Exponential Population Growth Calculator
When resources are unlimited, a population grows exponentially: it multiplies by the same factor in each equal time step. The continuous form, N(t) = N0 times e to the power of r times t, projects the population from its starting size, intrinsic growth rate, and elapsed time. This calculator returns the projected population and the doubling time, the interval in which the population doubles regardless of its current size. Enter your own measured growth rate; the equation is applied deterministically with no hidden constant.
Exponential growth formula
N(t) = N0 * e^(r * t)
doubling time = ln(2) / r
ln(2) is about 0.6931
growth is proportional to current size
With N0 = 500, r = 0.03 per year, at t = 10 years, N(t) is 500 times e^(0.3), about 675, and the doubling time is about 23.1 years.
Population growth facts
- Exponential growth assumes unlimited resources and a constant rate.
- The population multiplies by the same factor each equal time step.
- Doubling time depends only on the rate, not the current size.
- Real populations eventually slow as resources become limiting.
- For limited resources, use the logistic model with a carrying capacity.
Exponential growth: frequently asked questions
What is exponential population growth?
Exponential growth assumes a constant per-capita growth rate with unlimited resources. The continuous form is N(t) = N0 times e to the power of r times t, where N0 is the starting population, r is the intrinsic growth rate, and t is elapsed time. The population grows by a fixed proportion in each equal time interval.
How is doubling time calculated?
For continuous exponential growth the doubling time is the natural logarithm of 2 divided by the growth rate r, that is about 0.6931 divided by r. It tells you how long the population takes to double in size and is independent of the current size.
When is exponential growth a good model?
Exponential growth fits populations with abundant resources and no significant limits, such as bacteria early in a culture or an invasive species entering a new habitat. As resources become limiting, the logistic model, which adds a carrying capacity, becomes more realistic.
What units should I use?
Use any consistent units. The growth rate r is per unit time (for example per year or per hour), and time t uses the same unit. The initial and projected populations share the same count unit, and the doubling time is reported in that time unit.
Where does the growth rate come from?
The intrinsic growth rate r is an empirical, population-specific value estimated from observed data. Because it is measured rather than universal, you enter it yourself; the calculator only applies the deterministic exponential growth equation.
Official sources
- U.S. Census Bureau: U.S. Census Bureau population topics.
- USGS: USGS population dynamics research.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.