CFU/mL from plate counts (including dilution)
In microbiology, a colony-forming unit (CFU) is an operational estimate of viable cells (or clumps of cells) that can grow into visible
colonies on an agar plate. When a diluted sample is plated, the colony count can be converted into an estimate of the original sample
concentration, usually reported as CFU per milliliter (CFU/mL).
Core idea
If you plate a known volume from a known dilution, each colony corresponds to one CFU in the plated aliquot. You then “scale back” by the
plated volume and by the dilution factor to estimate the concentration in the original sample.
Main formula used by the calculator
\[
\mathrm{CFU/mL} = \frac{C}{d \cdot V_{\mathrm{mL}}}
\]
where C is the number of colonies counted on the plate, d is the decimal dilution factor (for example, 10-5 = 0.00001),
and VmL is the plated volume expressed in milliliters.
Volume conversion (µL to mL)
Plated volumes are often measured in microliters. The calculator converts to milliliters before applying the CFU/mL formula:
\[
V_{\mathrm{mL}} = \frac{V_{\mu \mathrm{L}}}{1000}
\]
Example: 100 µL = 0.1 mL.
How dilution is interpreted
The calculator supports common lab notations and converts them to a decimal dilution factor d:
\[
10^{-5} \Rightarrow d = 10^{-5}
\qquad\qquad
1:100000 \Rightarrow d = \frac{1}{100000} = 10^{-5}
\]
A larger negative exponent means a more diluted sample (for example, 10-6 is ten times more dilute than 10-5).
Single plate workflow
With one colony count at one dilution, the calculation is a direct application of the formula:
\[
\mathrm{CFU/mL} = \frac{C}{d \cdot V_{\mathrm{mL}}}
\]
The calculator also flags whether that plate is within the chosen countable range.
Replicates at the same dilution
When multiple plates are counted at the same dilution, the calculator uses the mean colony count:
\[
\bar{C}=\frac{1}{n}\sum_{i=1}^{n} C_i
\qquad\Rightarrow\qquad
\mathrm{CFU/mL} = \frac{\bar{C}}{d \cdot V_{\mathrm{mL}}}
\]
It also reports the sample standard deviation (SD) of colony counts:
\[
s_C=\sqrt{\frac{\sum_{i=1}^{n}(C_i-\bar{C})^2}{n-1}}
\]
Because CFU/mL is a constant multiple of the colony count, the SD scales the same way:
\[
s_{\mathrm{CFU/mL}}=\frac{s_C}{d \cdot V_{\mathrm{mL}}}
\]
Multiple dilutions and “countable plates”
In a dilution series, some plates may have too few colonies (high random error) or too many colonies (merged colonies and undercounting).
For this reason, labs often use a countable range (commonly 30–300 colonies) and choose a dilution where at least one plate falls
in that range.
In multi-dilution mode, the calculator groups plates by dilution and computes a CFU/mL estimate per dilution (typically from the mean of the
countable plates). It can then auto-select a recommended dilution whose mean colony count is closest to the middle of the countable band,
while allowing you to override the selection.
How to interpret the visualizations
The calculator shows (1) a plate series diagram summarizing dilution → plated volume → CFU/mL, (2) a bar chart of colony counts with the
countable band highlighted, and (3) for multiple dilutions, a CFU/mL vs dilution consistency plot. Consistent CFU/mL estimates across adjacent
dilutions suggest reliable technique and counting; large differences often indicate counting outside the optimal range, pipetting error, or colony clumping.
Assumptions and practical notes
This method assumes colonies arise from viable units that are well dispersed, the plated aliquot is representative of the sample, and the dilution steps
and plated volume are accurate. Clumping, uneven spreading, and confluent growth can bias CFU estimates. Always consider the countable range flag and the
consistency across dilutions before trusting a final value.
