Population Growth Rate Calculator

Calculate the annual population growth rate, projected future population, and doubling time using standard demographic models.

Initial Population (P₀)

Final Population (Pₜ)

Number of Years (t)

Years to Project Into Future (optional)

Results will appear here.

Continuous Exponential Growth Rate:
r = ln(P_t / P₀) / t

CAGR (Compound Annual Growth Rate):
CAGR = (P_t / P₀)^1/t − 1

Future Population Projection:
P_future = P_t × e^{(r × t_future)}

Exact Doubling Time:
T_double = ln(2) / r ≈ 0.6931 / r

Rule of 70 (approximate doubling time):
T_double ≈ 70 / r%

The continuous exponential model assumes a constant, instantaneous growth rate throughout the period.
CAGR uses discrete annual compounding and is commonly used in demographic and economic reporting.
The Rule of 70 is an approximation valid for small growth rates (<10%/yr); exact doubling time uses the natural logarithm.
Future projections assume the same growth rate r continues unchanged beyond the observed period.
No migration, carrying capacity, or logistic constraints are modeled; this is a simple exponential model.
Formula reference: Preston, S., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell.
United Nations, Department of Economic and Social Affairs, Population Division — standard demographic growth rate methodology.

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