Microbial Generation Time Calculator
During exponential growth a microbial population doubles at a steady interval called the generation or doubling time. This calculator works it out from two counts: the initial population, the final population, and the time between them. It finds the number of doublings as the base-2 logarithm of the growth ratio, then divides the elapsed time by that to give the generation time. It also reports the number of generations and the specific growth rate. Use any consistent unit (CFU, cells per mL, or proportional optical density).
Generation time formula
generations n = log2(Nf / N0) = ln(Nf / N0) / ln(2)
generation time g = elapsed time t / n
specific growth rate mu = ln(Nf / N0) / t
also g = ln(2) / mu
Example: 1000 to 64000 = 6 doublings; 120 / 6 = 20 min
The generation time carries the same time unit you enter for elapsed time. Use the same count units for N0 and Nf.
Microbial growth context
- Generation time applies during the exponential (log) growth phase.
- Each generation is one doubling of the population.
- Counts may be CFU, cells per mL, or proportional optical density.
- The specific growth rate mu is the exponential rate constant.
- If the final count is not greater than the initial count, the result is n/a.
Generation time: frequently asked questions
What is generation (doubling) time?
Generation time is how long a microbial population takes to double during exponential (log-phase) growth. It is found from the number of doublings that occurred over the elapsed time: generation time equals elapsed time divided by the number of generations.
How do you calculate the number of generations?
The number of generations n equals log base 2 of the final count divided by the initial count, which is the same as (ln Nf minus ln N0) divided by ln 2. Each generation represents one doubling of the population.
What is the specific growth rate?
The specific growth rate (mu) is the natural log of the final count divided by the initial count, all divided by the elapsed time: mu = ln(Nf / N0) / t. It is the exponential rate constant and relates to generation time by mu = ln 2 divided by generation time.
What counts can I use?
Any consistent measure of population size works: colony-forming units, cells per mL, or optical density proportional to cell number. The ratio of final to initial is what matters, so both counts must be in the same units.
Why must the final count exceed the initial count?
Generation time describes growth, so the final count must be larger than the initial count. If the population did not grow, there are no completed doublings and the calculator returns n/a.
Official sources
- NCBI Bookshelf: National Center for Biotechnology Information.
- National Institutes of Health: NIH home.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.