Population Growth Calculator (Exponential and Logistic)
Enter the starting population, growth rate and time to project its size.
Your numbers
Your results
Population at that time
Population at that time
—
Doubling time (exponential phase)
—
Current growth per time unit
—
Share of carrying capacity
—
Population Growth Calculator (Exponential and Logistic) by TheCalcTools
How the Population Growth Calculator (Exponential and Logistic) works
Exponential growth assumes unlimited resources: N(t) = N₀ e^(rt). Logistic growth slows as the population approaches the carrying capacity K, giving an S-shaped curve.
In the logistic model, growth is fastest at half the carrying capacity.
The formula
Exponential: N = N₀ e^(rt); Logistic: N = K ÷ (1 + ((K − N₀) ÷ N₀) e^(−rt))
Worked example
Using the default values shown in the calculator:
| Model | Logistic (carrying capacity) |
|---|---|
| Starting population | 100 |
| Intrinsic growth rate r (per time unit) | 0.3 |
| Time | 10 |
| Carrying capacity K | 1000 |
- Logistic growth from 100 with r = 0.3 and K = 1,000 reaches 691 after 10 time units.
Result:
| Population at that time | 690.6 |
|---|---|
| Doubling time (exponential phase) | 2.310 |
| Current growth per time unit | 64.11 |
| Share of carrying capacity | 69.1% |
Frequently asked questions
What is r?
The intrinsic rate of increase: births minus deaths per individual per time unit when resources are plentiful.
Sources and further reading
Related calculators
More in Biology · All calculators
This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.