Tempo de duplicação
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The population doubling time calculator estimates how long it takes for a population to double in size, given a constant growth rate. It uses the formula t2 = ln(2)/r, where 'ln(2)' is the natural logarithm of 2 (approximately 0.693) and 'r' is the growth rate per time unit. This is useful in ecological studies to predict species growth or in epidemiology to analyze disease spread.
To use the calculator, input the population's growth rate (r), typically expressed as a decimal (e.g., 0.05 for 5% annually). The result provides the time required for doubling, assuming exponential growth. This model assumes a constant growth rate, which may not align with real-world scenarios involving resource limitations or environmental changes.
Cautions: The formula is valid only for stable growth rates. In complex situations like migration, fluctuating birth/death rates, or competition, the result will be an approximation. Use precise data and, if possible, validate with more sophisticated models for real-world scenarios.
Frequently asked questions
How does the doubling time formula work?
The formula t2 = ln(2)/r calculates the time needed for a population to double under constant exponential growth. The ln(2) constant arises from the mathematical nature of exponential growth.
What are the results used for?
Results help predict population growth in ecological studies, plan species conservation, or analyze disease spread in epidemiology.
Can the calculator be used for other growth types?
No, the formula applies only to constant exponential growth. Scenarios with limited growth (like logistic) require model adjustments.
Why use ln(2) instead of another value?
The ln(2) is derived from the exponential growth equation (N(t) = N0 * e^(rt)), where t = ln(2)/r solves for when N(t) = 2*N0.