Work out how fast a bacterial culture grows during log phase: the final cell count, the starting count, the time needed, or the generation time (doubling time). This free bacterial growth calculator also gives the number of generations, the growth rate constant and a growth curve.
Bacterial growth formulas
Worked example: E. coli
A culture starts with 1,000 cells and E. coli doubles every 20 minutes. After 3 hours (180 minutes) it has gone through 180 / 20 = 9 generations, so N = 1,000 × 2⁹ = 512,000 cells. Working backwards, if a culture grows from 10³ to 5.12 × 10⁵ cells in 3 hours, n = 3.3 × log(512) = 9 and g = 180 / 9 = 20 minutes.
Typical generation times
| Organism | Generation time | Conditions |
|---|---|---|
| Vibrio natriegens | about 10 min | Rich medium, 37 °C |
| Escherichia coli | about 20 min | LB broth, 37 °C |
| Bacillus subtilis | about 25–30 min | Rich medium |
| Staphylococcus aureus | about 30 min | Rich medium, 37 °C |
| Saccharomyces cerevisiae (yeast) | about 90 min | YPD, 30 °C |
| Mycobacterium tuberculosis | about 15–20 h | Culture medium |
The formula only holds during the exponential (log) phase. In a real culture growth slows in stationary phase when nutrients run out, so very long times give unrealistic numbers.
Frequently asked questions
What is generation time?
The time it takes a bacterial population to double during exponential growth. It is also called doubling time.
How do I calculate the number of generations?
Use n = (log N − log N₀) / log 2, or n = 3.3 × log(N / N₀). Then generation time g = t / n.
How do I find the generation time with this calculator?
Enter the initial count, the final count and the growth time, and leave the generation time box empty.
Can I use CFU/mL instead of cell numbers?
Yes. N and N₀ only need the same unit, so cells, CFU or CFU/mL all work.
Why does my answer look too large?
The formula assumes unlimited log-phase growth. Real cultures reach stationary phase, usually around 10⁹ cells/mL in broth.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.