How to calculate growth rate: 













During balanced growth, the growth mimics a first order chemical reaction. 






dN/dt =kN 






N is the concentration of cells, t the time and k is the growth rate constant. 






The dimension of the specific growth rate k are reciprocal time, usually expressed as reciprocal hours, or hr^1. 






Integration of previous equation between the limits of 0 and t and N1 and N2 gives following equation. 






ln(N2/N1)=k(t2t1) 













converting the previous equation to logarithmns to the base of 10, we get 






log10N2log10N1 = k(t2t1)/2.303 




















If one determines the number of bacterial CFUs present at various times and plots the log of that number, one gets a straight line (in log phase) 






From the slope of the line, we can calculate the specific growth rate k of the culture, which is the most encompassing parameter of how fast a 






particular bacterium growths in a particular media. For example, if a culture contains 10^3 cells at time t1 and 10^8 cells at t2 6 hours later, 






the specific growth rate k is 













k= (83) 2.303/6, which equals k=1.92 hr^1 






The dimension of the specific growth rate k are reciprocal time, usually expressed as reciprocal hours, or hr^1. 




















How to calculate Generation or Doubling time: 













The rate of growth of a bacterial culture is oftern described by the time required for the number of cells to increase by a factor of 2, or the 






DOUBLING TIME or GENERATION TIME, g. 













The relationship between g and k can be established by using following equation. 




















ln(N2/N1)=k(t2t1) 






ln is the natural logs (log^e) 






N2 is cell number at t2 and N1 is the cell number at t1 






k is the growth rate 













Since when N2 = 2N1, t2t1 becomes equal to g 






Substituting values for t and N into the previous equation, we obtain following: 






g=ln2/k = 0.693k 













(reference: Physiology of the bacterial cell, a molecular approach by Frederick C. Neidhardt, John Ingraham and Moselio Schaechter) 





