NSW · HSCBiology
Bacterial generation time
Compute generation time g and specific growth rate μ from a starting count N₀, final count Nₜ, and elapsed time t.
Formula
n = log₂(Nₜ / N₀)
g = t / n
μ = ln(2) / g
Here n is the number of doublings, g the generation (doubling) time, and μ the specific growth rate.
Inputs
Generation time g = t / n, where n = log₂(Nₜ / N₀) is the number of doublings.
Result
Number of generations (doublings)
n = log₂(Nₜ/N₀) = 7.000
Generation time
0.571 hours
g = t / n
Specific growth rate
μ = ln(2) / g = 1.2130 per hour
Worked example
A culture grows from N₀ = 1 000 cells to Nₜ = 128 000 cells over t = 4 hours.
n = log₂(128 000 / 1 000) = log₂(128) = 7 doublings.
g = t / n = 4 / 7 ≈ 0.571 hours ≈ 34.3 minutes per generation.
μ = ln(2) / g ≈ 0.693 / 0.571 ≈ 1.21 per hour.
How this calculator works
The calculator computes the number of doublings as log₂(Nₜ/N₀), then divides the elapsed time by that count to get the generation time. The specific growth rate uses ln(2)/g.
Common questions
- What is generation time?
- The time taken for a population of cells to double in number under unrestricted growth, typically reported in minutes for bacteria.
- How is n calculated?
- n = log₂(Nₜ / N₀). If a culture grows from 10³ to 10⁹ cells, n = log₂(10⁶) ≈ 19.93 doublings.
- What is the specific growth rate μ?
- μ relates to generation time by μ = ln(2) / g. For E. coli with g = 20 minutes, μ ≈ 0.0347 min⁻¹ or 2.08 h⁻¹.
- Why must Nₜ ≥ N₀?
- The model assumes growth, so log₂(Nₜ / N₀) must be non-negative. If Nₜ < N₀ you'd be observing population decline and need a different model.