sample for the next step. Three consecutive tenfold steps produce 10⁻³, not 3 × 10⁻¹. The concentration is one thousandth of the original. These arithmetic examples are not a microbial culture protocol; actual practical work follows your institution’s approved supervision and procedures.
Worked example 1: unequal dilution steps
Imagine an analytical sample is diluted first by taking 2 mL into a final volume of 10 mL, then taking 1 mL of that mixture into a final volume of 20 mL. The first fraction is 2/10 = 1/5. The second is 1/20. Overall d = (1/5)(1/20) = 1/100.
If the final concentration is 0.8 mg/mL, the original is 0.8 ÷ 0.01 = 80 mg/mL. Check by going forward: 80/5 = 16, then 16/20 = 0.8 mg/mL. This reverse check catches many factor-of-ten errors.
How to calculate CFU/mL
A colony-forming unit (CFU) is an operational measure of organisms capable of forming a visible colony under the particular conditions used. One colony need not correspond to one original cell: cells can occur in groups, and some cells may not form colonies in those conditions.
C = counted colonies
d = cumulative dilution fraction
V = plated volume in millilitres
The denominator d × V is the equivalent volume of the original sample represented on the plate. The colony count is divided by that original-equivalent volume. Keep V in millilitres when the requested answer is CFU per millilitre.
Worked example 2: the 0.1 mL trap
A simulated plate has 86 colonies from 0.1 mL of a 10⁻⁴ dilution. Calculate:
86 / (10⁻⁴ × 0.1) = 86 / 10⁻⁵ = 8.6 × 10⁶ CFU/mL.
Multiplying only by 10⁴ gives 8.6 × 10⁵, which is ten times too low because only one tenth of a millilitre was examined. Conversely, if 1.0 mL had been examined with the same count and dilution, 8.6 × 10⁵ CFU/mL would be correct.
| Volume given | Volume in mL | Volume correction 1/V |
|---|---|---|
| 1,000 µL | 1.0 | 1 |
| 200 µL | 0.2 | 5 |
| 100 µL | 0.1 | 10 |
| 50 µL | 0.05 | 20 |
Worked example 3: replicate plates
Two simulated plates at the same dilution, 10⁻⁵, and the same volume, 0.1 mL, contain 64 and 72 colonies. Their mean is 68. The estimate is 68/(10⁻⁵ × 0.1) = 6.8 × 10⁷ CFU/mL.
You can verify it by pooling counts and original-equivalent volumes: (64 + 72)/(2 × 10⁻⁵ × 0.1) gives the same result. Do not average raw counts from different dilutions and then apply one arbitrarily chosen dilution. Standard laboratory methods may prescribe specific weighting and acceptance rules.
Choosing counts and reporting uncertainty
The frequently taught “30–300 colonies” interval is a classroom convention, not a universal requirement for every organism, plate or validated method. Low counts have substantial sampling variability; crowded plates can merge colonies and bias counts downward. Use the range and reporting rules specified by your course or analytical method.
For a teaching dataset, record the raw counts, dilution fraction, volume, excluded observations and reason for exclusion. Report sensible significant figures; a calculator’s long decimal output does not create experimental precision. Technical replicate plates describe repeatability within a sample; they are not independent biological samples.
Frequently asked questions
Does zero colonies mean zero organisms?
No. It means none were detected in the tested portion under those conditions. A small examined volume, dilution or limited culturability can explain a zero count. Report according to the method’s detection-limit convention.
Can CFU/mL be used directly as cells/mL?
Not without justification. Clumping and culturability can make the two quantities differ. State exactly what was measured.
Why do I divide by a very small number?
You are scaling a count from a tiny original-equivalent volume up to one millilitre of the original sample. The resulting estimate should therefore be larger than the raw count.
A reliable calculation routine
- Write each step as transferred volume / final volume.
- Multiply to obtain the cumulative fraction.
- Convert the examined volume to millilitres.
- Substitute C, d and V with units.
- Check the power of ten and explain any reporting limitations.
Interactive practice quiz
Choose an answer for each question, then check your score. Explanations appear below each question; your answers stay in this browser tab.
Related lessons and sources
Explore Laboratory Techniques, Bacteriology and Virology and our chi-square worked examples for another approach to biological count data.
- University of Vermont: Serial dilution calculations — cumulative fractions and original concentration.
- Hillsborough College: Serial dilution and standard plate count — colony counts, dilution and countable-plate considerations.
All datasets and quiz questions are original simulated examples for learning. This lesson teaches calculations rather than unsupervised culture procedures.
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