Generation Time Calculator

Calculate Bacterial Doubling Time, Growth Rate & Number of Generations

Published: November 15, 2025 | Updated: November 15, 2025

Published by: RevisionTown Team

Generation time (also known as doubling time) is the time required for a bacterial population to double in number through binary fission. This fundamental parameter in microbiology helps researchers understand bacterial growth kinetics, optimize culture conditions, predict population dynamics, and assess antibiotic effectiveness.

This calculator determines generation time, growth rate, and the number of generations from initial and final population counts, making it essential for microbiology labs, fermentation studies, clinical diagnostics, and educational purposes.

Generation Time Calculator

Initial Number of Bacteria — N(0):

Starting population size (e.g., 1000 cells)

Final Number of Bacteria — N(t):

Final population size after growth period (e.g., 8000 cells)

Elapsed Time:

Time period between initial and final measurements

Generation Time Formulas

1. Generation Time Formula

Calculate the time required for population to double:

g = (t × ln(2)) / ln(N(t)/N(0))

Where: g = generation time, t = elapsed time, N(0) = initial population, N(t) = final population, ln = natural logarithm

Alternative form: g = t / n, where n = number of generations

2. Number of Generations Formula

Calculate how many times the population doubled:

n = ln(N(t)/N(0)) / ln(2)

Alternative: n = log₂(N(t)/N(0)) or n = 3.3 × log₁₀(N(t)/N(0))

Example: Population increases from 1000 to 8000 → n = ln(8000/1000)/ln(2) = ln(8)/ln(2) = 3 generations

3. Growth Rate Formula

Calculate the exponential growth rate constant:

k = ln(N(t)/N(0)) / t

Relationship to generation time: k = ln(2) / g, therefore: k = 1/g × ln(2)

Growth rate k is measured in doublings per unit time (e.g., doublings/hour). It's the reciprocal of generation time multiplied by ln(2).

4. Exponential Growth Equation

Predict future population size:

N(t) = N(0) × 2ⁿ
or
N(t) = N(0) × e^kt

This formula allows prediction of population at any time during exponential growth phase, where e ≈ 2.718 (Euler's number).

5. Specific Growth Rate (μ)

Calculate instantaneous growth rate:

μ = (ln N(t) - ln N(0)) / t

Relationship: μ = k = ln(2)/g (units: time^-1, e.g., h^-1)

Specific growth rate μ (mu) is widely used in fermentation and bioprocess engineering to characterize bacterial growth.

How to Use the Generation Time Calculator

Step 1: Measure Initial Population

Determine the starting bacterial count N(0) using colony forming unit (CFU) counting, optical density (OD600), or other quantification methods. Record the exact time of this measurement.

Step 2: Incubate and Grow

Allow bacteria to grow under optimal conditions during the exponential (log) phase. This is when generation time is constant and most meaningful. Avoid lag and stationary phases.

Step 3: Measure Final Population

At a later time point, measure the final population N(t) using the same method as initial count. Calculate the elapsed time between measurements accurately.

Step 4: Calculate and Interpret

Enter all values into the calculator. Results include generation time (doubling time), number of generations, and growth rate. Compare with known values for your bacterial species.

Generation Time Calculation Examples

Example 1: E. coli Culture

Given: N(0) = 1,000 cells, N(t) = 8,000 cells, Time = 60 minutes

Step 1 - Number of generations:

n = ln(8000/1000) / ln(2) = ln(8) / ln(2) = 2.079 / 0.693 = 3 generations

Step 2 - Generation time:

g = 60 minutes / 3 = 20 minutes

Step 3 - Growth rate:

k = ln(2) / 20 min = 0.693 / 20 = 0.0347 min⁻¹ or 3 doublings/hour

Example 2: Slow-Growing Mycobacterium

Given: N(0) = 1.5 × 10⁵ CFU/mL, N(t) = 9.6 × 10⁵ CFU/mL, Time = 48 hours

Number of generations:

n = ln(9.6×10⁵ / 1.5×10⁵) / ln(2) = ln(6.4) / 0.693 = 2.68 generations

Generation time:

g = 48 hours / 2.68 = 17.9 hours

This slower generation time is typical for Mycobacterium tuberculosis (15-20 hours), much slower than E. coli's 20 minutes.

