Rule of 72 Calculator
Quickly estimate how many years it takes money to double at a given growth rate — and see how that compares to the exact math.
How the Rule of 72 works
Exact doubling time = ln(2) ÷ ln(1 + Rate)
The Rule of 72 is a mental shortcut, not an exact formula — it approximates the real logarithmic doubling-time equation closely enough to be useful without a calculator. Because 72 divides evenly by many common numbers, it's easy to compute in your head: at 6%, money doubles in about 12 years; at 9%, about 8 years; at 12%, about 6 years.
Rule of 72 estimate: 72 ÷ 8 = 9.0 years.
Exact doubling time: ln(2) ÷ ln(1.08) = 9.01 years — the Rule of 72 is accurate to within a hundredth of a year at this rate.
An unpaid credit card balance accruing at 24% APR: Rule of 72 estimate = 72 ÷ 24 = 3.0 years to double if left completely unpaid.
Exact doubling time: ln(2) ÷ ln(1.24) = 0.6931 ÷ 0.2151 = 3.22 years. The gap here (0.22 years, about 2.6 months) is noticeably wider than the 8% example above — confirming the rule drifts more at high rates, though it's still a useful quick warning about how fast unpaid high-interest debt compounds.
Rule of 72 vs. exact doubling time, by rate
| Rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 2% | 36.0 yrs | 35.0 yrs |
| 4% | 18.0 yrs | 17.7 yrs |
| 6% | 12.0 yrs | 11.9 yrs |
| 8% | 9.0 yrs | 9.0 yrs |
| 10% | 7.2 yrs | 7.3 yrs |
| 12% | 6.0 yrs | 6.1 yrs |
| 15% | 4.8 yrs | 5.0 yrs |
| 20% | 3.6 yrs | 3.8 yrs |
Where the Rule of 72 starts to drift
The approximation is tightest in the 6%-10% range, which happens to cover most typical long-term stock market and investment return assumptions — which is exactly why it's such a popular rule of thumb for retirement and investment planning. At very low rates (2%-3%) or very high rates (20%+), the estimate drifts further from the exact answer, though it's still a reasonable ballpark even then.
Common mistakes when using the Rule of 72
- Using the rate as a decimal instead of a whole number. Divide 72 by 8 (for 8%), not by 0.08 — the whole-number form is what makes the shortcut work.
- Expecting exact precision. It's a fast approximation for mental math, not a substitute for compound-interest calculations when precision matters.
- Forgetting it works for debt too. The same shortcut estimates how quickly an unpaid, interest-accruing debt balance doubles.
Frequently asked questions
What is the Rule of 72?
A quick shortcut for estimating doubling time: divide 72 by the annual growth rate as a whole number.
How accurate is the Rule of 72?
Very close for rates between about 6% and 10%; it drifts further from the exact logarithmic answer outside that range.
Can I use the Rule of 72 for debt instead of investments?
Yes — it works the same way for estimating how quickly an unpaid balance doubles.
Why 72 specifically, and not some other number?
It divides evenly by many common numbers, making mental math easy, while still closely approximating the true doubling formula.
Is there a more accurate version, like the Rule of 69 or 70?
The Rule of 69.3 is the most mathematically precise for continuous compounding; Rule of 70 is another common alternative. All are rounded approximations of the same formula.
Does the Rule of 72 work for inflation too?
Yes — divide 72 by the inflation rate to estimate how long it takes purchasing power to halve. At 3% inflation, that's 24 years.
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Note: The Rule of 72 is an approximation intended for quick mental estimates, not precise financial planning. Not financial advice. Last reviewed: September 2026.