Rule of 72 Calculator
The Rule of 72 is a mental-math shortcut for compound growth: divide 72 by an annual return to estimate the years it takes money to double. Enter a rate to see the doubling time, or enter a number of years to see the return required.
It is an approximation, not the exact compounding formula, but it is remarkably close for the single-digit and low-double-digit returns most investors deal with — which is why it has been taught for centuries.
Enter the annual return you expect to see how long it takes your money to double.
Years to double (Rule of 72)
9 yr
- Rule of 72 estimate
- 9 years
- Exact figure
- 9 years
- Difference
- 0 years
Calculation Formulas
Dividing 72 by the annual rate of return (as a whole-number percent) estimates how many years it takes an amount to double under compound growth.
Example:
At an 8% annual return: 72 ÷ 8 = 9 years to double.
Rearranged, dividing 72 by a number of years gives the annual return required for money to double in that time.
The precise compound-growth doubling time, where r is the annual rate as a decimal. The Rule of 72 approximates this and is shown alongside for comparison.
Key Figures
| Figure | Value | Description |
|---|---|---|
| Why 72 | 100 × ln(2) ≈ 69.3 | The mathematically exact numerator is about 69.3; 72 is used because it is close and divides evenly by 2, 3, 4, 6, 8, 9, and 12. |
| Most accurate near | ~8% | The approximation is closest to the exact figure around an 8% rate and drifts slightly at very low or very high rates. |
Note: Results are estimates for planning purposes. Rates, fees, taxes, and insurance vary by lender and location — confirm exact figures with a licensed professional before making financial decisions.
Standards & Sources
Last verified: July 2026
- Established mental-math heuristic
The Rule of 72 is a long-standing shortcut for compound growth, referenced as far back as Luca Pacioli’s 1494 work; it remains a standard teaching tool for understanding doubling time.
- Approximation, not exact
The rule estimates continuous doubling behavior; for precise figures — especially at extreme rates — the exact logarithmic formula shown in the methodology should be used.
How to Use This Calculator
- Choose whether you know the annual return (and want the doubling time) or the timeframe (and want the required return).
- Enter your annual rate of return, or the number of years you want your money to double in.
- Read the Rule-of-72 estimate.
- Compare it to the exact figure shown alongside to see how close the shortcut lands for your rate.
Frequently Asked Questions
What is the Rule of 72?
The Rule of 72 is a shortcut for estimating how long an investment takes to double: divide 72 by the annual rate of return. At 8% a year, for example, money doubles in roughly 72 ÷ 8 = 9 years. Rearranged, 72 ÷ years gives the return needed to double in a set time.
How accurate is the Rule of 72?
It is an approximation, but a close one for the returns most investors see. It is most accurate around 8%; at very low or very high rates the error grows. This calculator shows the exact doubling time alongside the estimate so you can see the difference for your rate.
What is the exact formula for doubling time?
The precise doubling time is ln(2) ÷ ln(1 + r), where r is the annual return as a decimal. The Rule of 72 approximates this because 72 is close to 100 × ln(2) ÷ ln(1.08), and 72 divides cleanly by many common rates.
Can I use the Rule of 72 for inflation?
Yes. Applied to an inflation rate, it estimates how long until prices double and your money loses half its purchasing power. At 3% inflation, that is about 72 ÷ 3 = 24 years — a useful way to picture the long-run cost of inflation.
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