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Generation Time Calculator

Calculate how fast a bacterial (or microbial) population grows during log phase — also called a bacteria growth rate problem. Use generation time g (time per doubling / doubling time), number of generations n, and growth rate constant k: g = t/n, n = log(N/N₀)/log 2, k = n/t. Includes steps, quick picks, and a mini growth-curve visual.

Background

In exponential (log) growth, bacteria divide by binary fission, so the population doubles each generation: N = N₀·2ⁿ. If you know the starting count N₀, ending count N, and elapsed time t, you can compute the number of generations n and the generation time g (doubling time).

Enter values

Tip: Use this when growth is approximately exponential (log phase).

We’ll keep answers in your chosen units.

Since n = log(N/N₀)/log(2), the log base doesn’t change the result. This option is just to match your class notation.

Any count units work (CFU/mL, cells/mL, total cells) as long as N and N₀ match.

Enter a number in your selected units (minutes or hours).

Time per generation (doubling). Same units as your time selection.

Options

Chips prefill values and calculate immediately.

Result

No results yet. Enter values and click Calculate.

How to use this calculator

  • Pick a mode (generation time, final population, time, growth rate, or generations).
  • Enter the values you know (e.g., N₀, N, and t).
  • Click Calculate to get the answer, a mini growth curve, and step-by-step.

How this calculator works

  • Exponential growth model: N = N₀·2ⁿ.
  • Generations from counts: n = log(N/N₀) / log(2).
  • Generation time: g = t/n (time per doubling).
  • Growth rate constant: k = n/t (generations per unit time).

Formula & Equation Used

Exponential growth: N = N₀·2ⁿ

Generations: n = log(N/N₀) / log(2)

Generation time: g = t/n

Growth rate constant: k = n/t

Example Problem & Step-by-Step Solution

Example 1 — Find generation time

A culture grows from N₀ = 1.0×10⁶ to N = 8.0×10⁶ in t = 120 min. Find n and g.

  1. Compute ratio: N/N₀ = 8.0
  2. Generations: n = log(8)/log(2) = 3
  3. Generation time: g = t/n = 120/3 = 40 min

Because 8× is exactly 3 doublings (1→2→4→8), the math stays super clean.

Example 2 — Predict final population

Starting at N₀ = 5.0×10⁴, the generation time is g = 30 min. After t = 3 hr, what is N?

  1. Convert time: 3 hr = 180 min
  2. Generations: n = t/g = 180/30 = 6
  3. Final count: N = N₀·2⁶ = 5.0×10⁴·64 = 3.2×10⁶

Example 3 — Solve time

A culture grows from N₀ = 1.0×10³ to N = 1.0×10⁶. If g = 20 min, how long did it grow?

  1. Generations: n = log(10³)/log(2) ≈ 9.966
  2. Time: t = n·g ≈ 9.966·20 ≈ 199.3 min

Real lab data rarely lands on perfect powers of 2 — decimals are normal.

Frequently Asked Questions

Q: Is “generation time” the same as “doubling time”?

In binary fission during log phase, yes — generation time is essentially the doubling time.

Q: Does it matter if I use log₁₀ or ln?

No. In n = log(N/N₀)/log(2), the log base cancels out.

Q: When should I NOT use this?

If growth isn’t exponential (lag phase, stationary phase, or death phase), this model can be misleading.

Q: Is this a bacteria growth rate calculator?

Yes. In log phase, bacterial growth rate problems are commonly solved using generations n, generation time (doubling time) g, and growth rate constant k.