Logística — dN/dt
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The logistic population growth calculator (dN/dt) estimates population change over time with limited resources. It uses the formula dN/dt = rN(1 - N/K), where 'r' is the intrinsic growth rate, 'N' is the current population size, and 'K' is the environmental carrying capacity. This model is ideal for predicting population growth until an ecological limit is reached.
The formula calculates population variation (dN/dt) by multiplying the growth rate 'r', current population 'N', and the factor (1 - N/K), representing resource availability. When N is small, growth is exponential; as N approaches K, growth slows. It is widely used in ecology, species management, and evolutionary biology studies.
Apply this calculator for scenarios like predicting population growth in protected areas, analyzing biological invasions, or conservation planning. Accurate values for 'r' and 'K' are crucial, as they depend on specific environmental and species data. The model assumes 'K' and 'r' remain constant, which may not reflect real-world natural systems.
If the population exceeds the carrying capacity (N > K), the model predicts a decline in dN/dt, reflecting environmental stress. However, factors like migration, climate change, or interactions with other species might not be included. Always validate results with empirical data for better accuracy.
Frequently asked questions
What is carrying capacity (K) in the logistic model?
Carrying capacity (K) is the maximum number of individuals an environment can sustain, considering resources like food, water, and space.
How to determine the growth rate 'r'?
The rate 'r' is calculated from population birth, death, and migration data, usually obtained through field studies or scientific databases.
Does the logistic model work for all species?
No. It's more applicable to species with growth regulated by limited resources, such as plants, insects, or populations in closed environments.
What happens if the population exceeds K in the calculation?
When N > K, the dN/dt rate becomes negative, indicating population decline due to resource scarcity.
Can I use this calculator to predict future populations?
Yes, but you need to input 'r' and 'K' values based on historical data and current environmental conditions.