Population Growth Calculator
Exponential growth describes a population that increases by a constant proportion of itself over time, the model that fits early, resource-rich growth of bacteria, cells, or organisms. This calculator projects the future size from a starting population, a per-period growth rate, and elapsed time using the continuous formula N(t) equals N0 times e to the power r times t. It also reports the net increase and the doubling time. Enter your rate as a percentage; a negative rate models decline.
Exponential growth formula
r = rate% / 100
N(t) = N0 * e^(r * t)
net increase = N(t) - N0
doubling time = ln(2) / r (r > 0)
Example: 1000 at 2% for 10 periods ~ 1,221.40
The model uses continuous compounding. A negative rate produces decline and no finite doubling time.
Population growth context
- Exponential growth assumes unlimited resources and a constant rate.
- Real populations slow as they approach a carrying capacity (logistic model).
- The growth rate r is the per-period intrinsic rate of increase.
- Doubling time only applies when the rate is positive.
- Use consistent units: if r is per year, t must be in years.
Population growth: frequently asked questions
What is the exponential growth formula?
The continuous exponential growth model is N(t) = N0 times e raised to (r times t), where N0 is the starting population, r is the intrinsic growth rate per unit time as a decimal, and t is elapsed time. The population grows by a constant proportion each instant.
What is the difference between exponential and logistic growth?
Exponential growth assumes unlimited resources, so the population keeps accelerating. Logistic growth adds a carrying capacity that slows growth as the population approaches an environmental limit. Use exponential for early, unconstrained growth; use a logistic model when resources cap the population.
How do I enter the growth rate?
Enter the per-period growth rate as a percentage. For example a 2 percent annual rate is entered as 2, which the calculator converts to the decimal 0.02 before applying the exponential formula. A negative rate models decline.
What is the doubling time?
Doubling time is how long the population takes to double at a constant continuous rate, equal to the natural log of 2 divided by r. The calculator reports it when the growth rate is positive.
Is this model realistic for long periods?
Exponential growth is accurate only while resources are abundant. Over long periods, real populations face limits, so they follow logistic or more complex dynamics. Treat long-range exponential projections as upper bounds, not forecasts.
Official sources
- U.S. Census Bureau: Census Bureau home.
- NCBI Bookshelf: National Center for Biotechnology Information.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.