OD growth rate calculator
Specific growth rate, doubling time and lag from a measured OD600 time course.
Specific growth rate, doubling time and lag from a measured OD600 time course.
A growing culture passes through a lag phase, an exponential (log) phase, a slow-down and a stationary phase. Only in the exponential phase does every cell divide at a constant rate, and only there is the specific growth rate µ defined. In that phase OD rises exponentially, so its natural logarithm rises in a straight line:
The slope of that line is µ, in units of 1/time. It is found by least-squares linear regression of ln(OD) against time over the exponential-phase readings. Using all of those readings instead of just two makes the estimate far less sensitive to the noise in any one measurement, and the R² of the fit shows whether the chosen readings really are exponential.
The doubling time, or generation time, is the time for OD to double while growth is exponential. A culture with µ = 1.2 h⁻¹ doubles every 0.693 / 1.2 = 0.58 h, about 35 minutes. In growth-rate units some papers use doublings per hour instead, which is µ / ln(2).
An E. coli culture is read every 30 minutes (the built-in example). From 0 to 1 h the OD barely moves (0.020, 0.024, 0.035), and after 4.5 h it flattens towards 1.8. The calculator picks the readings from 1.5 h (OD 0.049) to 4 h (OD 0.526) as the exponential phase. Regression of ln(OD) on time over those 6 points gives a slope ofµ = 0.960 h⁻¹ with R² = 0.9992, so the doubling time is 0.693 / 0.960 =0.722 h, or 43.3 minutes. A quick check with the end points alone: ln(0.526 / 0.049) / 2.5 h = 0.949 h⁻¹, close to the regression value. Extending the fitted line back to the starting OD of 0.020 gives a lag time of 0.57 h (34 minutes).
The lag time is where the fitted exponential line, extended backwards, crosses the OD of the first reading. It answers the question of how much time the culture lost before it reached full growth rate. The estimate depends on a reliable first reading, which is hard at very low OD, so subtract a proper blank and start the series at inoculation. If the culture was already growing exponentially at the first reading, the lag is reported as none.
By default the calculator finds them itself. It fits a line to every run of consecutive readings (3 to 5, depending on how many you have), takes the run with the steepest slope among those with R² of at least 0.95, merges in adjacent runs whose slope is within 5 % of it, and refits over the merged range. This follows the method of Hall et al. (2014,Mol. Biol. Evol. 31:232). The result is the maximum specific growth rate, µmax, which is what is normally reported. To choose the range yourself, enter a start and an end time under the data; the chart and the table show which readings were used.
| Organism and condition | µ (h⁻¹) | Doubling time |
|---|---|---|
| E. coli, LB, 37 °C | 1.7–2.1 | 20–25 min |
| E. coli, M9 glucose, 37 °C | 0.6–0.9 | 45–70 min |
| B. subtilis, LB, 37 °C | 1.4–2.0 | 20–30 min |
| S. cerevisiae, YPD, 30 °C | 0.40–0.46 | 90–105 min |
| P. pastoris, glycerol, 30 °C | 0.17–0.26 | 2.7–4 h |
With only two OD readings, or to predict when a culture will reach a target OD for induction or harvest, use the bacterial growth calculator. For cell counts, CFU/mL or a known growth rate constant, use thedoubling time calculator. To turn plate counts into CFU/mL, see the CFU calculator.
Take the natural log of each OD600 reading and plot it against time. During exponential growth the points fall on a straight line whose slope is the specific growth rate µ. Fit the line by linear regression over the exponential phase only, leaving out the lag phase at the start and the slow-down towards stationary phase at the end. The doubling time is ln(2) / µ.
It slides a short window along the ln(OD) curve, fits a line in each position and keeps the window with the steepest well-fitting slope. Neighbouring windows whose slope is within 5 percent of that maximum are merged in, and the line is refitted over the merged range. This is the approach of Hall and colleagues (2014). You can override it by entering your own start and end times.
For a bacterial culture measured carefully, R² of the log-linear fit is normally above 0.99. Values below about 0.98 usually mean that the fit window includes part of the lag or the deceleration phase, that the readings are outside the linear range of the instrument, or that no blank was subtracted so low readings are inflated.
The fitted exponential line is extended back to the starting OD. The time at which it crosses that level is the lag time: how long the culture would have had to wait, doing nothing, before growing at full rate from the start. It is a geometric definition, so it needs a reading at or near inoculation.
Yes. Medium and the cuvette or plate absorb and scatter some light, and that constant offset bends the log plot at low OD, which lowers the apparent growth rate. Enter the OD of sterile medium as the blank. In a plate reader this matters more, because the offset is often 0.08 to 0.1 and the early culture readings are not much higher.