Rule of 72 Calculator — Investment Doubling Time
Find out how many years it takes for an investment to double using the famous Rule of 72 — just divide 72 by your annual interest rate. Compare with the exact result from logarithms.
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Estimated doubling time: 72 ÷ rate
- 1
Annual rate
7%72 is a convenient approximation of 100 × ln(2) ≈ 69.3, most accurate for rates between 4% and 12%. - 2
Doubling years (Rule of 72)
72 ÷ 7 = 10.3
How does this calculator work?
Divide 72 by your annual rate to get approximate years to double your money (Rule of 72). At 6%: 72 ÷ 6 = 12 years. The exact answer is ln(2) ÷ ln(1 + r/100). The rule is accurate within 1–2% of the exact figure for rates between 2% and 15%, and the same logic applies to inflation, debt growth, or any compounding quantity.
Formula
How this is calculated
The Rule of 72 is a mental-math shortcut for compound interest: dividing 72 by the annual rate (as a percentage) gives a close estimate of the number of years needed for an investment to double in value. For example, at 6% per year: 72 ÷ 6 = 12 years. The rule works because 72 is close to 100 × ln(2) ≈ 69.3, and the small over-estimate compensates for the first-order Taylor approximation error at moderate rates — making 72 more accurate than 70 for rates between roughly 4% and 12%.
The exact doubling time is derived from the compound-interest equation: P × (1 + r)^t = 2P, which solves to t = ln(2) / ln(1 + r/100). At low rates the two answers are nearly identical; at very high rates (above ~25%) the Rule of 72 starts to over-estimate and the exact formula should be preferred.
Compounding magnifies wealth non-linearly: every successive doubling requires the same number of years but moves a much larger absolute amount. This is why long time horizons and consistent reinvestment make such a large difference to end wealth — a point the growth curve in this calculator makes visually clear. The rule applies equally to inflation eroding purchasing power, population growth, and the spread of any quantity that compounds at a fixed rate.
Frequently asked questions
100 × ln(2) ≈ 69.3 is the mathematically exact constant. Rule of 70 (used in economics) and Rule of 72 are both approximations, but 72 is more convenient because it has many factors (2, 3, 4, 6, 8, 9, 12) and its small over-estimate of 69.3 cancels with approximation error, making it more accurate at rates between 4% and 12%.
The classic rule assumes annual compounding. For monthly compounding, divide the monthly rate into 72 to get doubling months, or use the nominal annual rate for a close approximation. The exact formula works for any compounding period when you substitute the per-period rate.
Yes — at 3% inflation, 72 ÷ 3 = 24 years for prices to double. For a loan, 72 ÷ APR tells you how quickly the outstanding balance doubles if no payments are made. The rule applies to any quantity growing (or eroding) at a fixed percentage rate.
Also known as
TG we-Calculate Editorial Team. (2026). Rule of 72 Calculator — Investment Doubling Time [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rule-of-72-calculator
TG we-Calculate Editorial Team. "Rule of 72 Calculator — Investment Doubling Time." TG we-Calculate. 2026. https://we-calculate.com/calculator/rule-of-72-calculator.
TG we-Calculate Editorial Team, "Rule of 72 Calculator — Investment Doubling Time," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rule-of-72-calculator
@misc{wecalculate_rule_of_72_calculator, title = {Rule of 72 Calculator — Investment Doubling Time}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rule-of-72-calculator}}, year = {2026}, note = {TG we-Calculate} }
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