GIFSQ Tools · Module 3 — Food Microbiology & Enumeration · Tool 050 of 500
The exponential growth rate of a culture. Enter the starting and final counts and the elapsed time to get the specific growth rate (mu) and the doubling time.
Try sample values — fills the form with the worked example below.
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Specific growth rate, μ (/h)
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Doubling time (h)
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Doubling time (min)
Equation: μ = (ln N − ln N₀) ÷ t · doubling time t_d = ln 2 ÷ μ, where t is the elapsed time in hours.
Method: Exponential-growth model, standard food microbiology (FDA BAM growth concepts; Brock Biology of Microorganisms). μ is the specific growth rate, usually given per hour.
Assumptions: growth is exponential over the measured interval (log phase); temperature and nutrients stay constant; no lag phase inside the interval.
Limitations: lag and stationary phases are excluded; μ is an average over the interval, not an instantaneous rate.
Rounding: μ to 3 decimal places; doubling time to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Exponential-growth model, standard food microbiology (FDA BAM growth concepts; Brock Biology of Microorganisms). μ is the specific growth rate, usually given per hour.
Assumptions: growth is exponential over the measured interval (log phase); temperature and nutrients stay constant; no lag phase inside the interval.
Limitations: lag and stationary phases are excluded; μ is an average over the interval, not an instantaneous rate.
Rounding: μ to 3 decimal places; doubling time to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: A culture grows from 1,000 to 16,000 cells in 2 hours. μ = ln(16) ÷ 2 = 2.7726 ÷ 2 = 1.386 /h; doubling time = ln 2 ÷ 1.386 = 0.50 h (30 min).
Enter values above to see results.
μ and generation time describe the same growth: doubling time = ln 2 ÷ μ. Values apply to the log phase only — lag and stationary phases need a different model. Tool 050 of 500 — GIFSQ
