Population Growth Rate Calculator
Find the growth rate of a population from an initial size, a final size and the time between them — both the continuous rate r and the percent change.
How it works
r = ln(N / N₀) ÷ t · effective per-period growth = eʳ − 1 · total change = (N − N₀) ÷ N₀
For a population changing exponentially, N = N₀·eʳᵗ, so the intrinsic growth rate is the natural log of the fold change divided by the elapsed time. The continuous rate r is the instantaneous per-capita rate; converting it with eʳ − 1 gives the effective growth per period that compounding produces. A positive r means growth, zero means a stable population and a negative r means decline.
Worked example
A population rises from 5,000 to 8,000 over 10 years. r = ln(8000 ÷ 5000) ÷ 10 = ln(1.6) ÷ 10 ≈ 0.047, or 4.7% per year continuous — an effective 4.81% per year, and a 60% total increase over the decade.
Sources: Population growth — Wikipedia
Frequently asked questions
What is the difference between r and percent growth?
r is the continuous (instantaneous) rate used in the exponential model N = N₀eʳᵗ. The effective percent growth per year is eʳ − 1, which is slightly larger because it accounts for compounding within the year.
What does a negative growth rate mean?
The population is shrinking. If the final size is below the initial size the log of the fold change is negative, giving a negative r — the exponential-decline case.
Does this assume unlimited resources?
Yes — it fits a simple exponential (density-independent) model. Real populations eventually hit carrying capacity, where a logistic model that levels off is more realistic.
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Educational estimate, not medical or laboratory advice — verify formulas, units and assumptions for your specific protocol.