What this calculator does
Logistic population growth works out population size over time under a fixed carrying capacity (Verhulst model). Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormuladN/dt = rN(1−N/K); N(t) = K / (1 + ((K−N₀)/N₀)e^(−rt))
The inputs explained
| Field | What to enter |
|---|---|
| Initial population N₀ (individuals) | A number, measured in individuals. Starts at 50. |
| Carrying capacity K (individuals) | A number, measured in individuals. Starts at 1000. |
| Intrinsic growth rate r (/year) | A number, measured in /year. Starts at 0.3. |
| Time elapsed (years) | A number, measured in years. Starts at 10. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with initial population n₀
Every other input is held at the calculator’s starting values while initial population n₀ varies. Select any row to load that scenario into the calculator.
How the answer changes with initial population n₀