Generation Time Calculator

What this generation time calculator does

This calculator estimates generation time (also called doubling time) for a growing population such as bacteria. You enter a starting population \(N_0\), an ending population \(N_t\), and the elapsed time \(t\). The results include the estimated number of generations, generation time, growth rate, and a time-series table.

Key formulas used

The number of generations is computed from the growth ratio:

\[ n = \log_2\left(\frac{N_t}{N_0}\right) \]

Generation time is the elapsed time per generation:

\[ g = \frac{t}{n} \]

To populate the results table, the calculator also uses an exponential growth model over time:

\[ N(t) = N_0 \cdot e^{k t} \]

where the growth rate \(k\) is:

\[ k = \frac{\ln\left(\frac{N_t}{N_0}\right)}{t} \]

How to interpret the results

If your inputs represent a culture in the exponential (log) phase, the generation time \(g\) can be a useful summary of how quickly the population is doubling. The time-series table shows the expected population trend from time 0 to time \(t\) based on the same growth rate.

Common input mistakes

Final population not larger than initial

If \(N_t \le N_0\), the population did not grow over the interval, so a meaningful doubling time cannot be computed.

Unit mismatch

Large errors often come from mixing minutes, hours, and days. Always ensure the unit you pick matches the time between measurements.

Practical note for lab measurements

Generation time is most reliable when measurements are taken during steady exponential growth. If growth is slowing (for example due to nutrient limits), doubling time estimated from long intervals can be misleading.