About the Doubling Time Calculator
This doubling time calculator works out how fast a population of bacteria, yeast or cultured cells is growing during exponential (log-phase) growth. Enter the starting and final counts — cells, colony-forming units, OD600 readings or any quantity proportional to cell number — and the time between them, and it returns the doubling (generation) time, the specific growth rate µ and the number of doublings.
Switch to projection mode to go the other way: from a known doubling time, predict how many cells you will have after a given time, which is useful for planning when to passage cultures, harvest cells or start an experiment. A growth chart shows the population over the period.
The calculation assumes steady exponential growth with no lag or stationary phase in the window you measure. Take both readings during log phase for an accurate doubling time; including a lag phase makes the culture look slower than it really is.
With the default inputs, the doubling time is 24. Change any value above to recalculate instantly.
How to use the doubling time calculator
- 1Choose whether to find the doubling time or project a final count.
- 2Enter the starting count (cells, CFU/mL or OD).
- 3Enter the final count, or the known doubling time for a projection.
- 4Enter the elapsed time and pick its unit.
- 5Read the doubling time, growth rate and number of generations.
Formula and method
During exponential growth every cell divides in a fixed time, so the population follows N = N₀ × 2^(t/Td). Taking logarithms, the number of doublings in time t is n = log₂(N/N₀), and the doubling (generation) time is Td = t ÷ n = t × ln 2 ÷ ln(N/N₀).
The specific growth rate µ = ln(N/N₀) ÷ t is the natural-log rate constant used in microbiology and bioprocess models; it relates to doubling time by Td = ln 2 ÷ µ ≈ 0.693 ÷ µ. Doublings per unit time (1/Td) is sometimes called the growth-rate constant k.
- N₀, N
- Initial and final cell number (or a proportional measure)
- t
- Time between the two measurements
- Td
- Doubling (generation) time
- µ
- Specific growth rate (per time unit)
Worked examples
Mammalian cells over three days
2.0 × 10⁵ cells grew to 1.6 × 10⁶ — an 8-fold increase, which is log₂(8) = 3 doublings. 72 hours ÷ 3 = a 24-hour doubling time, typical of many cell lines.
E. coli in log phase
A 64-fold rise is 6 doublings. 120 minutes ÷ 6 = 20 minutes per generation, the classic doubling time of E. coli in rich broth at 37 °C.
Planning a passage
With a 30-hour doubling time, 96 hours allows 96 ÷ 30 = 3.2 doublings. 5 × 10⁵ × 2^3.2 ≈ 4.59 × 10⁶ cells, so a flask seeded today will be ready in four days.
Frequently asked questions
How do you calculate doubling time?+
Divide the elapsed time by the number of doublings, where doublings = log₂(final ÷ initial). Equivalently, Td = t × ln 2 ÷ ln(N/N₀). For example, an 8-fold rise in 72 hours is 3 doublings, so Td = 24 hours.
What is the difference between doubling time and generation time?+
For a population growing by binary fission they are the same: the time for the number of cells to double. Generation time is the term used in microbiology, population doubling time in cell culture.
How is growth rate related to doubling time?+
The specific growth rate µ = ln 2 ÷ Td ≈ 0.693 ÷ Td. A culture with a 1-hour doubling time has µ ≈ 0.69 per hour. Some texts use k = 1/Td, the number of doublings per unit time.
Can I use OD600 instead of cell counts?+
Yes, as long as the optical density is in the linear range (usually below about 0.4–0.8 for most spectrophotometers) and proportional to cell number. Ratios cancel the units, so the doubling time is the same.
Why does my doubling time look too long?+
Common causes are measuring during the lag or stationary phase, cells being counted while they detach or die, or nutrient limitation. Use two points well inside the exponential phase for an accurate value.