Bacteria Growth Calculator

Starting count, N(0)

Final count, N(t)

Doubling (generation) time

Elapsed time

Enter any three of the four fields and leave the one you want to find blank. With a starting count, a doubling time, and an elapsed time, the calculator predicts the final population.

Please input values into the fields

Fill in the fields on the left and the population appears here.

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Show the growth curve

Plot the population from the start through the elapsed time.

Show the step-by-step table

List the population at evenly spaced points in time.

The bacterial growth calculator tool predicts how a population of bacteria in the exponential (also called logarithmic) growth phase will change over time. Bacteria reproduce by binary fission. One cell divides into two, and those two cells divide into four, so that the number increases geometrically.

When you enter the initial count, doubling time, and elapsed time, the tool returns the final population size, number of generations, and growth rate. If a field is left blank, the calculator will calculate this value.

What is meant by bacterial growth?

In the logarithmic phase each cell divides in a certain time interval as long as there are enough nutrients and space available. The time it takes for the number of cells to double is called doubling time or generation time by microbiologists. As every existing cell divides again, the population does not grow linearly but exponentially. Therefore, a long doubling time can result in a very large number of cells after only a few hours.

How to use this calculator tool:

Enter at least three of the four fields: initial population size, doubling time, elapsed time or final population size.

Leave blank the field for the value you want to calculate and the calculator will automatically fill it in. Use the same unit of time for both the doubling time and the elapsed time as the calculation is based on the ratio between these two values. The results panel also shows the corresponding growth rate, number of generations and factor by which the population has grown.

The formula for exponential growth.

If doubling time is used, the number of cells after a period of time t is the product of the initial number and two raised to the power of the number of doublings.

N(t) = N_0 \times 2^{\,t / T_d}

N(0) is the initial number, N(t) is the number after time t has elapsed, and Td is the doubling time (generation). The number of generations results from dividing the elapsed time by the doubling time and also corresponds to the logarithm with base 2 of the growth factor.

n = \frac{t}{T_d} = \log_2\!\left(\frac{N(t)}{N_0}\right)

Assume that the number of cells in a culture is 50,000 at the start and it doubles every 30 minutes.

After 3 hours (180 minutes), the number of generations would be 180 divided by 30, which equals 6. The final number would be 50,000 times 2 to the sixth power.

N = 50{,}000 \times 2^{6} = 50{,}000 \times 64 = 3{,}200{,}000

Conversely, if a culture grows from 1,000,000 to 8,000,000 in 120 minutes, then it has doubled three times since two cubed is eight. The doubling time would be 40 minutes which is the result of dividing 120 by 3. The table below shows each symbol and an example value.

Symbol	Meaning	Example
N(0)	Starting count	50,000
Td	Doubling (generation) time	30 minutes
t	Elapsed time	180 minutes
n	Number of generations	6
N(t)	Final count	3,200,000

Generation time, doubling time and growth rate

So we can calculate the growth rate per time unit, which is two to the power of one over doubling time, minus one.

The growth curve of bacteria and its phases:

A closed culture goes through four phases, and this calculator models the second phase.

Phase	What happens
Lag	Cells adapt to the medium; little to no division yet.
Log (exponential)	Steady doubling at the generation time. This is the phase the calculator models.
Stationary	Nutrients run low and waste builds up; division balances death and the count flattens.
Death	Resources are exhausted and the viable count falls.

Typical doubling times:

Published doubling time data is usually based on ideal laboratory conditions, so should be considered as values in the upper end of the spectrum. Here are some known examples:

Organism	Approximate doubling time
Escherichia coli	20 minutes
Bacillus subtilis	30 minutes
Staphylococcus aureus	30 to 40 minutes
Mycobacterium tuberculosis	12 to 24 hours

Applications:

Food teams use it to estimate growth rates at increased storage temperatures. A two-hour heat phase means something very different for an organism doubling every 20 minutes than one doubling every two hours. Fermentation, risk assessment of contamination and modelling early infections all rely on the same exponential relationship.

Tips for accurate results:

Determine the doubling time from a reliable source that includes information on optimal temperature and media conditions. Even a few degrees below optimum temperature can significantly increase doubling time. Use the same units for doubling time and elapsed time. This model assumes unlimited nutrients and space, so it is applicable during the exponential phase but overestimates results when an actual culture enters the stationary phase. Exponential growth is no longer applicable to populations that are decreasing in number.

Frequently asked questions

Are generation time and doubling time the same?

Yes. Both terms refer to the time it takes for a population to double during the exponential phase. In microbiology, the term generation time is more commonly used while in general biology and ecology doubling time is more common but the numbers are identical.

Is there a difference in using natural logarithm or base 10 logarithm?

No, it is not a problem as long as the values are consistent. The generation number is the logarithm of the doubling factor divided by the logarithm of two. When using logarithms with a uniform base, that base cancels out in the ratio. This calculator does the math internally, so only numbers and time need to be entered.

How can you determine the doubling time from two measured values?

Enter the initial number, final number and elapsed time, leaving the doubling time field blank. The calculator will calculate this by multiplying the logarithm of two by the elapsed time, then dividing by the logarithm of the doubling factor.

What growth rate corresponds to a given doubling time?

The growth rate per unit of time is two to the power of the reciprocal of the doubling time, minus one. If the doubling time is 20 minutes, then the growth rate per minute is about 3.5 percent. This converted value will automatically appear in the result field.

When should this calculator not be used?

This model should not be used outside the logistic phase. As growth is not exponential during the lag, stationary and death phases predictions can be misleading. The model also assumes that there are enough nutrients and space available which will eventually become exhausted in real cultures.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

MicrobeNotes: Bacterial Growth Curve and Phases
Overview of the lag, log, stationary, and death phases of bacterial growth.
Wikipedia: Bacterial growth
Binary fission, generation time, and the exponential growth model.