Calculates how long a population (or any exponentially growing quantity) takes to double at a given percentage growth rate per period.
How it works
The natural log of 2 is divided by the growth rate to give the exact doubling time; the commonly taught “Rule of 70” (70 divided by the growth rate) is shown alongside as a well-known quick estimate.
What this does not include
This does not include projecting the population forward from a known doubling time — for that direction, use this site’s bacterial growth calculator instead.
How to use this calculator
- Enter the growth rate per period as a percentage.
A worked example
A population growing at 2% per year: doubling time ≈ 34.6574 years (Rule of 70 approximation: 35 years).
A population growing at 7% per year: doubling time ≈ 9.9021 years (Rule of 70: 10 years) — much faster growth dramatically shortens the doubling time.
What the variables mean
| Variable | Meaning |
|---|---|
| Growth rate | Annual population growth rate, as a percentage |
Edge cases worth knowing
The Rule of 70 is a quick mental approximation, not the exact answer. Dividing 70 by the growth rate gets remarkably close to the precise logarithmic calculation, which is why it’s a popular shortcut despite being an estimate.
Zero growth rate makes doubling time infinite — a population that never grows never doubles, so the calculator declines to show a result.
Frequently asked questions
Why does the “Rule of 70” use 70 instead of the exact ln(2) figure?
Because 70 is close to 100 × ln(2) (about 69.3) and divides evenly by more common growth rates, making it an easy mental-math approximation that’s still reasonably accurate.
Does this only apply to human population growth?
No — the same math applies to any quantity growing exponentially at a fixed percentage rate, including investments, viral spread, or wildlife populations.
Why does a small change in growth rate have such a large effect on doubling time?
Because the relationship is inversely proportional — halving the growth rate roughly doubles the time needed to double the population.
