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Colony Count Calculator (CFU/mL)

Calculate colony-forming units per mL from plate counts at several dilutions, using only plates in the countable range and the weighted mean of two successive dilutions.

Formula

N=∑CV (n1+0.1 n2) d1N = \dfrac{\sum C}{V\,(n_1 + 0.1\,n_2)\,d_1}
per dilution:CFU/mL=CˉV d\text{per dilution:}\quad \mathrm{CFU/mL} = \dfrac{\bar{C}}{V\,d}
ΣC\Sigma C
total colonies on the countable plates of the two dilutions
n1, n2n_1,\ n_2
number of countable plates at the first and second dilution
d1d_1
the dilution of the first retained dilution, as a fraction (10⁻² is 0.01)
VV
volume plated per plate, in mL

How it works

To count organisms in a culture, it is diluted in steps and plated; each viable cell grows into a colony. Only plates within the countable range are used: too few colonies gives a count with a large statistical error, and too many is crowded and undercounted. The range depends on the method, commonly 25 to 250 or 30 to 300, and 10 to 300 in some ISO methods, so it is an input.

When plates at two successive dilutions are countable, the weighted mean of ISO 7218 combines them. The formula counts the second dilution's plates as a tenth as many, because they are ten times more dilute, which gives each plate its proper weight. With a single dilution it reduces to the ordinary mean.

Worked example

1 mL plated in duplicate from 10⁻² (168 and 215 colonies) and 10⁻³ (14 and 25), with a countable range of 10 to 300.

  1. All four plates are countable: ΣC = 168 + 215 + 14 + 25 = 422; n₁ = 2, n₂ = 2.
  2. N = 422 / (1 × (2 + 0.2) × 0.01) = 19,182 CFU/mL.

About 1.9 × 10⁴ CFU/mL. Each dilution alone gives 1.92 × 10⁴ and 1.95 × 10⁴, in good agreement.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Each colony arose from a single colony-forming unit, and cells were well dispersed.
  • The dilutions and the plated volumes are accurate.
  • The countable range you set is the one your method specifies.

Common mistakes

  • Counting a plate outside the range because it is the only one. Plate again at another dilution.
  • Reporting more than two significant figures. Counting and pipetting errors do not support more.
  • Listing the dilutions in the wrong order.

Related tools

CFU Calculator (Colony-Forming Units per mL)Viable count from a plate count and dilutionOpen calculatorSerial Dilution CalculatorTransfer volumes and the concentration in every tubeOpen calculatorDilution Factor and Ratio CalculatorFold dilution, 1 : N notation and the volumes behind itOpen calculatorTransformation Efficiency CalculatorColony-forming units per microgram of DNAOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.