Doubling Time Calculator
Find the doubling time, number of generations and growth rate of a culture from two counts, and the time needed to reach a target count.
Exponential growth
Bacteria, yeast and cultured cells growing without limits divide at a steady rate, so their number doubles at regular intervals: N = N₀ × 2^(t ÷ td), where td is the doubling time, also called the generation time. Taking logarithms, the number of generations between two counts is log₂(N ÷ N₀) and the doubling time is the elapsed time divided by that number. The specific growth rate, k = ln(N ÷ N₀) ÷ t, is the same information in natural-log units: td = ln 2 ÷ k.
A worked example
A culture of Escherichia coli goes from 200,000 to 12,800,000 cells per millilitre in 120 minutes. The ratio is 64, which is 2⁶, so the cells went through 6 generations and the doubling time is 120 ÷ 6 = 20 minutes, a typical figure for E. coli in rich medium at 37 °C. The growth rate is ln 64 ÷ 120 = 0.0347 per minute. If the growth stayed exponential, reaching 10⁹ cells per millilitre would take 20 × log₂(10⁹ ÷ 200,000) = 245.8 minutes, just over four hours, from the first count. In practice, cultures in shake flasks leave exponential growth before that density as nutrients and oxygen run short.
Typical doubling times
Doubling times vary enormously. E. coli manages about 20 minutes in rich medium at 37 °C, and Vibrio natriegens under 10 minutes; baker’s yeast takes about 90 minutes; many mammalian cell lines take 20 to 30 hours, and Mycobacterium tuberculosis about 20 hours. Temperature, medium and oxygen supply all change the figure, so a doubling time is a property of an organism under particular conditions. A common misconception is that a culture keeps doubling at the same rate indefinitely; after a lag phase it grows exponentially for a limited time, then slows into stationary phase, and finally declines.
Measuring it well
Take both counts in the exponential phase, where a plot of log count against time is a straight line; several points and a fitted line are better than two. Counts from optical density are only proportional to cell number over a limited range, typically up to an OD₆₀₀ of about 0.4 to 0.6 in a standard spectrophotometer, so dilute dense samples before measuring. Colony counts measure viable cells, which can differ from total counts. If the final count is lower than the first, the population is declining and the same arithmetic gives a halving time instead.
How to use it
- Enter the starting and final counts, in any consistent unit such as cells per millilitre or OD.
- Enter the time between them and choose the unit.
- Read the doubling time, the number of generations and the growth rate.
- Optionally enter a target count to estimate when the culture will reach it.
Questions from the teaching lab
How do you calculate doubling time?
Divide the elapsed time by the number of generations, which is log₂(final count ÷ starting count). A culture growing from 200,000 to 12,800,000 cells in 120 minutes has increased 64-fold, 6 generations, so its doubling time is 20 minutes.
What is the doubling time of E. coli?
About 20 minutes in rich medium such as LB at 37 °C with good aeration, and considerably longer in minimal medium or at lower temperatures. The figure applies only during exponential growth, not during the lag or stationary phases.
What is the difference between growth rate and doubling time?
They describe the same thing in different units. The specific growth rate k is ln(N ÷ N₀) ÷ t, and the doubling time is ln 2 ÷ k. A doubling time of 20 minutes corresponds to a growth rate of about 0.0347 per minute.
Why does my culture grow slower than the calculated rate?
Because exponential growth only lasts while nutrients, oxygen and space are plentiful. Cultures start with a lag phase and slow down as they approach stationary phase, so counts taken outside the exponential phase give longer apparent doubling times.
Disclaimer: Genetics results apply textbook models, Mendelian ratios, Hardy-Weinberg equilibrium and simple Tm formulas, to the values you enter. They are for education and are not medical advice, genetic counselling or parentage testing. Real inheritance involves linkage, variants and family history these models leave out: anyone concerned about a condition, a pregnancy or a test result should speak to a doctor or genetic counsellor.