Cell Doubling Time Calculator

Initial measurement (N0)

Final measurement (N)

Elapsed time

Doubling time

Start with your initial and final measurements. Add the elapsed time and the calculator returns the doubling time and growth rate.

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Show the growth curve

Plot the population climbing as an exponential curve over time.

Show the doublings table

List the population after each doubling, with the time it reaches.

The doubling time of a cell is the amount of time it takes for a population to double during exponential growth. It is one of the most useful pieces of data that can be obtained from a culture and allows passage schedules to be planned, two cell lines compared or problems detected before other changes occur in cells.

Measure the same population twice with a known amount of time between measurements. This calculator will perform calculations for exponential growth and provide doubling rate, doubling time, and growth rate. If you enter doubling time it is calculated. Alternatively, you can input a doubling time to predict what size the population will be at that point.

The underlying mathematical principle is this:

Cells in the log phase are growing exponentially. This means that each cell divides at nearly the same rate, and with each doubling, the number of cells in the population doubles.

N = N_0 \cdot 2^{n}

In this case N0 is the initial value, N is the later counted value and n is the number of doublings, also called generation time. If you solve for n, you get a simple formula. As the base cancels out, it doesn't matter which logarithm is used.

n = \frac{\log(N / N_0)}{\log(2)}

If the elapsed time t is known, then doubling time can be found by dividing this time into the number of doublings, from which growth rate can also be calculated.

T_d = \frac{t}{n}, \qquad r = \frac{\ln(2)}{T_d} \approx \frac{0.693}{T_d}

If the same relationship is expressed in continuous form, it results in the familiar exponential model N = N0*e^(rt). Thus doubling time and growth rate contain different units but are equivalent information.

A complete example:

Suppose you seed 5,000 cells and count 100,000 cells 24 hours later. The number of doublings is the logarithm base 2 of 20 since the cell population has increased by a factor of 20.

n = \frac{\log(100{,}000 / 5{,}000)}{\log(2)} = \frac{\log(20)}{\log(2)} \approx 4.32

If you divide the time of 24 by 4.32 doublings, it gives a doubling time of about 5.6 hours and an equivalent growth rate of about 0.125 per hour.

T_d = \frac{24}{4.32} \approx 5.6\ \text{h}, \qquad r = \frac{0.693}{5.6} \approx 0.125\ \text{h}^{-1}

How to use this calculator:

Measure the same population using the same method at two different times. For example, count cells with the same counting grid, measure OD600 with the same spectrophotometer or perform flow cytometry with the same gate settings. Enter the first measurement in the "Initial Value" field and the second measurement in the "Final Value" field. Enter the time elapsed between the two measurements in the "Elapsed Time" field. The doubling time, growth rate, and number of doublings will be displayed to the right.

The reference values do not have to be cell counts per milliliter. If a particular parameter has a linear relationship with the cell count, any value can be used, such as OD600, confluency rate, CFU/mL or arbitrary fluorescence units. However, both measurements must use the same parameter. If doubling time is already known, you can enter it along with the starting value and time span, leaving the "ending value" field blank to predict future cell counts.

Typical doubling times

The doubling time varies widely depending on the species and conditions. The following table shows a rough range for the exponential growth phase under typical laboratory conditions.

Organism or cell type	Typical doubling time
Escherichia coli (rich media)	About 20 minutes
Saccharomyces cerevisiae (yeast)	About 90 minutes
Most mammalian cell lines	18 to 24 hours
Mycobacterium tuberculosis	15 to 24 hours
Slow primary cells	Days

Application examples

In research, doubling time determines when a cell divides. If you know that a particular cell line doubles every 22 hours, then you can plan to seed on Friday without having to return to the lab Saturday. In microbiology, doubling times are used to compare the adaptability of strains or to see if a genetic deletion has slowed growth. In cancer research departments, doubling times are tracked to describe the invasiveness of tumor cell lines and to measure how drugs affect growth. In biotechnology, an abnormality in doubling time often indicates problems with media, temperature, or oxygenation before other parameters are changed.

Important notes

Exponential growth only takes place during the log-exponential phase. Even if cells are in a latency phase or enter a plateau phase, the formula still provides values but they no longer represent what you actually want to determine.
Make sure that the objects being compared are identical. The results of cell counting with a hemocytometer can differ from those of flow cytometry and this difference may appear as an apparent increase or decrease.
Correct for dilutions. If a dilution was performed between two time points, first multiply the ending value by the dilution factor to bring it back to its original value. Forgetting to account for the dilution factor is the most common reason that doubling times appear unrealistically good.
Repeat experiments. A single culture flask will give you one value but three culture flasks can help determine if this is a reliable value.

Frequently asked questions

What is the difference between growth rate and doubling time?

Both quantities contain the same information, differing only in their units. The growth rate r is an exponential constant while doubling time is the amount of time it takes for a population to double. The relationship between the two is given by Td = ln(2) / r. Doubling time is easier for many people to understand because it is expressed in terms of hours or minutes.

Are doubling time and generation time the same thing?

In ideal exponential growth, such as binary fission during the log phase, generation time is essentially equal to doubling time. In populations that divide at regular intervals, these two terms can be used interchangeably.

Is there a difference between using natural logarithms or base-10 logarithms?

No. The formula n = log(N / N0) / log(2) balances the logarithm bases, so that both natural logarithms and base-10 logarithms will give the same doubling times. This calculator performs this operation.

What does doubling mean for decimals?

This means that the population size has increased by a factor between two powers of 2. For example, n = 2.5 means that the multiplier is 2 to the power of 2.5 and the initial count value was multiplied by approximately 5.66.

Can this be used for populations that are declining?

It is not very suitable for that. This model assumes a growing population and requires the ending value to be greater than the starting value. If the counts are decreasing it is decay and in this case a half-life model should be used.

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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

StatPearls: Bacterial Growth
Overview of the bacterial growth curve, log phase, and generation time.
Wikipedia: Doubling time
Definition and derivation of doubling time for exponential growth.