How to use the Rule of 72 Calculator
- Choose whether you want the years to double or the return required.
- Enter the annual return, or the number of years you have.
- Compare the rule-of-72 estimate against the exact answer shown beside it.
- Use the rule of 114 line when you want tripling time instead.
- Apply the same arithmetic to inflation or debt to see how fast they work against you.
How the calculation works
The rule works because the exact doubling time is ln 2 divided by ln(1 + r), and for small rates ln(1 + r) is approximately r. That gives 69.3 divided by the rate as a percentage. The number 72 is used instead because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, and because the small upward adjustment happens to improve accuracy in the 6%–10% range where most investment returns fall.
Accuracy is excellent in the middle and degrades at the extremes. At 8% the rule gives 9.00 years against an exact 9.01 — error under a day. At 2% it gives 36 years against 35.0, and at 30% it gives 2.4 against 2.64. For hyperinflation or credit card rates, use the exact formula; for anything a portfolio plausibly returns, the mental arithmetic is fine.
The rule's real value is that it makes compounding intuitive without a calculator. Eight percent doubles in nine years, so a 36-year career is four doublings — sixteen times the money. It also runs in reverse: at 3% inflation, prices double in 24 years, and at a 24% credit card rate, an unpaid balance doubles in three. Related constants extend it: 114 for tripling and 144 for quadrupling.
Years to double ≈ 72 / r; exact = ln 2 / ln(1 + r/100); tripling ≈ 114 / r; quadrupling ≈ 144 / rSource: Pacioli, Summa de Arithmetica (1494), earliest known statement; standard compound interest mathematics for the exact form.
Worked example
An 8% annual return — roughly the long-run average for a diversified stock portfolio.
- Rule of 72: 72 ÷ 8 = 9.00 years.
- Exact: ln 2 ÷ ln 1.08 = 0.6931 ÷ 0.07696 = 9.01 years.
- Tripling: 114 ÷ 8 = 14.25 years.
- Two doublings = 18 years to quadruple.
Nine years to double, and the approximation is off by four days — accurate enough for any decision made without a spreadsheet.
Frequently asked questions
Why 72 and not 69.3?+
69.3 is mathematically exact for continuous compounding, but 72 has far more whole-number divisors and is slightly more accurate for annual compounding in the 6%–10% range.
How accurate is the rule?+
Within about 1% between 4% and 12%. It degrades noticeably below 2% and above 20%, where the exact formula is worth using.
Does it work for inflation and debt?+
Yes, identically. At 3% inflation prices double in 24 years; at a 24% card rate an untouched balance doubles in three.
What is the rule of 114?+
The tripling equivalent. Divide 114 by the rate for years to triple, and 144 for years to quadruple.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.