Cell doubling time calculator.
Find how fast a culture grows. Enter the starting and ending cell counts and the time between them to get the doubling time, the number of doublings and the growth rate.
Counts and time
LiveDoubling time is the time for the population to double. It uses the natural log of the fold increase over the elapsed time.
Doubling time
8.00 h
for the population to double
Assumes steady exponential growth. For lab estimates. Calculations run in your browser; nothing you enter is stored.
How it works
Log of the growth
Doubling time is how long a growing population takes to double in number. During exponential growth, the doubling time is the elapsed time multiplied by the natural log of 2, divided by the natural log of the fold increase from start to finish.
Going from 10,000 to 80,000 cells is an eight-fold rise, which is three doublings. Over 24 hours that is a doubling time of 8 hours.
Reference
Fold increase to doublings.
How many times a population has doubled for a given fold increase.
| Fold increase | Doublings |
|---|---|
| 2x | 1.00 |
| 4x | 2.00 |
| 8x | 3.00 |
| 16x | 4.00 |
| 100x | 6.64 |
| 1000x | 9.97 |
The full guide
The complete guide to doubling time.
What doubling time means, how it is calculated, and how it relates to growth rate.
What is doubling time?
Doubling time is the period a population needs to double during exponential growth. It is a simple, intuitive measure of how fast cells, bacteria or any growing quantity are multiplying. A shorter doubling time means faster growth.
It stays constant only while growth is truly exponential, before resources run low and the culture levels off.
How it is calculated
You take the natural log of the final count divided by the initial count to get the total growth, then the doubling time is the elapsed time times ln(2) divided by that figure. Equivalently, count the doublings as log base 2 of the fold increase, then divide the time by the doublings.
An eight-fold rise is exactly three doublings, so any time over an eight-fold rise divides by three.
Doubling time and growth rate
Growth rate and doubling time are two views of the same thing. The specific growth rate is the natural log of the fold increase divided by time, and doubling time is ln(2) divided by that rate. A higher rate means a shorter doubling time.
Use whichever your field prefers; microbiologists often quote doubling or generation time, while modellers use the rate constant.
Using the numbers
Doubling time helps you plan experiments, compare conditions and predict when a culture will reach a target density. Measure two counts a known time apart, ideally during the exponential phase, for the cleanest estimate.
If growth has slowed, the calculated doubling time will be longer than the true exponential rate.
The formula
Time to
double.
Doubling time is the elapsed time times ln(2), divided by the natural log of the fold increase.
Generation time ›# Doubling time
doublings = log2(final / initial)
Td = time × ln(2) / ln(final/initial)
# worked example
24 × ln2 / ln(8) = 8.00 hQuestions
Doubling questions.
How do I calculate doubling time?
+
Take the natural log of the final count over the initial count, then doubling time is the elapsed time times ln(2) divided by that value. From 10,000 to 80,000 in 24 hours is 8 hours.
What is the difference between doubling time and generation time?
+
They are essentially the same idea: the time to double or for one generation. Microbiology often calls it generation time and quotes it in minutes; cell biology tends to say doubling time in hours.
How many doublings is an 8-fold increase?
+
Three. Each doubling multiplies by two, and two to the power of three is eight, so an eight-fold rise is exactly three doublings.
Why should I measure during exponential growth?
+
Doubling time is only constant while growth is exponential. Once nutrients run low the culture slows, so counts taken later give a longer, less meaningful doubling time.
Is this doubling time calculator free?
+
Yes. It is completely free with no sign-up, and every calculation runs locally in your browser, so nothing you enter is stored or sent anywhere.
About the developer
Jean Borg
Jean builds and maintains every calculator on freecalculators.pro from Malta, with a focus on tools that are fast, free and show their working. The cell doubling time calculator uses standard exponential-growth maths and is for lab estimates.