Logistic Growth

The Logistic Growth calculator computes the logistic growth based on the per capita growth rate of population, population size and carrying capacity.

INSTRUCTIONS: Choose units and enter the following:

• (r_max) Maximum per capita Growth Rate of population
• (N) Population Size
• (K) Carrying Capacity

Logistic Growth (dN/dt): The calculator returns the logistic growth rate in growth per day.   However, this can be automatically converted to compatible units via the pull-down menu (e.g. growth per month).

The Math / Science

The growth rate of a population without constraints is exponential, where every new organism can reproduce at the rate it was produced.  In reality, resources often limit the growth of a population as population sizes reach the limits that can be sustained by the resources available at hand.  For this reason, a purely exponential model is inaccurate and a model that flattens as it reaches the capacity of the environment is more useful.  The logistic growth model is one.  It produces an s-shaped curve that maxes out at a boundary defined by a maximum carrying capacity. 

The logistic growth formula is:

     `(dN)/(dt) = r_max * N * ((K-N)/K)`

where:

1. dN/dt - Logistic Growth
2. r_max - maximum per capita growth rate of population
3. N - population size
4. K -  carrying capacity

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