How to use this calculator
This tool models the exponential (log) phase of microbial growth. Enter a starting population, the culture's doubling time (how long it takes to double under these conditions), and the elapsed growth time, then click Calculate to get the final population, the number of generations elapsed, the specific growth rate, and the fold increase. Click Reset to restore the example values.
The formula
During log-phase growth, population size follows N(t) = N0 × 2^(t/g), where N0 is the initial population, t is elapsed time, and g is the doubling time (in the same time units as t). The number of generations elapsed is simply t ÷ g. This is mathematically equivalent to the continuous form N(t) = N0 × e^(μt), where the specific growth rate μ = ln(2) / g.
Understanding the inputs
Initial population is usually expressed in colony-forming units per milliliter (CFU/mL) from a plate count or optical-density estimate. Doubling time depends heavily on the organism and conditions — E. coli can double in about 20 minutes in nutrient-rich broth at 37°C, while many environmental bacteria take several hours and slow growers like Mycobacterium tuberculosis take roughly a day. Growth time is the total elapsed incubation period you want to project forward to.
Interpreting the results
Final population and generations elapsed are the primary outputs — how large the culture has grown and how many doublings that represents. Growth rate (μ) expresses the same doubling behavior as a per-hour rate, useful for comparing organisms or conditions. Fold increase shows the multiple by which the population has grown. Remember this formula assumes unrestricted exponential growth; real batch cultures slow down and enter a stationary phase once nutrients deplete, typically somewhere around 10⁹–10¹⁰ CFU/mL for many bacteria, so results far beyond that density are a theoretical projection rather than a lab-confirmed outcome.