Rule of 72 Calculator
The Rule of 72 is a quick mental-math approximation for how long it takes an investment to double at a given annual growth rate: years ≈ 72 ÷ rate.
The shortcut and the real answer, side by side
The tool prints both figures so you can see how close the mental shortcut gets:
Rule of 72 years = 72 / rate
exact years = ln(2) / ln(1 + rate/100)At the default 8%, 72 / 8 = 9.0 years and the exact answer is 9.0 as well. The shortcut works because ln(2) is 0.693, so the honest numerator would be 69.3; 72 is used instead because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, and the extra 2.7 quietly cancels the error at the rates people actually deal with.
Where the approximation drifts
Accuracy is best from roughly 6% to 10% and degrades either side of it:
| Rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 yrs | 35.0 yrs |
| 6% | 12.0 yrs | 11.9 yrs |
| 8% | 9.0 yrs | 9.0 yrs |
| 12% | 6.0 yrs | 6.1 yrs |
| 20% | 3.6 yrs | 3.8 yrs |
Below the sweet spot the shortcut is pessimistic, above it optimistic. The gap only passes a whole year at rates under about 2%; at high rates doubling is so quick that being 5% out is a matter of weeks.
Frequently asked questions
How long does it take to double your money at 7%?
72 / 7 = 10.3 years by the shortcut, and 10.2 by exact compounding - close enough that the two answers are about a fortnight apart.
Why 72 rather than 69?
69.3 is mathematically correct for continuous compounding, but it divides cleanly by almost nothing. 72 has far more whole-number factors and happens to fit annual compounding better in the 6% to 10% band.
Does the Rule of 72 work for inflation and debt?
Yes, in both directions. At 3% inflation prices double in about 24 years, so money loses half its buying power. A card charging 24% doubles the balance in roughly 3 years if you never pay it down.