Cell Doubling Time & Growth Rate Calculator
Doubling time, growth rate and generations from counts or OD, plus seeding plans and PDL.
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Result
Growth on a log scale
If growth continues at this rate
Your readings and the fit
Cells over time
Passages
How it was worked out
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About the Cell Doubling Time & Growth Rate Calculator
Work out how fast a cell culture or a bacterial culture grows, the way a lab does it. From two counts (cells, cells/mL, CFU/mL or optical density) and the time between them you get the doubling time (generation time), the specific growth rate μ, the number of generations, the division rate and, if you give the starting population doubling level, the PDL at the end. From a time course of readings it fits a straight line to ln N against time over the points you choose, so lag and plateau points can be left out, and gives the doubling time with a 95 % interval and R². Plan and seed works the other way: from a doubling time (and a lag, if your cells pause after passaging) it gives the count at a time, the time to reach a count, or the cells to seed for a harvest, with the seeding density and the volume of cell suspension to add. Passages adds up the population doublings of a passage record into the PDL.
The formulas are the ones of the ATCC culture guide and of microbiology textbooks: N = N₀·2ⁿ, T_d = t·ln 2 ÷ ln(N ÷ N₀) and PDL = S + 3.32·(log X_e − log X_b). For the doubling time of hCG in pregnancy, use the hCG doubling time calculator instead.
With a Pro pass, copy the result or download it as a CSV, or unlock this one result. Without a pass the free preview shows the doubling time, PDL or planning result in full, with the first rows of each table and the first step of the working; other figures are hidden.
How to use it
- Choose what to work out: from two counts, from a time course, a plan, or a passage record; set the time unit.
- Type your readings. For a time course, paste two columns (time and reading) from a spreadsheet and pick the points of the exponential phase; for OD, subtract the blank.
- For a plan, enter the doubling time and choose what you need: cells after a time, the time to a number of cells, or the cells to seed (with the flask’s area and your cell suspension, if you like).
- Read the doubling time, the chart on a log scale, the tables and the working. Copy the result or download the CSV with a Pro pass, or after unlocking this result.
Examples
100,000 → 800,000 cells in 72 h
Doubling time 24 h; μ = 0.0289 h⁻¹ (0.693 per day); 3 generations
10⁶ → 6.4 × 10⁷ CFU/mL in 2 h
6 generations: a doubling time of 20 min
0 h 1.0 × 10⁵, 12 h 1.5 × 10⁵ … 72 h 8.3 × 10⁵ cells/mL (7 points)
Doubling time 23.9 h (95 % interval 23.2 to 24.6 h); μ = 0.0290 h⁻¹; R² = 0.9993
2,000,000 cells wanted after 72 h, doubling time 24 h, 75 cm² flask, suspension of 1,000,000 cells/mL
Seed 250,000 cells: 3,333 cells/cm², 250 µL of the suspension
5 × 10⁵ seeded and 3.8, 3.6 and 3.1 × 10⁶ harvested every 3 days, from PDL 12
PD 2.93, 2.85 and 2.63; PDL 20.4; doubling times 24.6, 25.3 and 27.4 h
Common uses
- Cell culture: the doubling time of a cell line, how many cells to seed for an experiment, and the PDL of a passage record
- Microbiology: the generation time of a bacterial or yeast culture from counts, CFU or OD600
- Lab reports and coursework on exponential growth, with the working shown
- Checking whether a culture is still in exponential growth from the straightness of its log plot
The formulas
- Generations: n = log₂(N ÷ N₀) = (ln N − ln N₀) ÷ ln 2, because each generation doubles the cells: N = N₀·2ⁿ
- Doubling time: T_d = t ÷ n = t·ln 2 ÷ ln(N ÷ N₀), ATCC’s DT = T ln 2 ÷ ln(X_e ÷ X_b)
- Specific growth rate: μ = ln(N ÷ N₀) ÷ t = ln 2 ÷ T_d, per hour; the division rate is n ÷ t generations per hour
- Time course: ln N = ln N₀ + μt is a straight line, so μ is the least-squares slope of ln N against t, with its standard error and a 95 % interval from Student’s t with n − 2 degrees of freedom
- Population doubling level: PDL = S + 3.32·(log₁₀ X_e − log₁₀ X_b) for each passage (3.32 ≈ 1 ÷ log₁₀ 2), where S is the PDL at the start
- Planning: N(t) = N₀·2^((t − lag) ÷ T_d) after the lag, so the time to a count is lag + T_d·log₂(N ÷ N₀) and the cells to seed are N ÷ 2^((t − lag) ÷ T_d)
Which readings to use
A culture grows in phases: a lag after seeding or passaging, then exponential (log) growth, then a plateau when space or medium runs out. Cells grow at different rates in each, so a doubling time from two readings that span more than one phase is a mixture of them. Use readings from the exponential phase, which is fairly constant and reproducible for given conditions; on the chart’s log scale it is the straight part. ATCC recommends keeping cell lines in that phase and subculturing them before they reach confluence.
