Calculate generations, time per generation, and specific growth rate from two population counts.
| Generations | – |
| Time per generation | – |
| Growth rate μ (1/time) | – |
Use this calculator when a culture of bacteria or any other population that divides in two grew from one count to another over a known time. It is suitable for flask checks and microbiology calculations that assume binary fission.
The number of generations is log₂ of the final count divided by the initial count. Time per generation is elapsed time divided by that number of generations. The specific growth rate μ is ln(2) divided by generation time, which is the same as ln(final ÷ initial) ÷ elapsed time. Use any consistent clock unit (hours, minutes, or days); generation time is returned in that same unit and μ is in 1/time.
If the population does not change, generations, generation time, and growth rate are reported as zero. The final count must be at least the initial count, and both counts must be positive.
Initial count: The cell count or optical density at the start.
Final count: The count at the end of the interval. It must be greater than or equal to the initial count.
Elapsed time: How long the culture grew, in the time unit you want back.
Generations: Number of doublings between the two counts.
Time per generation: Mean time between doublings, in the same unit as elapsed time.
Growth rate μ (1/time): Specific growth rate, equal to ln(2) divided by generation time.
Related calculators