Doubling time calculator
Doubling (generation) time of a bacterial or cell culture from two counts, or the count and the time needed for growth, using N = N0 × 2^(t ÷ td).
What is doubling time, and how is it different from generation time?
For cells that divide by binary fission, the generation time is also called the doubling time: the time it takes the population to double through one round of division (OpenStax Microbiology, section 9.1). The number of cells after n generations is N = N0 × 2^n. Because n = t ÷ td, you can write the same growth as N = N0 × 2^(t ÷ td). Doubling time is a property of the strain and the conditions (medium, temperature, oxygen); the same species can double in minutes in one lab setting and take far longer in another.
How do I calculate doubling time from two counts?
Divide the later count by the earlier one, take the base-2 logarithm to get the number of doublings, and divide the elapsed time by that number: td = t ÷ log2(N ÷ N0). Example: a culture goes from 2,500 to 80,000 cells in 5 hours. The ratio is 32, which is 2^5, so there were 5 doublings and td = 5 ÷ 5 = 1 hours (60 minutes). The growth rate constant is k = ln 2 ÷ td = 0.6931 per hour, so N = N0 × e^(kt) gives the same curve in natural-exponential form.
Worked example: one cell dividing every 30 minutes
OpenStax Microbiology gives the case of a single cell that divides every 30 minutes for 24 hours. That is 1,440 ÷ 30 = 48 generations, so N = 2^48 = 2.815 × 10¹⁴, which the book rounds to 2.8 × 10¹⁴ cells. Real cultures never get there: nutrients run out and wastes build up long before. The number is useful mostly as a reminder of how fast exponential growth is and why a lab culture must be checked often. Starting from 1,000 cells with a 45-minute doubling time, one hour gives 1.33 doublings and about 2,520 cells.
How long until my culture reaches a target count?
Solve for time: t = td × log2(target ÷ start). From 10⁶ to 10⁹ cells is a thousandfold increase, or log2(1000) = 9.966 doublings. With a doubling time of 20 minutes that takes 199.3 minutes, about 3.32 hours. A tenfold increase always takes 3.32 doublings, whatever the starting count. Use the mode “Time to reach a target” and enter the start, the target and the doubling time you measured in your own conditions.
Why does the lag phase matter?
Batch cultures do not grow at the exponential rate from the first minute. In the lag phase the number of cells does not change: cells enlarge, become metabolically active, synthesize the proteins they need and repair damage from the transfer to new medium (OpenStax Microbiology, section 9.1). Exponential growth follows, then a stationary phase and death. The doubling time only applies to the exponential phase. If you take your two counts across the lag phase, the apparent doubling time will be too long, and if you extend the calculation into the stationary phase it will give a count far above what actually grows.
Common mistakes
Mixing time units is the most frequent one: if the doubling time is in minutes, the elapsed time must be too (the unit selector converts the results, but both inputs share one unit). Another is using counts from different methods, for example total cell counts at one point and colony counts at another, which differ by the dead and non-culturable cells. A third is reading an optical-density value as a cell number without a calibration for that organism; the relation is commonly only proportional at low density. Finally, a single pair of counts is a rough estimate: use at least three points in the exponential phase and a straight line on a log plot for a better doubling time.
Limits of this method
The model assumes every cell divides at the same steady rate and that none die. It fits exponential growth of single-celled organisms in a non-limiting medium. It does not describe cell lines that spend a fixed time in each cycle phase, populations with significant death, or growth that slows as the population nears its carrying capacity (the logistic model). For growth stated as a percentage per period, or for money, use the exponential growth calculator or the rule of 72 calculator instead.
For study and bench planning only; follow your lab’s protocol. Sources: OpenStax, Microbiology, section 9.1 “How Microbes Grow” (generation time, N = N0 × 2^n, the 30-minute example, the lag phase). The link between the doubling time and k is our derivation. Related: exponential growth calculator, half-life calculator, log calculator, rule of 72 calculator, cell count calculator and serial dilution calculator.