Rule of 72 Calculator
Estimate how many years an investment takes to double at a given rate — and check it against the exact figure.
Exact doubling time ≈ 9.01 years — the Rule of 72 is off by 0.01 years.
The Rule of 72 estimates doubling time by dividing 72 by the annual percent rate. At 8%, 72 ÷ 8 = 9 years to double your money. The exact figure is ln(2) ÷ ln(1.08) ≈ 9.01 years, so the shortcut is within a couple of weeks — close enough for quick mental math.
What the Rule of 72 is
The Rule of 72 is a mental-math shortcut for compound growth. Divide 72 by the annual growth rate (as a percent) and you get roughly the number of years it takes for a quantity to double. It works for anything that compounds at a steady rate — investment returns, savings, or even how quickly inflation halves your buying power. The same idea runs in reverse: divide 72 by a target number of years to find the rate you would need to double in that time.
Rate is the annual growth as a percent; the exact formula uses natural logs and is what the estimate approximates.
Worked example
Suppose an index fund returns about 8% a year. How long until it doubles?
- 1 Pick the direction. To find years, start from the rate; to find the rate, start from the years.
- 2 Take the annual rate as a whole percent. Use 8 for 8%, not 0.08 — the Rule of 72 works with the percent number directly.
- 3 Divide 72 by the rate. 72 ÷ 8 = 9, so the money doubles in about 9 years.
- 4 Compare with the exact value. ln(2) ÷ ln(1.08) = 0.6931 ÷ 0.07696 ≈ 9.01 years — the estimate is off by only about 0.01 years.
- 5 Read the result. The Rule of 72 gives 9 years; the true doubling time is 9.01 years, a difference of well under 1%.
Rule of 72 vs. exact doubling time
The shortcut is closest for rates around 6%–10% and drifts a little at the extremes.
| Annual rate | Rule of 72 (years) | Exact (years) |
|---|---|---|
| 2% | 36 | 35.0 |
| 6% | 12 | 11.9 |
| 8% | 9 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6 | 6.1 |
Why 72, and where it drifts
Why 72 and not 69. The mathematically exact constant is ln(2) × 100 ≈ 69.3, so the purest version is the “Rule of 69.3.” But 72 wins for mental math because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12 — the rates people actually use. It also happens to track the true doubling time more closely once you account for how compounding is quoted annually, which is why 72 is the number everyone remembers.
Where the approximation drifts. The rule is most accurate for rates between roughly 6% and 10%. At very low rates it slightly overstates the time (2% suggests 36 years versus a true 35.0), and at high rates it understates it. For a tighter estimate at low rates some people use 70 (the “Rule of 70”), and 69.3 is the exact constant. For everyday planning the gap is small enough to ignore — the point is a quick sense of scale, not a precise forecast.