Rule of 72 Calculator
At a 7% annual return, the Rule of 72 says your money doubles in about 10.3 years (72 divided by 7). This calculator estimates how long an investment takes to double from its yearly rate of return. Enter the rate to see the doubling time, the exact mathematical figure for comparison, and how long the same return takes to triple your money.
Quick answer
The Rule of 72 divides 72 by your annual return to estimate the years it takes to double.
What this tells you
- •The Rule of 72 divides 72 by your annual return to estimate the years it takes to double.
- •It is a mental shortcut, so it works best for returns roughly between 4% and 15%.
- •The Rule of 114 does the same job for tripling your money instead of doubling it.
How to Use
- 1Enter your expected annual rate of return as a percentage, such as 7 for 7%.
- 2Calculate to see the estimated years to double using the Rule of 72.
- 3Compare it to the exact doubling time, which uses the real compounding math.
- 4Check the years to triple, based on the related Rule of 114.
How It Works
Formula
Years to double = 72 / annual return
Years to triple = 114 / annual return
Exact years to double = ln(2) / ln(1 + rate)
Example: 72 / 7 = 10.3 years to double at a 7% returnThe Rule of 72 is an approximation of the exact compounding formula. Dividing 72 by the percentage return gives a close estimate of the doubling time without a calculator. It is most accurate for mid-range returns and drifts a little at very low or very high rates, which is why the exact figure is shown alongside it.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Doubling at a 7% stock-market return
72 divided by 7 is 10.29. A 7% average return, close to long-run stock-market figures, doubles your money in a little over ten years.
Doubling at a 2.5% savings rate
72 divided by 2.5 is 28.8. At a low savings-account rate, doubling takes nearly three decades, which shows why low returns struggle to outpace inflation.
Years to Double Your Money by Annual Return
The Rule of 72 estimate next to the exact doubling time for common annual returns. The shortcut stays within a few months of the exact figure across the normal range.
| Annual return | Rule of 72 (years) | Exact (years) |
|---|---|---|
| 1% | 72.0 | 69.7 |
| 2% | 36.0 | 35.0 |
| 3% | 24.0 | 23.4 |
| 4% | 18.0 | 17.7 |
| 5% | 14.4 | 14.2 |
| 6% | 12.0 | 11.9 |
| 7% | 10.3 | 10.2 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
| 15% | 4.8 | 5.0 |
Years to double = 72 / return. The exact column uses ln(2) / ln(1 + rate). The two agree most closely around 8%, where 72 is the natural fit.
Common mistakes
- Using 72 for tripling, when tripling needs the Rule of 114
- Trusting the rule at very high returns, where it overstates the doubling time by half a year or more
- Forgetting that the rate must be a real after-inflation return to measure doubling in buying power
Limitations
The Rule of 72 is an estimate, not the exact compounding formula. It assumes a single fixed annual return with no additional contributions, fees, or taxes, and it is most accurate for returns between about 4% and 15%. Real investment returns vary year to year, so treat the result as a rough planning figure rather than a guarantee.