What is a bacterial growth curve?

A bacterial growth curve is a plot of the number of bacterial cells (or optical density) versus time in a closed culture. It typically shows four phases: lag, exponential (log), stationary, and death. The curve is usually drawn on a semi-logarithmic scale with log10(CFU) on the y-axis and time on the x-axis.

How do you calculate bacterial growth during the exponential phase?

During the exponential phase, bacterial growth can be modeled as N(t) = N0 × 2^(t/g), where N0 is the initial cell count, N(t) is the cell count at time t, and g is the generation (doubling) time. In log10 form, log10 N(t) = log10 N0 + t × log10(2)/g.

How can I estimate doubling time from a growth curve?

To estimate doubling time from a growth curve, identify the linear portion of the log-phase on a semi-log plot, pick two points (t1, N1) and (t2, N2), compute the slope μ = [ln(N2) − ln(N1)] / (t2 − t1), and then calculate doubling time as g = ln(2) / μ. The calculator can do this automatically if you enter two time points and their CFU or OD values.

What is the difference between CFU and OD in growth curves?

CFU (colony-forming units) is a direct measure of viable cells obtained by plating dilutions and counting colonies. OD (optical density, usually at 600 nm) is an indirect turbidity measurement that correlates with total biomass (viable and non-viable cells) within a certain range. OD is faster but must be calibrated to CFU for quantitative work.

Can this calculator model lag, stationary, and death phases?

Yes. You can specify a lag time, exponential growth duration, stationary phase duration, and death phase duration. The calculator uses a piecewise model: constant cell count during lag, exponential growth during log phase, plateau during stationary, and exponential decay during death. The resulting curve is plotted on a semi-log chart.

Bacterial Growth Curve Calculator

Model lag, exponential, stationary, and death phases of a bacterial culture. Compute cell counts, doubling time, and visualize the growth curve on a semi-log plot.

Bacterial Growth Curve Simulator

Input type

Y-axis scale

Initial value N₀

Initial CFU/mL or OD at t = 0.

Generation (doubling) time g

Time required for the population to double during log phase.

Total simulation time

Lag phase duration

Exponential (log) phase duration

Stationary phase duration

Include death phase after stationary

Key results

Doubling time g

–

In minutes and hours.

Max value at end of log phase

–

CFU/mL or OD at t = lag + log.

Total number of generations

–

During exponential phase.

Tip: You can export the simulated data as CSV for plotting in Excel, R, or GraphPad.

Time (h)	Time (min)	Value	log₁₀(Value)	Phase
Run a simulation to see tabulated results.

Estimate doubling time from two measurements

If you have two measurements in the exponential phase (CFU or OD), you can estimate the specific growth rate and doubling time.

t₁ (h)

N₁

t₂ (h)

N₂

Understanding the bacterial growth curve

In a closed batch culture, a bacterial population typically follows a characteristic growth curve when plotted as cell number (or optical density) versus time. On a semi-logarithmic plot (log₁₀ N vs. time), four main phases are observed:

Lag phase – cells adapt to the new environment, synthesize enzymes, but do not divide rapidly.
Exponential (log) phase – cells divide at a constant rate; growth is exponential and the log plot is linear.
Stationary phase – nutrient depletion and waste accumulation balance growth and death; net growth is ~0.
Death (decline) phase – death rate exceeds growth rate; viable cell numbers decrease, often exponentially.

Mathematical model used in this calculator

The calculator uses a simple piecewise model that captures the essential shape of the growth curve. Time is internally converted to hours. Let:

\( N_0 \) = initial cell count (CFU/mL) or OD
\( g \) = generation (doubling) time in hours
\( t \) = time in hours
\( t_\text{lag} \) = lag phase duration
\( t_\text{log} \) = exponential phase duration
\( t_\text{stat} \) = stationary phase duration

Exponential growth (log phase)

The population during the log phase is modeled as:

\( N(t) = N_0 \cdot 2^{\dfrac{t - t_\text{lag}}{g}} \quad \text{for } t_\text{lag} \le t \le t_\text{lag} + t_\text{log} \)

In natural logarithms, this is equivalent to:

\( N(t) = N_0 \cdot e^{\mu (t - t_\text{lag})} \), where \( \mu = \dfrac{\ln 2}{g} \) is the specific growth rate.

Piecewise model for all phases

The calculator approximates the full curve as:

Lag: \( N(t) = N_0 \) for \( 0 \le t < t_\text{lag} \)
Log: \( N(t) = N_0 \cdot 2^{(t - t_\text{lag})/g} \) for \( t_\text{lag} \le t < t_\text{lag} + t_\text{log} \)
Stationary: \( N(t) = N_\text{max} \) for \( t_\text{lag} + t_\text{log} \le t < t_\text{lag} + t_\text{log} + t_\text{stat} \)
Death (optional): \( N(t) = N_\text{max} \cdot e^{-k (t - t_\text{lag} - t_\text{log} - t_\text{stat})} \) afterwards, where \( k \) is the death rate constant.

Here \( N_\text{max} = N_0 \cdot 2^{t_\text{log}/g} \) is the population at the end of the log phase.

How to estimate doubling time from experimental data

When you have experimental measurements (CFU or OD) in the exponential phase, you can estimate the specific growth rate \( \mu \) and doubling time \( g \) using two points:

Choose two time points \( t_1 \) and \( t_2 \) within the linear log-phase region.
Record the corresponding values \( N_1 \) and \( N_2 \) (CFU or OD).
Compute the specific growth rate: \( \mu = \dfrac{\ln N_2 - \ln N_1}{t_2 - t_1} \).
Compute the doubling time: \( g = \dfrac{\ln 2}{\mu} \).

The “Estimate doubling time from two measurements” tool above performs exactly this calculation for you.

CFU vs. OD: which should I use?

CFU (colony-forming units) – measures viable cells; obtained by serial dilution and plating. Highly accurate but labor-intensive.
OD (optical density) – measures turbidity (total biomass); quick and non-destructive but must be calibrated to CFU for quantitative work.

In many teaching labs, OD₆₀₀ is used to monitor growth in real time, and a calibration curve (OD vs. CFU/mL) is used to convert between the two.

Practical tips for working with bacterial growth curves

Always include replicates to account for biological and technical variability.
Use a semi-log plot (log₁₀ N vs. time) to clearly identify the exponential phase.
Keep cultures well mixed and incubated at the appropriate temperature and aeration.
When using OD, stay within the linear range of the spectrophotometer (often OD < 0.8–1.0).
For accurate CFU counts, choose plates with 30–300 colonies after dilution.