Example 3: Yeast Fermentation

Given: Initial OD₆₀₀ = 0.1, Final OD₆₀₀ = 3.2, Time = 12 hours

Number of generations:

n = ln(3.2/0.1) / ln(2) = ln(32) / 0.693 = 5 generations

Generation time:

g = 12 hours / 5 = 2.4 hours (144 minutes)

This is typical for Saccharomyces cerevisiae under optimal fermentation conditions.

Typical Generation Times for Common Bacteria

Organism	Generation Time	Conditions
Escherichia coli	15-20 minutes	Optimal (37°C, rich medium)
Staphylococcus aureus	25-30 minutes	Optimal (37°C)
Bacillus subtilis	25-35 minutes	Optimal (30-37°C)
Vibrio natriegens	9-10 minutes	Fastest-growing (37°C)
Streptococcus pyogenes	25-45 minutes	Optimal (37°C)
Mycobacterium tuberculosis	15-20 hours	Slow-growing (37°C)
Treponema pallidum	30-33 hours	Very slow (in vivo)
Saccharomyces cerevisiae	90-120 minutes	Yeast (30°C, aerobic)

Factors Affecting Generation Time

Temperature

Effect: Each organism has optimal, minimum, and maximum temperatures. Generation time increases significantly outside the optimal range. Rule of thumb: Generation time doubles for every 10°C decrease below optimum.

Nutrient Availability

Effect: Rich media (e.g., LB broth) support faster growth than minimal media. Limiting nutrients increase generation time. Carbon source, nitrogen, and trace elements all impact growth rate.

pH Levels

Effect: Most bacteria grow best at neutral pH (6.5-7.5). Acidophiles prefer pH 2-5, alkaliphiles pH 8.5-11.5. Suboptimal pH increases generation time and can halt growth.

Oxygen Availability

Effect: Obligate aerobes require oxygen; anaerobes are inhibited by it. Facultative anaerobes grow faster aerobically. Oxygen tension dramatically affects generation time for aerobic organisms.

Inhibitory Substances

Effect: Antibiotics, heavy metals, metabolic wastes, and other inhibitors increase generation time or stop growth entirely. This is the basis for antimicrobial therapy and preservation.

Applications of Generation Time

Clinical Microbiology

Understanding generation time helps predict infection progression, design antibiotic dosing schedules, and determine appropriate culture incubation times for pathogen identification.

Industrial Fermentation

Optimize production of antibiotics, enzymes, amino acids, and other bioproducts by maximizing growth rate during exponential phase and controlling culture conditions.

Food Microbiology

Predict food spoilage rates, design preservation methods, establish shelf-life, and ensure food safety by understanding how quickly contaminants multiply under storage conditions.

Environmental Microbiology

Model bacterial population dynamics in natural environments, bioremediation processes, wastewater treatment, and ecological studies of microbial communities.

Research and Education

Teach fundamental concepts of microbial growth, exponential mathematics, and population dynamics. Essential for microbiology lab courses and research planning.

Frequently Asked Questions

What is generation time in microbiology?

Generation time (also called doubling time) is the time required for a bacterial population to double in number through binary fission. It varies widely among species: E. coli has a generation time of about 20 minutes under optimal conditions, while Mycobacterium tuberculosis takes 15-20 hours.

How do you calculate generation time?

Use the formula: Generation Time (g) = (t × ln(2)) / ln(N(t)/N(0)), where t is elapsed time, N(0) is initial population, and N(t) is final population. Alternatively: g = t / n, where n is the number of generations calculated as ln(N(t)/N(0)) / ln(2).

What is the difference between generation time and growth rate?

Generation time is the time per doubling (measured in minutes or hours), while growth rate (k) is the number of doublings per unit time. They are reciprocals: k = 1/g. A shorter generation time means faster growth rate.

Why is generation time important?

Generation time is crucial for understanding bacterial pathogenicity, optimizing fermentation processes, planning laboratory experiments, predicting food spoilage, and designing antibiotic treatments. Faster-growing bacteria can cause infections more rapidly.

What factors affect bacterial generation time?

Generation time is affected by temperature, pH, nutrient availability, oxygen levels, water activity, presence of inhibitors, and bacterial species. Optimal conditions minimize generation time, while stress conditions increase it significantly.

How do you measure bacterial population for generation time calculation?

Common methods include: spectrophotometry (measuring optical density at 600 nm), viable plate counts (CFU counting), direct microscopic counts, flow cytometry, and turbidity measurements. Use the same method for initial and final counts.

What is the exponential (log) phase?

The exponential phase is when bacteria grow at maximum, constant rate with shortest generation time. Cells are healthiest and most uniform. This is the ideal phase for measuring generation time and for using bacteria in experiments.

