Project bacterial population growth from the starting count, doubling time and elapsed time under ideal exponential growth.
MODEL: ideal exponential phase only. Real cultures have a lag phase, then exponential growth, then stationary and death phases as nutrients deplete and waste accumulates — this tool does not model those.
Final population (cells)
How to use this tool
The initial cell count (CFU or cells) at the start of exponential growth.
The generation time in hours — for E. coli in rich medium this is roughly 20 minutes (0.33 h).
How long the culture grows, in hours, and optionally a target count to see how long reaching it would take.
Final count, generations elapsed and growth rate μ = ln 2 / doubling time are shown.
Formula & worked example
Start 1000 cells, doubling time 0.5 h, 4 h elapsed: 8 generations, final population 1000 × 2⁸ = 256,000 cells, μ ≈ 1.386 per hour, and 1,000,000 cells would be reached in about 4.98 h.
Limitations — read this before you rely on it
Exponential-phase model only. It ignores lag phase, nutrient depletion, waste inhibition, death, and any change in doubling time with temperature or medium.
Frequently asked questions
The time for a population to double once during exponential growth. It depends on species, medium, temperature and aeration — it is not a universal constant.
Nutrients run out, waste builds up and growth slows into stationary phase. Exponential projections far into the future are unrealistic.
μ = ln 2 / doubling time, in per-hour units. It is the continuous-time growth rate used in microbiology and bioreactor models.
The maths is identical, but CFU (colony-forming units) counts only viable, colony-forming cells, while a microscope count includes dead cells too.
Yes, as long as doubling time and elapsed time use the same unit — the result's rate unit then matches that unit too.