What Is Cell Doubling Time?
Cell doubling time is the time it takes a culture to double in number during exponential growth. It follows from the counts at two times: td = t × ln 2 ÷ ln(N ÷ N₀), and the number of generations is log₂(N ÷ N₀).
Enter the starting and final counts or densities, the elapsed time and its unit. The calculator returns the doubling time in your unit and in minutes, the generations, the specific growth rate, the percent growth per time unit and, optionally, the time to reach a target count. Two charts show the growth curve and the straight line it makes on a log₂ scale.
Below are the formulas, variables, a worked example and answers about log phase and why doubling time changes.
How to Use the Cell Doubling Time Calculator
- Enter the starting and final cell counts or densities.
- Enter the elapsed time and its unit.
- Optionally add a target count.
- Read the doubling time, growth rate and generations.
Cell Doubling Time Formula
Doubling time
Specific growth rate
Generations
Cell Doubling Time Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| N₀ | Starting cell count or density | |
| N | Final cell count or density | |
| t | Elapsed time | |
| td | Doubling time | |
| μ | Specific growth rate | ln(N ÷ N₀) ÷ t |
Cell Doubling Time Worked Example
A culture grows from 100,000 to 850,000 cells in 72 hours. The fold change is 8.5, so the generations are log₂(8.5) = 3.09 and the doubling time is 72 ÷ 3.09 = 23.3 hours. The growth rate is ln(8.5) ÷ 72 = 0.0297 per hour.
With the example values loaded in the calculator above, the steps are:
- Generations = log₂(N ÷ N₀) = log₂(850,000 ÷ 100,000) = 3.08746.
- Doubling time td = t ÷ generations = 72 ÷ 3.08746 = 23.3201 hours.
- Growth rate μ = ln(N ÷ N₀) ÷ t = 0.0297231 per hour; also td = ln 2 ÷ μ = 23.3201.
Result: Doubling time td = 23.3201 hours; Number of generations (doublings) = 3.08746.
How to Read a Doubling Time
Doubling time is how long the population takes to double during exponential growth. A culture that grows from 100,000 to 850,000 cells in 72 hours has a fold change of 8.5, which is log₂(8.5) = 3.09 doublings, so the doubling time is 72 ÷ 3.09 = 23.3 hours.
The result is an average over the whole period. If the cells were in a lag phase at the start or reached a plateau at the end, the true exponential doubling time is shorter. Use two counts taken inside the growth phase.
Where Cell Doubling Time Is Used
Cell culture
Estimate the doubling time of a cell line from two counts or two densities taken during the exponential phase.
Planning passages
Predict how many hours until a culture reaches a target count.
Growth rate
Convert between the specific growth rate μ and the doubling time, which are related by td = ln 2 ÷ μ.
Bacterial growth
The same maths applies to any population that grows by a fixed factor per unit time.
Common Cell Doubling Time Mistakes to Avoid
- Use counts from the exponential phase. Counts from lag or plateau give a doubling time that is too long.
- Keep the time unit consistent. Choose the time unit that matches your elapsed time.
- Doubling time only makes sense when the population grew. If the final count is smaller, the population is decaying.
- Measure the counts the same way each time, because counting error can look like growth.
Cell Doubling Time Terms and Definitions
- Doubling time
- The time for the population to double.
- Generation
- One doubling of the cell population.
Cell Doubling Time FAQs
How do you calculate cell doubling time?
Use td = t × ln 2 ÷ ln(N ÷ N₀), where N₀ is the starting count, N is the final count and t is the elapsed time. For 100,000 to 850,000 cells in 72 hours, td = 72 × 0.693 ÷ 2.14 = 23.3 hours.
How many generations have occurred?
The number of generations is log₂(N ÷ N₀). For a fold change of 8.5 that is 3.09, which means the population doubled a little over three times.
What is the relation between growth rate and doubling time?
The specific growth rate is μ = ln(N ÷ N₀) ÷ t, and the doubling time is ln 2 ÷ μ. A faster growth rate means a shorter doubling time.
Why does my doubling time change over time?
Real cultures pass through lag, exponential and plateau phases. The doubling time is only constant in the exponential phase, so calculate it from counts taken within that window.