Bacterial Growth Rate Calculator
Number of generations, generation time and specific growth rate from two cell counts.
Generations n = log₂(N ÷ N₀) = 3.3 × log₁₀(N ÷ N₀). Generation time g = t ÷ n. Specific growth rate μ = ln(N ÷ N₀) ÷ t. Growing from 10⁴ to 10⁷ cells in 5 h is 9.97 generations, g = 30 min.
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How to use it
- Enter the starting count N₀ and the final count N (CFU/mL, cells/mL or OD in the log phase).
- Enter the time between the two counts.
- Read generations, generation time and specific growth rate.
What you enter
- Starting count N₀
- Final count N
- Time
What you get
- Number of generations
- Generation time
- Specific growth rate μ
- Growth rate constant k
Formula
n = log₂(N/N₀) | g = t ÷ n | μ = ln(N/N₀) ÷ t | k = n ÷ t
Worked example
Input: N₀ = 1 × 10⁴, N = 1 × 10⁷, t = 5 h
Result: n = 9.97, g = 30.1 min, μ = 1.38 h⁻¹
Typical of a fast-growing bacterium in log phase.
Questions
How do you calculate the number of generations?
n = log₂(N ÷ N₀), or equivalently 3.3 × (log₁₀N − log₁₀N₀).
How do you calculate generation time?
Divide the time elapsed by the number of generations: g = t ÷ n.
What is the difference between μ and k?
μ = ln(N ÷ N₀) ÷ t is the specific growth rate (per hour, natural log). k = n ÷ t is generations per hour. μ = k × ln 2.
What is the generation time of E. coli?
About 20 minutes in rich medium at 37 °C, and longer in minimal medium or at lower temperatures.
Limitations
- Valid only for exponential (log) phase growth; counts in lag or stationary phase underestimate the rate.
References
Related reading
- How to Calculate the Number of Generations in a Bacterial Culture
- How to Calculate the Specific Growth Rate of a Microorganism from Batch Culture Data
More Cell Culture
- Cell Viability & Hemocytometer Counting Calculator
- Cell Doubling Time & Specific Growth Rate Calculator
- Cell Seeding and Dilution Calculator
All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.