Calculadora de Capacidade de Suporte
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
N(t) = K / (1 + ((K−N₀)/N₀)×e^(−r×t)); dN/dt = r×N×(1−N/K)
About this calculator
This calculator models logistic population growth, allowing you to estimate population size over time and the instantaneous growth rate. The carrying capacity (K) represents the maximum number of individuals the environment can sustain stably, considering limited resources like food, space, and water.
The formula used is N(t) = K / (1 + ((K - N₀) / N₀) × e^(-r × t)), where N₀ is the initial population, r is the intrinsic growth rate, and t is time. The instantaneous growth rate is given by dN/dt = r × N × (1 - N/K), which decreases as the population approaches K.
Use this tool to predict population growth in ecological studies, species conservation, natural resource management, or agricultural planning. For example, when introducing a species to a new habitat, you can simulate how long it will take to reach carrying capacity.
Cautions: carrying capacity can change with environmental shifts, and the growth rate r is an approximation. The model assumes constant conditions and no migration, which may not be realistic. Always validate with field data.
Frequently asked questions
What does carrying capacity (K) mean?
It is the maximum population size that the environment can sustain indefinitely, given available resources.
Can I use this calculator to predict human populations?
Yes, but with caution, as factors like technology and migration alter carrying capacity.
What is the difference between exponential and logistic growth?
Exponential growth is unlimited, while logistic growth stabilizes at K due to limited resources.
How do I obtain the growth rate r?
r can be estimated from birth and death data, or by fitting the model to population data.
Does the model work for populations with migration?
The basic model ignores migration. For populations with significant migration, more complex models are needed.