Rule of 72 Calculator
Estimate how many years money takes to double at a given rate (or the rate needed to double in a set time) and see how close the shortcut is to the exact answer.
Money doubles in about
9.0 years
- Exact (yearly compounding)
- 9.01 years
- Error of the rule
- -0.1%
- Quadruples in
- 18.0 years
Rule of 72 vs exact
| Rate | 72 ÷ rate | Exact years | Error |
|---|---|---|---|
| 1% | 72.0 | 69.66 | 3.4% |
| 2% | 36.0 | 35.00 | 2.8% |
| 3% | 24.0 | 23.45 | 2.3% |
| 4% | 18.0 | 17.67 | 1.9% |
| 5% | 14.4 | 14.21 | 1.4% |
| 6% | 12.0 | 11.90 | 0.9% |
| 7% | 10.3 | 10.24 | 0.4% |
| 8% | 9.0 | 9.01 | -0.1% |
| 9% | 8.0 | 8.04 | -0.5% |
| 10% | 7.2 | 7.27 | -1.0% |
| 12% | 6.0 | 6.12 | -1.9% |
| 15% | 4.8 | 4.96 | -3.2% |
| 18% | 4.0 | 4.19 | -4.5% |
| 20% | 3.6 | 3.80 | -5.3% |
| 24% | 3.0 | 3.22 | -6.9% |
Where the 72 comes from
The exact doubling time is ln 2 ÷ ln(1 + r). Multiply it by the rate and you get the “magic number” that would make the shortcut perfect at that rate. Slide the rate and watch it drift.
At 8%, money doubles in exactly 9.01 years.
The perfect constant here is 72.1. Right next to 72: this is the rule’s sweet spot.
As rates approach zero, the constant falls toward 69.3 (100 × ln 2), the value for continuous compounding.
How to use the Rule of 72
Years to double ≈ 72 ÷ rate · Rate needed ≈ 72 ÷ years
Use the whole-number percentage, not the decimal: at 6%, 72 ÷ 6 = 12 years. It works for anything that compounds, including investment growth, inflation, population and unpaid debt. For precise numbers or regular contributions, use the compound interest calculator.
Frequently asked questions
What is the Rule of 72?
A shortcut for compound growth: divide 72 by the annual percentage rate to estimate how many years it takes money to double. At 8%, 72 ÷ 8 = 9 years. The exact answer is 9.01 years.
How accurate is the Rule of 72?
Very accurate between about 6% and 10%, within a few percent of the exact answer. At low rates it slightly overestimates the time and at very high rates it underestimates. The table on this page compares the two.
Why 72 and not 69 or 70?
The exact doubling time with continuous compounding is ln(2) ÷ r ≈ 69.3 ÷ r. With yearly compounding the right constant rises with the rate, to about 72 near 8%. 72 is also easy to divide by 2, 3, 4, 6, 8, 9 and 12, which makes mental math quick.
Can I use the Rule of 72 for inflation or debt?
Yes. At 3% inflation, prices double in about 24 years. A credit card at 24% APR doubles an unpaid balance in about 3 years.