Bacteria Specific Growth Rate Calculator

This online Empirical Monod Equation calculator is used to measure the dependence of the growth rate on the substrate concentration of bacteria or aerobic metabolism.


Bacteria Specific Growth Rate(Monod Equation) works

Monod equation, which was developed by Jacques Monod in the 1940s.

The empirical Monod equation is the most common rate expression to describe the growth of microorganisms in general and hydrogen-producing bacteria in particular.

Formula :

Bacteria Specific Growth Rate (μ) = μmax ( SKs - S )


μ - Specific growth rate in time -1

μmax - Maximum specific growth rate (time-1)

S - concentration of subrate in solution (mass/unit volumn).It is also known as affinity constant.

Ks - Half velocity constant (mass/unit volumn)

This Monod formula to describe the relationship between the specific growth rate and the substrate concentration.

There are 2 constants in this equation, μmax, the maximum specific growth rate, and Ks , the half-saturation constant, which is defined as the substrate concentration at which growth occurs at one half the value of μmax.

Both μmax and Ks reflect intrinsic physiological properties of a particular type of microorganism.

Monod assumed that no nutrients other than the substrate are limiting and that no toxic by-products of metabolism build up.

The Monod Growth Constants

Both μmax and Ks are constants that reflect:

i) The intrinsic properties of the degrading microorganism.

ii) The limiting substrate

iii) The temperature of growth

The following table provides representative values of μmax and Ks for growth of different microorganisms on a variety of sub-strates at different temperatures and for oligotrophs and copiotrophs in soil.

OrganismGrowth temperature (°C) Limiting nutrientμmax (1/h)Ks (mg/l)
Escherichia coli37Glucose0.8-1.42-4
Escherichia coli37Lactose0.820
Saccharomyces cerevisiae30Glucose0.5-0.625
Pseudomonas sp.25Succinate0.3880
Pseudomonas sp.34Succinate0.4713
Oligotrophs in soil  0.010.01
Copiotrophs in soil  0.0453
Source: Adapted from Blanch and Clark (1996), Miller and Bartha (1989), Zelenev et al. (2005)