Can generation time change during a culture?

Yes. Generation time is constant only during exponential phase. It increases during lag phase (adaptation), becomes undefined in stationary phase (growth = death), and increases dramatically as nutrients deplete or toxins accumulate.

Tips for Accurate Generation Time Measurement

1. Measure During Exponential Phase

Only calculate generation time during log phase when growth rate is constant. Plot growth curve to identify this phase or take measurements when culture is actively growing.

2. Use Consistent Methods

Measure initial and final populations with the same technique. Don't mix CFU counts with OD readings or different dilution protocols—this introduces systematic errors.

3. Ensure Optimal Growth Conditions

Maintain consistent temperature, adequate aeration, appropriate pH, and sufficient nutrients. Suboptimal conditions give longer, less reproducible generation times.

4. Take Multiple Measurements

Measure population at 3-4 time points and calculate generation time from multiple intervals. Average the results for better accuracy and identify any irregularities.

5. Use Logarithmic Scale

Plot cell numbers on logarithmic scale (semi-log plot). Exponential phase appears as straight line, making it easy to identify and calculate slope for generation time.

6. Consider Biological Replicates

Perform experiments in triplicate. Biological variation exists even with pure cultures. Statistical analysis of replicates provides confidence intervals for generation time.

Master Bacterial Growth Kinetics

Generation time is a fundamental parameter in microbiology that reveals how quickly bacteria multiply under specific conditions. This calculator simplifies the mathematical complexity of exponential growth calculations, providing instant results for generation time, growth rate, and number of doublings from simple population measurements.

Whether you're conducting research, optimizing industrial fermentation, studying pathogen dynamics, or learning microbiology principles, understanding generation time is essential. Use this tool to analyze bacterial growth patterns, compare different conditions, predict population sizes, and make informed decisions in clinical, industrial, and research applications. Remember that generation time is most meaningful during exponential phase—always ensure measurements are taken when bacteria are actively growing under optimal conditions.

Exponential growths model many phenomena, from biology to finance: with this bacterial generation time calculator you will discover how to calculate bacterial growth over time, its main features, and parameters. Here you’ll learn:

The rules of bacterial population growth;
How to calculate the bacterial growth rate; and
What is generation time of bacteria populations.

If you want to find out more about bacterial population growth, why it is important, and about an interesting bacterial experiment, then keep on reading!

What is exponential growth?

Exponential growth models are used when a quantity, a function, or, in our case, the size of a bacteria population increases over time by a constant percent increase per time unit, with the size of the increment depending on the value of the function at the last step. This form of bacterial growth is essential to the modern world, including the cleaning water in a wastewater plant!

Exponential growth models often describe functions with “lazy” beginnings followed by explosive increases; exponentials are, in fact, the fastest-growing functions in mathematics.

Learn more about these modes with our exponential growth calculator!

Two behaviours of exponential growth. — The two contrasting behaviors of an exponential function.

We got a taste of exponential growth during the coronavirus pandemic: a few cases one day, a little bit more the day after, and then things went out of control: without precautions, the initial phases of an epidemic follows the exponential — then, luckily it slows down.

How do we calculate the generation time of bacteria?

The equation that controls the exponential growth is:

N (t) = N (t_{0}) \cdot (1 + r)^{t - t_{0}}

where:

$N (t)$ — Population at time $t$
$N (t_{0})$ — Initial number of bacteria, at the starting time, $t_{0}$ ;
$r$ — Growth rate, that is the increment per time unit; and
$t - t_{0}$ — Elapsed time.

Often, the time $t_{0}$ is set to , which simplifies the equation to:

N (t) = N (0) \cdot (1 + r)^{t}

This is how to calculate the bacterial growth rate, $r$ , we rearrange the formula:

r = {\frac{N (t)}{N (0)}}^{\frac{1}{t}} - 1

What is generation time?

A commonly used quantity in the study of populations is the generation time, $t_{d}$ , that is, the required time for the population to double in size through binary fission:

\begin{aligned} N (t_{d}) & = 2 \cdot N (0) \\ = N (0) \cdot (1 + r)^{t_{d}} \end{aligned}

The doubling time is:

t_{d} = \frac{\ln (2)}{\ln (1 + r)} = t \cdot \frac{\ln (2)}{\ln (\frac{N (t)}{N (0)})}

We have a tool that teaches you how to calculate generation time in a cell culture: the cell doubling time calculator.

What if we look at things in reverse?

