Bacterial Growth Rate Calculator
This calculator uses the exponential bacterial growth model N = N0 x 2(t/g), where N0 is the initial cell count, t is the elapsed time, g is the generation (doubling) time, and N is the final cell count. It also computes the number of generations completed and the specific growth rate (mu = ln(2) / g). This model applies to the logarithmic (exponential) growth phase when nutrients are not limiting. It is used in microbiology labs to plan cultures, estimate contamination levels, and design fermentation processes.
Bacterial growth formula
N = N0 x 2^(t / g)
n = t / g
mu = ln(2) / g
Where N0 is initial cell count, t is elapsed time, g is generation (doubling) time, n is number of generations, and mu is the specific growth rate constant.
Typical generation times
- E. coli at 37 C: approximately 20 minutes (0.33 hours).
- Staphylococcus aureus: approximately 27-30 minutes.
- Mycobacterium tuberculosis: approximately 12-16 hours.
- Clostridium perfringens (optimal): approximately 8-10 minutes (fastest known).
Frequently asked questions
What is bacterial exponential growth?
During the exponential (log) phase, bacteria divide at a constant rate. Each cell splits into two at each generation. The population doubles every generation time (g), so after n generations the population is N0 times 2 to the power of n.
What is generation time?
Generation time (also called doubling time) is the time required for a bacterial population to double in size under optimal growth conditions. Common values range from about 20 minutes for E. coli at 37 degrees Celsius to hours or days for slow-growing organisms.
How do I calculate the number of generations?
Number of generations (n) = t / g, where t is elapsed time and g is the generation time, both in the same units. For example, if t = 2 hours and g = 0.5 hours, n = 4 generations.
What is the specific growth rate (mu)?
The specific growth rate mu = ln(2) / g, where g is the generation time. It represents the fractional increase in population per unit time. For E. coli with g = 20 min (0.333 h), mu = 0.693 / 0.333 = 2.08 per hour.
Why does this model only apply to exponential phase?
Real bacterial growth also includes a lag phase (adjustment), stationary phase (nutrient limitation or toxin accumulation), and death phase. The exponential model N = N0 times 2^(t/g) applies only during the log phase when nutrients are unlimited.
Official sources
- NCBI Bookshelf, Madigan et al.: Microbial Growth.
- CDC: Food Safety and bacterial growth guidelines.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.