Doubling Time Calculator
Enter a growth rate (annual percentage) to find how many periods until a quantity doubles — using the exact logarithm formula and the quick Rule-of-72 approximation, with a growth curve for context.
%
Compounding model
periods
Periods needed for the quantity to double at this growth rate
- 1
1 + r/100
1 + 7% ÷ 100 = 1.07 - 2
ln(2)
0.693147 - 3
ln(1 + r)
ln(1.07) = 0.067659 - 4
Doubling time t = ln(2) ÷ ln(1 + r)
0.693147 ÷ 0.067659 = 10.2448Exact periodic-compounding formula; compare Rule of 72 ≈ 72 ÷ r%.
How does this calculator work?
Doubling time is t = log(2) / log(1 + r) for periodic compounding and t = ln 2 / r for continuous growth (r as a decimal). The Rule of 72 gives a quick mental estimate: just divide 72 by the percentage rate. At 7% per year the exact answer is ≈10.24 years and Rule of 72 gives ≈10.29 years — within 1% of each other.
Formula
How this is calculated
A quantity grows at a fixed rate r per period. Under periodic (compound) growth — like annual compound interest — after t periods the multiplier is (1 + r)^t. Setting this equal to 2 and solving for t gives t = log(2) / log(1 + r). Under continuous exponential growth the multiplier is e^(rt), which equals 2 when rt = ln 2, so t = ln 2 / r (where r is expressed as a decimal fraction, e.g. 0.07 for 7%).
The Rule of 72 is a mental-arithmetic shortcut: divide 72 by the percentage rate to get an approximate doubling time in periods. At 7% per year, 72/7 ≈ 10.3 years, while the exact formula gives ln(2)/ln(1.07) ≈ 10.24 years — very close. The rule is most accurate between roughly 2% and 12%; it overestimates at high rates and underestimates at very low ones. The difference between the exact result and the Rule of 72 is shown in the stat panel so you can judge the approximation.
The growth curve plots one unit growing at the given rate over the projection period you specify, so you can see visually where each doubling occurs. The doublings count shows how many complete times the value doubles within that projection window.
Frequently asked questions
The Rule of 72 says the doubling time in years is approximately 72 divided by the annual percentage rate. It is accurate to within 1–2% for rates between 2% and 15%; it gives a slight overestimate at higher rates. For exact results, use t = log(2)/log(1 + r).
Periodic compounding applies the growth rate once per period: the multiplier is (1 + r)^t. Continuous compounding applies it infinitely often: the multiplier is e^(rt). Continuous compounding gives a slightly shorter doubling time for the same nominal rate.
Yes. For population growth enter the annual growth rate in percent and choose continuous compounding (the standard model in biology). For radioactive decay the "doubling time" becomes the half-life — enter the decay rate and the result is the half-life (the negative case is symmetric).
TG we-Calculate Editorial Team. (2026). Doubling Time Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/doubling-time-calculator
TG we-Calculate Editorial Team. "Doubling Time Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/doubling-time-calculator.
TG we-Calculate Editorial Team, "Doubling Time Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/doubling-time-calculator
@misc{wecalculate_doubling_time_calculator, title = {Doubling Time Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/doubling-time-calculator}}, year = {2026}, note = {TG we-Calculate} }
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