Project how a population changes over time, or work backwards to the growth rate or the time needed. This free population growth calculator handles exponential growth and logistic growth with a carrying capacity, and gives the doubling time and a growth curve.
Population growth formulas
Worked example
A town of 1,000 people grows at 3% per year. After 10 years, P = 1,000 × e^(0.03 × 10) = 1,350. Its doubling time is ln 2 / 0.03 ≈ 23.1 years (the rule of 70 gives 70 / 3 ≈ 23.3).
With logistic growth, 100 animals in a habitat that supports K = 1,000 and r = 20% per year reach 1,000 / (1 + 9e^(−2)) ≈ 451 after 10 years. Growth is fastest at K/2 = 500.
Exponential vs logistic growth
| Exponential | Logistic | |
|---|---|---|
| Curve shape | J-shaped | S-shaped (sigmoid) |
| Resources | Unlimited | Limited by carrying capacity K |
| Growth rate | Rises with population | Fastest at K/2, then slows |
| Good for | Early growth, bacteria, compound interest | Wildlife, yeast, market saturation |
Frequently asked questions
What is the formula for population growth?
For continuous exponential growth, P = P₀ × e^(rt), where r is the growth rate as a decimal and t is time in the same unit as the rate.
How do I calculate the growth rate?
Leave the rate box empty and enter both populations and the time. The calculator uses r = ln(P/P₀) / t and shows it as a percentage.
What is doubling time?
The time a population takes to double: ln 2 / r. A quick estimate is 70 divided by the percentage growth rate (the rule of 70).
What is carrying capacity?
The largest population an environment can support. In the logistic model, growth slows as the population approaches K and stops at K.
Can I use this for population decline?
Yes. Enter a negative growth rate in the exponential calculator to model a shrinking population and get its halving time.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.