The exponential model for bacterial population growth can be used to model a reduction in the number of individuals, similarly to the log reduction model (discover it with our log reduction calculator).

Researchers tried introducing a virus into a bacterial population; not all of the individuals would survive in the face of a growing viral infection. In mathematics, this translates to a negative growth rate, $r$ , associated with an exponential decay.

The doubling time in this “reversed model” corresponds to the half-life; you can try our half-life calculator, too!

Testing our generation time calculator

On the 24th of February 1988, in a laboratory at Michigan State University, the longest evolutionary experiment in history began. Twelve identical populations of E. Coli bacteria were left to evolve independently. In 2021, the experiment reached over 70 thousand generations, witnessing mutations on every possible nucleotide of the bacteria’s genetic code.

Daily, 1% of each population is transferred and primed to grow for another day: the curbing of 99% of the individuals daily is necessary because of exponential growth: let’s try our bacterial growth calculator with this experiment.

Let’s start with just 12 bacteria, one for each population. The growth rate of E. coli in the experiment is $\sim 0.2117$ , which in turn corresponds to a doubling time of $\sim 3.61$ hours. Let’s also say that the bacterial population is allowed to grow without limitations.

Now we input all of the values in the generation time calculator, assuming a day has passed:

N (24) = 12 \cdot (1 + 0.2117)^{24} = 1204

It may not look impressive, it’s the population of a small village, after all. But the day after this, the number would increase to 100,000, which is a modestly sized city. And at the end of the third day, we would have 10 million bacteria, as big as Tokyo. After a week (168 hours), the number of bacteria would be bigger than the number of stars in the Milky Way (we use this number in the Drake equation calculator):

\begin{aligned} N (168) & = 12 \cdot (1 + 0.2117)^{168} \\ = 1.22 \cdot 1 0^{15} \end{aligned}

The higher the growth rate, the shorter the generation time of bacteria. Remember to keep an eye on your colonies every now and then!

FAQs

What is exponential growth?

Exponential growth is a phenomenon where a quantity grows following an increment controlled by the exponent, and not a multiplicative coefficient. This implies slow initial increases, followed by explosive growth.

What is bacteria growth?

Bacterial growth is the process by which a population of microorganisms increases. The initial phase of the growth follows an exponential law, however, due to the limitedness of resources, this soon plateaus.

How fast do bacteria grow?

The speed with which a bacterial population grows is controlled by its generation time, that is, the time required for a doubling in the size of the population. Escherichia coli, a commonly studied bacteria, has a doubling time of about 20 minutes.

How do I calculate the doubling time of a population?

The doubling time t_d of a population depends on its original size, on the population at a given time t, and on the value of t itself, following the rule:

t_d = t × [ln(2) / ln(N(t) / N(0))]

Generation Time Calculator

Results:

Generation Time Formulas

1. Generation Time Formula

2. Number of Generations Formula

3. Growth Rate Formula

4. Exponential Growth Equation

5. Specific Growth Rate (μ)

How to Use the Generation Time Calculator

Step 1: Measure Initial Population

Step 2: Incubate and Grow

Step 3: Measure Final Population

Step 4: Calculate and Interpret

Generation Time Calculation Examples

Example 1: E. coli Culture

Example 2: Slow-Growing Mycobacterium

Example 3: Yeast Fermentation

Typical Generation Times for Common Bacteria

Factors Affecting Generation Time

Temperature

Nutrient Availability

pH Levels

Oxygen Availability

Inhibitory Substances

Applications of Generation Time

Clinical Microbiology

Industrial Fermentation

Food Microbiology

Environmental Microbiology

Research and Education

Frequently Asked Questions

What is generation time in microbiology?

How do you calculate generation time?

What is the difference between generation time and growth rate?

Why is generation time important?

What factors affect bacterial generation time?

How do you measure bacterial population for generation time calculation?

What is the exponential (log) phase?

Can generation time change during a culture?

Tips for Accurate Generation Time Measurement

1. Measure During Exponential Phase

2. Use Consistent Methods

3. Ensure Optimal Growth Conditions

4. Take Multiple Measurements

5. Use Logarithmic Scale

6. Consider Biological Replicates

Master Bacterial Growth Kinetics

What is exponential growth?

How do we calculate the generation time of bacteria?

What is generation time?

What if we look at things in reverse?

Testing our generation time calculator

What is exponential growth?

What is bacteria growth?

How fast do bacteria grow?

How do I calculate the doubling time of a population?

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