Generation Time Calculators

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Generation time (also called doubling time in microbiology) is the time required for a bacterial population to double in number during exponential growth. It equals the time between one cell division and the next. Generation time (g) is calculated as: g = t / n, where t = elapsed time and n = number of generations that occurred during t. Alternatively, g = (t₂ − t₁) × ln(2) / ln(N₂/N₁). Generation time is species- and condition-specific: E. coli in rich LB medium at 37°C grows with g ≈ 20 minutes; the same bacteria in minimal medium may have g of 60–90 minutes; slow-growing Mycobacterium tuberculosis has g ≈ 20 hours.

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Generation Time Formulas

g = (t₂ − t₁) × ln(2) / ln(N₂/N₁)

Or: g = (t₂ − t₁) / log₂(N₂/N₁)

g = 0.693 / μ (where μ = specific growth rate h⁻¹ from N = N₀e^(μt)).

Example: cell count rises from 2 × 10⁶ to 1.6 × 10⁷ in 90 minutes. N₂/N₁ = 8 = 2³ → 3 generations in 90 min → g = 90/3 = 30 minutes.

Exponential Growth Equation

N(t) = N₀ × 2^(t/g). Or: N(t) = N₀ × e^(μt). μ = ln(2)/g = 0.693/g.

Typical Generation Times

  • E. coli (LB, 37°C): ~20 minutes
  • E. coli (minimal medium, 37°C): ~60 min
  • Bacillus subtilis: 25–30 min
  • Staphylococcus aureus: ~30 min
  • Lactobacillus: 60–90 min
  • Mycobacterium tuberculosis: 18–24 hours
  • Mycobacterium leprae: ~14 days

Determining Generation Time Experimentally

Plot OD₆₀₀ vs. time on semi-log scale; slope = μ = ln(2)/g; g = 0.693/μ. Or: take samples at two time points during exponential phase; count by plate count (CFU/mL); calculate g from formula. Must use data from exponential phase only — lag and stationary phase data give incorrect g.

Glossary

Generation Time (g)
Time for a bacterial population to double during exponential growth: g = 0.693/μ = (t₂−t₁)×ln2/ln(N₂/N₁); E. coli in LB at 37°C ≈ 20 min; M. tuberculosis ≈ 20 h.
Specific Growth Rate (μ)
The exponential growth rate constant (h⁻¹): N = N₀e^(μt); μ = ln(2)/g = 0.693/g; derived from slope of ln(N) vs. time plot during exponential phase.
Exponential Phase
The period of constant doubling time in batch culture; the linear portion of ln(N) vs. time plot; μ is constant; used for generation time calculations; follows lag phase and precedes stationary phase.

Frequently Asked Questions

Generation time (g) = the time for a bacterial population to double: g = (t₂ − t₁) × ln(2) / ln(N₂/N₁) = (t₂ − t₁) / log₂(N₂/N₁). Alternative form: g = ln(2)/μ = 0.693/μ, where μ is the specific growth rate. Example: OD₆₀₀ goes from 0.1 to 0.8 in 2 hours (exponential phase): OD doubled 3 times (0.1 → 0.2 → 0.4 → 0.8). g = 120 min / 3 = 40 min. Or: μ from slope of ln(OD) vs. time plot; g = 0.693/μ. Always use data from the exponential phase — generation time calculations are invalid during lag or stationary phases.

Method 1 (OD semi-log plot): plot ln(OD₆₀₀) vs. time during exponential phase. Slope = μ (h⁻¹). g = 0.693/μ. Example: if ln(OD) increases from 0.69 to 2.08 over 60 minutes: slope = (2.08 − 0.69)/60 = 0.023 min⁻¹. μ = 0.023 min⁻¹. g = 0.693/0.023 = 30.1 minutes. Method 2 (two-point calculation): measure CFU/mL (or OD) at t₁ and t₂ during exponential phase: g = (t₂ − t₁) × 0.693 / ln(N₂/N₁). Select only time points from the linear portion of the semi-log plot (exponential phase). Include both time points and both N values in your lab report with the calculated g.

Generation time reflects how fast an organism can complete the entire growth cycle: DNA replication, cell growth, and division. It varies because: Nutrient richness: E. coli in rich LB (amino acids, nucleotides provided) = 20 min; in minimal medium (must synthesize everything from glucose) = 60 min — richer medium allows faster biosynthesis. Temperature: enzyme kinetics follow Q₁₀ ≈ 2; E. coli grows fastest at 37°C (optimal); slower at 25°C or 42°C. Organism: M. tuberculosis g ≈ 20 hours — its waxy cell wall (mycolic acids) is metabolically expensive to make; also, the organism replicates DNA very slowly and has an unusual cell division mechanism. Very slow growth makes TB hard to treat (antibiotics that target growing cells are less effective).

Specific growth rate (μ) and generation time (g) are inversely related: μ = ln(2)/g = 0.693/g. g = 0.693/μ. μ is the rate constant of exponential growth (h⁻¹): N = N₀ × e^(μt). g is the time for one population doubling (h or min). Example conversions: g = 20 min = 0.333 h → μ = 0.693/0.333 = 2.08 h⁻¹. g = 24 h → μ = 0.693/24 = 0.029 h⁻¹. μ = 1.386 h⁻¹ → g = 0.693/1.386 = 0.5 h = 30 min. μ represents the slope of a ln(N) vs. time plot; g represents the x-intercept interval for each doubling on the same plot.