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Bacterial Growth Rate Calculator

Calculate the specific growth rate, doubling time and number of generations of a culture from two measurements taken during exponential growth.

Formula

μ=ln⁡(N2/N1)t2−t1\mu = \dfrac{\ln(N_2/N_1)}{t_2 - t_1}
Td=ln⁡2μT_{\mathrm{d}} = \dfrac{\ln 2}{\mu}
generations=log⁡2N2N1\text{generations} = \log_2\dfrac{N_2}{N_1}
μ\mu
specific growth rate, per hour
N1, N2N_1,\ N_2
cell density or OD600 at the two time points
t2 − t1t_2\ -\ t_1
time between the measurements

How it works

In exponential phase a culture grows at a rate proportional to its own size. The specific growth rate µ is the slope of the natural logarithm of cell density against time, and the doubling time is ln 2 divided by µ.

The two measurements can be OD600 readings, cell counts or CFU, provided both use the same measure and both fall inside exponential phase.

Worked example

OD600 rises from 0.1 to 0.8 in 90 minutes.

  1. µ = ln(0.8 / 0.1) / 1.5 h = 2.079 / 1.5 = 1.386 per hour.
  2. Doubling time = 0.6931 / 1.386 = 0.5 h.

The culture doubles every 30 minutes, completing 3 generations in the interval.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Both measurements were taken during exponential growth, after the lag phase and before nutrients run short.
  • The measure used is proportional to cell number across the range, which for OD600 means staying in the linear range.

Common mistakes

  • Including lag or stationary phase, which lowers the apparent growth rate.
  • Using OD600 readings above the linear range without diluting.
  • Relying on two points. Fitting a line to several points on a log plot gives a more reliable rate.

Related tools

OD600 to Cell Density CalculatorEstimate bacterial cell density from optical densityOpen calculatorCFU Calculator (Colony-Forming Units per mL)Viable count from a plate count and dilutionOpen calculatorCell Doubling Time CalculatorDoubling time from two cell countsOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.