Growth rate constant

The rate of exponential growth can be described with the mean growth rate constant.

The mean growth rate constant (k) is the number of generations (n) per unit of time (t).

k = n / t

In case of microorganisms it is usually expressed as generations per hour.

If you know the number of bacteria N_t and the initial number of bacteria N₀ you can calculate the growth rate with the following formula.

k = log₂ (N_t / N₀) / t

or when using log10:

k = log₁₀(N_t / N₀) / 0.301 t

Note that it doesn't matter if we know the precise number of microorganisms or an indirect factor such as the optical density of a culture tube because the k is a relative value.

In a logarithmic growth chart the growth rate is the represented by the slope of the exponential phase.

Check out the generation time page to learn how the generation time is calculated.