Counts or optical density
Any measure proportional to the number of cells works, because the doubling time depends only on the ratio of two readings: cell counts, cells per mL, colony-forming units, or optical density (turbidity). Optical density is fast but follows cell density only within the range its calibration covers: subtract the blank (medium only), keep the same wavelength, dilute dense cultures and multiply back, and calibrate against counts when you need absolute numbers.
Sources
- ATCC, Animal Cell Culture Guide: the doubling time DT = T ln 2 ÷ ln(X_e ÷ X_b), the population doubling level and the growth phases
- OpenStax, Microbiology, 9.1 How Microbes Grow: N = N₀·2ⁿ, generation time, the growth curve and turbidity measurements
- J. Monod, The growth of bacterial cultures, Annu. Rev. Microbiol. 3, 371–394: growth rates of bacterial cultures
Limitations
- Assumes exponential growth over the readings used; it does not model lag, plateau or death phases (a lag can be added to a plan).
- Not for clinical markers: for hCG in pregnancy, use the hCG doubling time calculator.
- A PDL from counts is an estimate: it does not count cells that died or stopped dividing.
- Optical density gives relative growth; absolute cell numbers need a calibration against counts.
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Frequently asked questions
What do I get without a pass?
Without a pass, Cell Doubling Time & Growth Rate Calculator shows the doubling time, PDL or planning result in full, with the first rows of each table and the first step of the working; other figures are hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I calculate the doubling time of cells?
Count the cells at two times in the exponential phase. Doubling time = t × ln 2 ÷ ln(N ÷ N₀). For 100,000 cells becoming 800,000 in 72 hours: ln 8 = 2.079, so T_d = 72 × 0.693 ÷ 2.079 = 24 hours. The same is t ÷ n with n = log₂ 8 = 3 generations.
What is the difference between doubling time, generation time and growth rate?
For cells that divide in two, doubling time and generation time are the same: the time for the population to double. The specific growth rate μ = ln 2 ÷ T_d is the exponential rate per hour; the division rate n ÷ t counts generations per hour.
Can I use OD600 instead of cell counts?
Yes, as long as the readings are in the range where optical density follows cell density. Subtract the blank, use the same wavelength for every reading and dilute dense cultures. The doubling time only needs the ratio of the readings, so no calibration is needed for it.
Why is my doubling time longer than expected?
Usually because the readings include the lag phase after seeding or the plateau as the culture fills its vessel. Use the time-course option, plot the readings on the log scale and fit only the straight, exponential part.
How do I calculate the population doubling level (PDL)?
For each passage, PD = 3.32 × (log₁₀ cells harvested − log₁₀ cells seeded), which is log₂ of their ratio; add every passage’s PD to the PDL you started from. Seeding 5 × 10⁵ cells and harvesting 3.8 × 10⁶ adds 2.93 doublings.
How many cells should I seed to have a certain number at harvest?
Divide the number you want by 2 raised to the number of doublings until the harvest: N₀ = N ÷ 2^(t ÷ T_d). For 2,000,000 cells after 72 hours with a 24-hour doubling time, seed 2,000,000 ÷ 2³ = 250,000. Add the lag your cells show after passaging if they pause.