# Calculation of the bacterial growth rate from a spectrophotomer growth curve

Typically the microbial growth in liquid cultures is monitored by turbidity. Data is obtained with a spectrophotometer to measure optical density at 600nm. The slope of the bacterial kinetic curve in exponential phase is the growth rate.

But I have seen two ways of calculate the growth rate:

1. Growth rate = Maximum slope value of the Kinetic curve

2. $Log_{10}$ transformation of the growth data and then calculate the slope.

I think the second one is right if you want to calculate the generation time:

generation time = $\frac{ln(2)}{Growth rate}$.

What is the correct way to calculate the growth rate and then generation time?

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After you have the data plotted, the exponential growth phase should appear as a line with positive slope. The logarithmic scale on the Y axis will automatically transform the exponential curve into a straight line. To determine growth rate in terms of generation per hour, you need to get the optical density at time 0, which is the beginning of the exponential phase, and time t, which is just some other time on the exponential phase. Use this equation to determine growth rate: $k =\frac{log(X_t) - log(X_0)}{0.301t}$
Once you know the growth rate, you can determine the generation time with $t_{gen} = \frac{1}{k}$, which gives time for 1 generation in hours. To convert to minutes, just multiply by 60.