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Biology

Bacteria Generation Time Calculator

Updated · Standard formula, shown below

Generation time 21.26 min
Number of generations
5.64 generations
Result
Growth rate
2.822 generations/h
Result
Starting cell count
1000 cells
You entered

This calculator finds how long a bacterial population takes to double during exponential growth. Enter the starting cell count, the final count and the time between them, and you get the number of generations, the generation time and the growth rate.

Formula

During exponential growth Nt = N₀ × 2n, so the number of generations is n = (log Nt − log N₀) ÷ log 2. Generation time g = t ÷ n; growth rate k = n ÷ t (here per hour).

  • N₀: cells (or CFU/mL) at the start
  • Nt: cells at the end, in the same unit
  • t: elapsed time in minutes

Worked Example

A culture grows from 1,000 to 50,000 cells in 120 minutes.

  1. log₁₀ 50,000 − log₁₀ 1,000 = 4.69897 − 3 = 1.69897
  2. n = 1.69897 ÷ 0.30103 = 5.64 generations
  3. g = 120 ÷ 5.6439 = 21.26 min
  4. k = 5.6439 ÷ 2 h = 2.822 generations per hour

Limits and common mistakes

  • Use two counts taken during the log (exponential) phase only; lag and stationary phases give a misleading result.
  • Both counts need the same unit and the same dilution correction.
  • Natural logs work too, as long as both the top and the bottom use the same log.
Formula used
in n0 | Starting cell count | cells | 1000 | 0
in nt | Final cell count | cells | 50000 | 0
in t | Time elapsed | min | 120 | 0
out g | Generation time | min | t / ((log10(nt) - log10(n0)) / log10(2)) | 2
out gens | Number of generations | generations | (log10(nt) - log10(n0)) / log10(2) | 2
out k | Growth rate | generations/h | gens / (t / 60) | 3

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.