Population Growth Calculator
Enter the initial population, growth parameters, and time period to project future population. Supports exponential, linear, doubling-time, and logistic growth models.
Results
Final Population
—
Year-by-Year Projection
| Year | Population | Change | % Change |
|---|
Population Growth Formulas
Exponential
x(t) = x₀ × (1 + r)t
Future population = initial × (1 + growth rate) raised to t periods. Used for simple population projections.
Linear
Pt = P₀ + k × t
Population increases by a constant number k each period. Produces a straight-line increase.
Doubling Time
Pt = P₀ × 2t/D
Population doubles every D periods. D is the time required for the population to double in size.
Logistic (S-Curve)
P(t) = K·P₀·ert / (K + P₀·(ert − 1))
Growth slows as population approaches carrying capacity K. Produces an S-shaped curve.
Model How Populations Grow Over Time
Enter a starting population and growth rate, and this free calculator projects the future population using your choice of model — exponential, linear, logistic, or doubling-time.
Each model suits a different scenario: exponential for unchecked growth, logistic when resources cap the population. Results show the trajectory year by year.
Four growth models
Exponential, linear, logistic, and doubling-time models — pick the one that matches your scenario.
Year-by-year projection
See the projected population at each step, not just the final number, so the trend is easy to grasp.
Free and educational
A classroom-friendly tool for exploring demographics, biology, and the math of growth — no signup needed.
How to use
- Enter the starting population and growth rate.
- Choose a growth model.
- Click Calculate to see the year-by-year projection.
Frequently Asked Questions
What is exponential population growth?
Growth where the population increases by a fixed percentage each period, compounding over time — the J-curve seen when resources are unlimited.
When should I use the logistic model?
When growth is limited by a carrying capacity (food, space, resources) — the curve rises fast, then levels off.
What is doubling time?
The time it takes a population to double at a given growth rate — roughly 70 divided by the percentage growth rate.
Are projections exact?
No. Projections are mathematical estimates that assume the rate stays constant; real populations are affected by many changing factors.
Is the calculator free?
Yes, free with no signup.
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