Rule of 72 Calculator
Use the Rule of 72 to quickly estimate how many years it takes for a sum to double at a fixed annual return, with an exact calculation for comparison.
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At a glance:The Rule of 72 is a mental shortcut for estimating how long a sum takes to double under a fixed compound growth rate: doubling years ≈ 72 ÷ annual return%. It also works in reverse: to double within a target number of years, the required annual return ≈ 72 ÷ target years. The exact formula is doubling years = ln(2) ÷ ln(1 + annual return). The rule is most accurate around 6%–10%; the more extreme the rate, the larger the error, so use the exact calculation for important decisions.
Formula
Doubling years (estimate) = 72 ÷ annual return%.
Doubling years (exact) = ln(2) ÷ ln(1 + annual return).
$$t_{\\text{exact}} = \\dfrac{\\ln 2}{\\ln(1 + r/100)}$$How to Use
- Enter your expected fixed annual return or growth rate.
- View the Rule-of-72 estimate and the exact doubling years side by side.
FAQ
Why is it '72' and not another number?
72 is a convenient mental constant because it has many divisors (2, 3, 4, 6, 8, 9, 12), making common rates easy to divide. The theoretically closest constant is about 69.3 (ln 2 × 100), but 72 is very accurate in the usual 6%–10% range and far easier to compute mentally, so it is widely adopted.
How accurate is the Rule of 72?
It is quite accurate roughly between 6% and 10%, with an error of a few percent at most. The more extreme the rate (very low or very high), the larger the gap from the exact value. This calculator shows the exact calculation alongside for comparison.
Can I use it in reverse?
Yes. To double a sum within a target number of years, divide 72 by the target years to get the required annual return. For example, to double in 8 years you need about 72 ÷ 8 = 9% annual return.
Is the Rule of 72 only for investing?
No. It applies to any fixed-percentage compound growth or decay — for instance the years for prices to double under inflation, population or user growth, or debt doubling under compounding. At 3% inflation, prices double in about 72 ÷ 3 = 24 years. It also estimates 'halving' time for decline such as falling purchasing power.
Are there more accurate versions, like the Rule of 70 or 69?
Yes. The theoretically most accurate constant is 69.3 (ln 2 × 100), closest for continuous compounding; the Rule of 70 is often used for lower rates (inflation, population); the Rule of 72 is most practical for annual compounding around 6%–10%, balancing accuracy and ease. They differ only in the chosen approximation; for exact results use ln(2) ÷ ln(1 + rate).
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.