Model population growth that slows as it approaches carrying capacity.
Answer
4,013
Population at time t
Share of capacity: 80.26%
Net growth: 3,513
Remaining capacity: 987
Inflection population: 2,500
Examples
Time to K/2
18.31
| Time | Population | Share of capacity | Growth since previous |
|---|---|---|---|
| 0 | 500 | 10% | 0 |
| 5 | 842 | 16.84% | 342 |
| 10 | 1,347 | 26.95% | 506 |
| 15 | 2,010 | 40.2% | 662 |
| 20 | 2,753 | 55.05% | 743 |
| 25 | 3,453 | 69.06% | 700 |
| 30 | 4,013 | 80.26% | 560 |
N(t) = K / (1 + ((K - N0) / N0) x e^(-rt))The logistic model grows quickly when resources are available, then slows as population approaches carrying capacity.
| Symbol | Variable | Description |
|---|---|---|
| N0 | Initial population | Population at time 0. |
| K | Carrying capacity | Maximum sustainable population in the model. |
| r | Growth rate | Intrinsic growth rate per time unit. |
Enter model parameters
Use the same time unit for r, time, and table step.
Read the answer
The top result shows modeled population at the selected time.
Check the table
Use the table to see how growth slows as capacity is approached.
These values are usually enough to report a logistic growth projection.
| Output | Meaning |
|---|---|
| Share of capacity | How close N(t) is to K |
| Inflection population | K/2, where logistic growth rate is highest |
| Remaining capacity | K minus the modeled population |
Carrying Capacity Calculator
Estimate carrying capacity K from current population, growth rate, observed population change, and logistic growth assumptions.
Population Growth Calculator
Model exponential population growth over time in ecology.
Shannon Diversity Index Calculator
Calculate Shannon H', evenness, richness, effective species, and per-species contribution from abundance counts.