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`(dN)/(dt) = r_(max) * "N" *(( "K" - "N" )/ "K" )`

Enter a value for all fields

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**) Maximum per capita_{max}**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 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:

- dN/dt - Logistic Growth
- r
_{max}- maximum per capita growth rate of population - N - population size
- K - carrying capacity

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