Population Doubling Time Calculator
Convert a percentage growth rate into a doubling time using the exact continuous and discrete formulas, plus the quick rule-of-70 approximation.
How it works
Discrete: t = ln(2) / ln(1 + r) · Continuous: t = ln(2) / r = 0.6931 / r · Rule of 70: t ≈ 70 / r% (r as a decimal or percent as noted)
Doubling time is how long a steadily growing quantity takes to become twice its size. The exact answer depends on whether growth is compounded in discrete steps or continuous: the discrete form uses ln(1 + r), the continuous form uses r directly. For the small growth rates common in ecology and demography the two are close, which is why the rule of 70 — dividing 70 by the percentage rate — is a handy mental shortcut. The doubling time is independent of the current population size; only the rate matters.
Worked example
At 2% growth per year, the continuous doubling time is ln(2)/0.02 = 34.7 years, and the discrete (annually compounded) time is ln(2)/ln(1.02) = 35.0 years. The rule of 70 gives 70/2 = 35 years — essentially the same.
Sources: Doubling time — Wikipedia
Frequently asked questions
Why does the rule of 70 work?
It approximates ln(2) ≈ 0.70 and divides by the rate as a percentage. Since exact continuous doubling time is ln(2)/r, the rule of 70 is that formula rescaled to percentage rates, accurate to within a few percent for typical growth rates.
What's the difference between the discrete and continuous answers?
Discrete assumes growth is added in whole periods (annually compounded), using ln(1 + r). Continuous assumes growth is compounded instant by instant, using ln(2)/r. They converge as the rate gets small.
Does doubling time depend on the starting population?
No. Under constant exponential growth the time to double is the same whether you start with 100 or 100,000 individuals — it depends only on the growth rate.
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This calculator is for educational purposes. Double-check important results before acting on them.