Population Growth Calculator
Model growth. Explore ecological limits.
Exponential · Logistic · Birth & death rates
Population & Model
Result
Projected population at year 20
≈858 individualsModel estimate: 858.49 · Logistic growth
Carrying capacity (K = 1000)
Population Trajectory
Simulation Table
| Time | Model N(t) | Change from N₀ | Capacity used |
|---|
Habitat & Resource Limits
Illustrative habitat; animals do not represent the projected headcount.
Resources
Space
CompetitionConceptual resource indicators; not measured habitat scores.
Understanding the models
Exponential growth
N(t) = N₀ eʳᵗ
Logistic growth
N(t) = K / [1 + (K/N₀ − 1)e⁻ʳᵗ]
Birth & death rates
r = b − d
For N₀ = 0 the closed population remains zero. The logistic formula above assumes N₀ > 0. An exponential doubling reference ln(2)/r applies when r > 0; it is not a density-dependent logistic doubling time.
Limitations and time units
These are simple deterministic models, not fitted forecasts. They omit migration, environmental variability, age structure, resource changes and random events. K must be estimated from relevant evidence. Rate and time must use the same unit. Unit conversion uses 365.25 days/year and 365.25/12 days/month, not calendar dates.
Birth and death inputs specify continuous per-capita rates. For logistic growth, b−d supplies the intrinsic/low-density rate; actual per-capita net growth is r(1−N/K). Negative r with N₀ > K can create a mathematical singularity, so invalid horizons are rejected.
Frequently asked questions
Can population estimates be fractional?
Yes. A continuous model describes a theoretical population size, so fractional predictions are valid. The headline rounds for readability; graphs, tables and calculations retain the continuous values. It is not a literal fractional animal.
Is r the same as a discrete percentage?
No. Continuous r = 0.20 gives a one-unit multiplier e⁰·² ≈ 1.2214, or about 22.14% growth for the exponential model. A discrete multiplier 1.20 corresponds to continuous r = ln(1.20) ≈ 0.1823.
Can a population start above K?
Yes. With positive r, the logistic model predicts decline toward K when N₀ > K. This is a model behavior, not evidence that a measured habitat has that capacity.
Does every population follow an S-curve?
No. An S-shaped increase requires suitable initial conditions and positive r. Populations may decline, remain stable or fluctuate. The simple continuous logistic equation does not generate cycles or overshoot from an initial value below K.
Sources & References
Nature Education / ScitablePopulation growth and ecological limits.
OpenStax Biology 2eExponential and logistic population models.Educational model; sources do not imply institutional review or endorsement.
Model growth. Explore ecological limits.