How this calculator works
Binary fission multiplies a population by two per generation. The log ratio of two counts gives the number of generations; elapsed time divided by that number gives generation time. The model assumes a constant net growth rate and does not describe lag, nutrient exhaustion, stationary phase or death. Counts may be CFU estimates rather than exact individual cells.
Formula
N(t) = N0 × 2^(t/g). Generations = log2(N(t)/N0). Generation time g = t × ln(2)/ln(N(t)/N0). Natural-log growth rate per hour = ln(2) / g in hours.
Worked example
An increase from 100 to 800 CFU in 3 hours is three doublings, giving a generation time of 1 hour. An increase from 4 to 32 cells in 90 minutes is also three doublings, giving 30 minutes per generation.
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Frequently asked questions
Can I use a final count smaller than the initial count?
That describes net decline rather than a positive generation time. This tool rejects it in observation mode; use a decay model for declining populations.
Are generations per hour and growth rate the same?
No. Generations per hour is 1/g. The exponential rate uses natural logarithms and equals ln(2)/g.
Can I predict growth for an entire day?
Only if constant exponential growth remains plausible. Real cultures usually leave the exponential phase, so long projections can be misleading.