Rule of 72 (Doubling Time) Calculator
The Rule of 72 is a quick mental-math shortcut for compounding — this shows that estimate next to the exact answer.
How Rule of 72 (Doubling Time) Calculator Works
The Rule of 72 is a mental-math shortcut for estimating how long it takes an amount to double under compound interest, or what rate you'd need to double it in a set number of years -- this tool shows that quick estimate side by side with the exact, log-based answer so you can see how close the shortcut really is.
Formula & Method
When you know the rate, the Rule of 72 estimate is 72 ÷ rate years, while the exact doubling time (solved from (1 + rate/100)years = 2) is ln(2) ÷ ln(1 + rate/100). When you know the years, the Rule of 72 estimate is 72 ÷ years percent, while the exact required rate is (2(1/years) − 1) × 100 percent. Two closely related shortcuts are shown alongside as well: the Rule of 70 (70 ÷ rate or 70 ÷ years) and the more precise Rule of 69.3 (69.3 ÷ rate or 69.3 ÷ years), since 69.3 (approximately 100 × ln(2)) is the constant that's mathematically exact in the limit of continuous compounding, while 72 is chosen for its convenient divisibility by many small numbers.
Worked Example
At an 8% annual rate, the Rule of 72 estimates 9.00 years to double, versus an exact doubling time of 9.01 years -- the Rule of 70 estimate is 8.75 years and the Rule of 69.3 estimate is 8.66 years. Working the other direction, if you want to double your money in 10 years, the Rule of 72 says you need a 7.20% annual rate, versus an exact requirement of 7.18%.
Frequently Asked Questions
- How accurate is the Rule of 72 compared to the exact answer?
- It's remarkably close for typical rates -- within a few hundredths of a year at 8%, as shown in the example -- because 72 is a convenient round number close to the mathematically exact constant (100 × ln(2) ≈ 69.3). Accuracy drifts a bit more at very high or very low rates, which is why the exact figure is always shown alongside it.
- Why does this show a Rule of 70 and Rule of 69.3 estimate too?
- They're the same shortcut using a different constant. 69.3 is the theoretically exact constant for continuous compounding, 70 is another popular round-number approximation, and 72 is favored in practice because it divides evenly by more small numbers (2, 3, 4, 6, 8, 9, 12), making the mental math easier.
- Does the starting amount affect the doubling time?
- No -- doubling time and the rate needed to double depend only on the interest rate and time period, not on the amount. The starting amount field is optional and only used to show what that specific amount would grow to once it doubles.
- Does this account for taxes, fees, or inflation?
- No -- this is a pure compound-growth calculation based only on the nominal rate you enter. If you want to see the effect of inflation eroding purchasing power separately, use the Inflation Calculator.