Generation Time Calculator
Find the generation (doubling) time of a growing population from its starting and final size over a measured interval, plus the number of generations and the growth rate constant.
How it works
Generations n = log₂(Nₜ / N₀) · Generation time G = t / n · Growth rate constant k = n / t
Generation time (or doubling time) is how long a dividing population takes to double. Because each generation doubles the count, the number of generations over an interval is the base-2 logarithm of the fold increase, log₂(Nₜ/N₀). Dividing the elapsed time by that count gives the average time per generation, and its inverse — generations per unit time — is the growth rate constant k. This is the standard way microbiologists read a growth curve during the exponential (log) phase.
Worked example
A culture grows from 1,000 to 256,000 cells in 240 minutes. The fold increase is 256, so generations = log₂(256) = 8. Generation time = 240 ÷ 8 = 30 minutes, and k = 8 ÷ 240 = 0.033 divisions per minute.
Sources: Bacterial growth — Wikipedia
Frequently asked questions
Is generation time the same as doubling time?
For a population where every reproducing unit divides in two, yes — one generation doubles the count, so generation time equals doubling time. For sexually reproducing populations, demographers instead define generation time as the mean age of reproduction.
Why use a base-2 logarithm?
Because each generation multiplies the population by 2, the number of doublings that turns N₀ into Nₜ is exactly log₂(Nₜ/N₀). Using log₂ gives the generation count directly.
Does this only apply during exponential growth?
Yes. The formula assumes a constant doubling rate, which holds during the log (exponential) phase. In lag, stationary or death phases the growth rate changes and a single generation time no longer describes the culture.
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This calculator is for educational purposes. Double-check important results before acting on them.