Bacterial Growth Calculator (Doubling Time)
Work out how a bacterial culture grows. Find the final count, the doubling time from two counts or the time to reach a count with N = N₀ × 2^(t/g), see the generations and growth rate, add a carrying capacity, or turn an OD600 reading into cells/mL.
How to Use
- Choose what to find: the Final count, the Doubling time from two counts, the Time to reach a count, Logistic growth with a carrying capacity, or OD600 to cells/mL.
- Enter the starting count N₀ in cells (or CFU) per mL; e-notation such as 2e6 works.
- Enter the time and the doubling time with their units: minutes, hours, days or seconds can be mixed.
- For logistic growth add the carrying capacity K, the most cells the culture can hold. For OD600 enter your reading and your calibration factor.
- Read the answer in the highlighted field and readouts; the plot shows the curve on a log scale and Show Work lists every step.
Worked Example
Final count. 1,000 cells/mL with a 20 minute doubling time grow for 3 hours. Generations n = 180 ÷ 20 = 9, so N = 1,000 × 2⁹ = 512,000 cells/mL, a 512-fold increase. The specific growth rate is μ = ln 2 ÷ (1/3 h) = 2.079 per hour.
Doubling time from two counts. A culture goes from 2 × 10⁶ to 3.2 × 10⁷ cells/mL in 2 hours. That is a 16-fold rise, log₂ 16 = 4 generations, so g = 120 ÷ 4 = 30 minutes.
The common mistake: counting generations with the natural log. ln 16 = 2.773, not 4. Dividing 120 minutes by 2.773 gives a doubling time of 43.28 minutes, far too long. Generations need log base 2: log₂ x = ln x ÷ ln 2 = 3.3219 × log₁₀ x. The natural log belongs with μ, which is why μ = ln 2 ÷ g.
Show Work
Formulas
Growth Curves, from Verhulst to Monod
The levelling-off curve came first, and not from microbiology. In 1838 the Belgian mathematician Pierre-François Verhulst proposed what he later called the logistic equation as a model for human populations that cannot grow forever: growth slows as the population approaches a limit, the carrying capacity K.
For bacteria, the classic account is Jacques Monod’s 1949 review The Growth of Bacterial Cultures, which set out the phases of a batch culture: a lag while the cells adjust to the medium, exponential (log) growth at a constant doubling time, a stationary phase once the medium is spent, and finally decline. Monod also tied the growth rate to the concentration of the limiting nutrient, the Monod equation, which has the same form as the Michaelis–Menten equation for enzymes.
The exponential phase is where N = N₀ × 2^(t/g) holds. Doubling times vary enormously: fast-growing bacteria in rich medium can double in well under an hour, while slow growers such as Mycobacterium tuberculosis take many hours, which is why culturing them takes weeks.
About This Tool
This calculator works with the exponential growth law in its doubling-time form: give two of the starting count, final count, time and doubling time and it finds the missing one, with the number of generations, the specific growth rate μ and the fold increase. A logistic mode adds a carrying capacity so you can see how far a culture really gets, and an OD600 mode converts absorbance to cells/mL with a calibration factor you can change. Counts are plotted on a log scale, where exponential growth is a straight line.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Hemocytometer Calculator, Half-Life Calculator, and Exponential Growth Calculator.
Frequently Asked Questions
How do you calculate bacterial growth?
Use N = N₀ × 2^(t/g), where g is the doubling (generation) time. 1,000 cells doubling every 20 minutes go through 180 ÷ 20 = 9 generations in 3 hours, so N = 1,000 × 2⁹ = 512,000 cells.
How do I find the doubling time from two counts?
Count the generations as n = log₂(N ÷ N₀), then divide the time by n. A culture going from 2 × 10⁶ to 3.2 × 10⁷ cells/mL in 2 hours grew 16-fold, which is log₂ 16 = 4 generations, so g = 120 ÷ 4 = 30 minutes.
What is the specific growth rate μ?
It is the rate in the exponential form N = N₀e^(μt), and μ = ln 2 ÷ g. A 30 minute doubling time gives μ = 0.6931 ÷ 0.5 h = 1.386 per hour; a 20 minute doubling time gives 2.079 per hour. The number of divisions per hour, 1 ÷ g, is 2 and 3 respectively.
How do I convert OD600 to cells per mL?
Multiply the optical density by a calibration factor. A rough figure often quoted for E. coli is 8 × 10⁸ cells/mL per OD600 unit, so an OD of 0.5 is about 4 × 10⁸ cells/mL. The factor changes with the organism, cell size and the spectrophotometer, so calibrate it against a plate count for real work.
Why doesn’t a culture keep growing exponentially?
Nutrients run out and waste builds up, so growth slows and stops at a carrying capacity. 100 cells doubling every 20 minutes for 10 hours would reach 100 × 2³⁰ = 1.074 × 10¹¹ cells/mL if nothing limited them; logistic growth with K = 2 × 10⁹ gives 1.963 × 10⁹ cells/mL, 98.17% of K.
How do I use the Bacterial Growth Calculator (Doubling Time)?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Planning an experiment
Going from 10⁵ to 10⁹ cells/mL at a 30 minute doubling time takes 13.29 generations, or 6.644 hours.
Measuring a growth rate
Two counts 2 hours apart, 2 × 10⁶ and 3.2 × 10⁷ cells/mL, give a 30 minute doubling time and μ = 1.386 per hour.
Overnight cultures
A logistic model with K = 2 × 10⁹ shows 10⁶ cells/mL at a 30 minute doubling time pass half of K after 5.483 hours.
Spectrophotometer readings
An OD600 of 0.25 read on a 1:10 dilution is an undiluted OD of 2.5, about 2 × 10⁹ cells/mL with an 8 × 10⁸ factor.
Teaching exponential growth
One cell doubling every 20 minutes becomes 2⁹ = 512 cells in 3 hours and 2³⁰, over a billion, in 10 hours.
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