Cell Doubling Time Calculator
Enter the cell number at the start, the number at the end and the time between them, and get the doubling time, the specific growth rate, the number of generations and a log-scale chart of the growth. Two other modes predict the number of cells after a given time and the time needed to reach a target. Runs entirely in your browser. Free, no sign-up.
Results
31.82
Doubling time (h)
2.263
Generations
0.02179
Growth rate μ (per h)
4.8
Fold increase
2.20
Increase per h (%)
The same doubling time: 1,909 min = 31.82 h = 1.326 d.
The working
Td = t × ln 2 ÷ ln(N ÷ N₀) = 72 × 0.6931 ÷ ln(1.2 × 10⁶ ÷ 2.5 × 10⁵) = 31.82 h
μ = ln(N ÷ N₀) ÷ t = 1.569 ÷ 72 = 0.02179 per h
generations = log₂(N ÷ N₀) = 2.263
Growth on a log scale
These formulas assume exponential (log-phase) growth. If either count was taken in the lag or plateau phase, the result does not describe the cells' real doubling time.
How to Use the Cell Doubling Time Calculator
- 1. Choose what you know. Two counts and the time between them give the doubling time. A doubling time and a time give the final number. A doubling time and a target give the time needed.
- 2. Enter the counts. Use the same unit for both — cells, cells/mL, or optical density. Only the ratio matters.
- 3. Set the time and its unit. Minutes suit bacteria, hours and days suit cultured mammalian cells.
- 4. Read the result. The doubling time, growth rate and generations come with the working and a chart. A straight line on the log axis is exponential growth.
The Doubling Time Formula
During exponential growth the population doubles at a constant interval, Td, so after a time t the number of cells is N = N₀ × 2^(t ÷ Td). Solving for Td gives the formula, which can use logarithms in any base because the base cancels:
Doubling time
Td = t × ln 2 ÷ ln(N ÷ N₀)
Growth rate
μ = ln(N ÷ N₀) ÷ t, so Td = ln 2 ÷ μ ≈ 0.693 ÷ μ
Generations
n = log₂(N ÷ N₀) = t ÷ Td
This is the form given in Roth's Doubling Time Computing (2006): the duration times log 2, divided by the difference of the logarithms of the final and initial counts. The doubling time comes out in whatever unit you gave for the time. μ is the specific growth rate, in reciprocal time units; the percentage increase per unit of time is (e^μ − 1) × 100.
Worked Example: Cells Counted Three Days Apart
You seed a flask at 2.5 × 10⁵ cells and count 1.2 × 10⁶ after 72 hours. These are the calculator's default inputs.
- Fold increase: 1.2 × 10⁶ ÷ 2.5 × 10⁵ = 4.8, and ln 4.8 = 1.5686.
- Doubling time: 72 × 0.6931 ÷ 1.5686 = 31.82 hours, which is 1909 minutes or 1.326 days.
- Generations: log₂ 4.8 = 2.263 doublings in the 72 hours.
- Growth rate: μ = 1.5686 ÷ 72 = 0.02179 per hour, an increase of about 2.20% per hour.
Going the other way, a culture doubling every 24 hours grows from 2.5 × 10⁵ to 2.5 × 10⁵ × 2³ = 2 × 10⁶ cells in 72 hours, and to reach 1 × 10⁶ takes two doubling times, 48 hours. A textbook bacterial example: E. coli doubling every 20 minutes under good conditions turns one cell into 2²⁰ = 1,048,576 cells in 400 minutes.
When the Number Is Not a Real Doubling Time
- Lag phase. After seeding or thawing, cells often take a while to start dividing. A count that includes the lag gives a doubling time that is too long. Use counts that are both from the exponential phase.
- Plateau. Cultures slow as they approach confluence or run out of nutrients; the average over that period understates the true rate.
- Cell loss. A count taken after trypsinisation includes any cells that did not reattach. Count live cells and note the viability, for example with the Hemocytometer Cell Count Calculator.
- Different quantities. Cells per mL, cells per well and optical density can all be used if each is proportional to the number of cells, but optical density stops being linear at high density.
- Cumulative doublings. The population doubling level is log₂(cells harvested ÷ cells seeded), added up over passages. It counts doublings; it is not itself a time.
Frequently Asked Questions
- How do you calculate cell doubling time?
- Multiply the elapsed time by ln 2 (0.693) and divide by the natural log of the final count over the initial count. For 2.5 × 10⁵ cells growing to 1.2 × 10⁶ in 72 hours: 72 × 0.693 ÷ ln 4.8 = 31.8 hours. The answer is in the same unit as the time.
- What is the difference between doubling time and growth rate?
- Doubling time is how long it takes the population to double; the growth rate μ is the fractional increase per unit time under continuous growth. They are linked by Td = ln 2 ÷ μ. A faster growth rate means a shorter doubling time.
- What is the formula for the number of generations?
- n = log₂(N ÷ N₀), or equivalently t ÷ Td. A four-fold increase is two generations, an eight-fold increase three. For the number after n generations, N = N₀ × 2ⁿ.
- Can I use optical density instead of cell counts?
- Yes, if the optical density is proportional to the cell number, which is true only at low densities. Above roughly OD 0.4–0.5 in many spectrophotometers the relationship flattens, so dilute the culture and multiply back before using the values. The calculation needs only the ratio of the two readings.
- What is a typical doubling time?
- It depends entirely on the organism, the medium and the temperature. E. coli can double in about 20 minutes in rich medium at 37 °C, while cultured mammalian cell lines usually take roughly half a day to two days. Use the doubling time of your own culture, measured during exponential growth.
- Why is my doubling time longer than the published value?
- Common causes are counting in lag or plateau phase, cell loss at passage, a different medium or serum lot, a high passage number and overconfluent seeding. Counts of fewer than about 100 cells also carry a large random error, so check that your counting is reliable.