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CFU count calculator and decimal dilutions

From counted colonies to the concentration (CFU/mL), or the decimal dilution that makes a plate countable (30 to 300).

Parameters

Number of tenfold steps: d = 3 means 10⁻³. 0 = plated neat.

Result

Culture concentration

1.5 × 10⁹ CFU/mL

Calculation
150 × 10⁶ / 0.1 mL = 1.5 × 10⁹ CFU/mL
Countable range
between 30 and 300, countable
Dilution to plate
10⁻⁶
One colony would equal
1 × 10⁷ CFU/mL
10⁻⁴10⁻⁵10⁻⁶10⁻⁷10⁻⁸110100100010 000100 000dilution platedcolonies per plate30–30015 0001500150151.5
Note

The plate carries 150 colonies, within the countable range: the culture stands at 1.5 × 10⁹ CFU/mL.

Calculation, assumptions and sources

OverviewPlate counting: CFU/mL = colonies × 10^d / plated volume, where d is the number of decimal dilutions.

Plate counting: CFU/mL = colonies × 10^d / plated volume, where d is the number of decimal dilutions. The calculation gives the concentration of a counted plate, checking the countable range (30 to 300 colonies), or the dilution to plate so that an expected culture falls into it. A blank plate is reported as "below the detection limit".

Method & formulasCFU/mL = N × 10^d / V
CFU/mL = N × 10^d / Vexpected N = C × V / 10^d

Each visible colony was born from one colony-forming unit deposited on the agar; the count, carried back up the dilution cascade, returns the starting concentration. The second formula, the inverse of the first, is used to choose the dilution.

CFU (colony-forming unit)
whatever gives one colony: an isolated cell, a chain or a whole cluster.
Decimal dilution
a tenfold step: 1 mL of culture into 9 mL of diluent. d successive steps dilute by a factor 10^d.
Countable range
the 30 to 300 colonies per plate where the count is reliable.
Detection limit
the concentration a single colony on the plate would represent.
Validity domainPlate counting counts viable, culturable cells: stressed but living cells (VBNC state) do not grow.

Plate counting counts viable, culturable cells: stressed but living cells (VBNC state) do not grow. The calculation assumes exact dilutions; the pipetting error of each step compounds along the cascade, and six dilutions at 2% each give 12% on the result. The countable range holds for point colonies, not for swarming organisms (Proteus) that carpet the agar.

The 30 to 300 colony rangeColonies land on the agar at random: the count follows a Poisson distribution, with relative uncertainty 1/√N, that is 18% at 30 colonies and 32% at 10.

Colonies land on the agar at random: the count follows a Poisson distribution, with relative uncertainty 1/√N, that is 18% at 30 colonies and 32% at 10. Above 300, colonies touch and merge, and the count underestimates. The counts of a decimal series fall tenfold per dilution and the range spans one decade: one plate of the series always falls inside it.

Reading the resultA saturated E. coli culture holds about 10⁹ CFU/mL.

A saturated E. coli culture holds about 10⁹ CFU/mL. In routine work, two or three bracketing dilutions are plated. The standard volume is 0.1 mL for surface plating, 1 mL for pour plating.