Rule of 72 Calculator
The Rule of 72 is a quick mental shortcut for compound growth: divide 72 by your annual return to estimate the years it takes to double your money. This calculator solves either way, compares the rule against the mathematically exact answer, lets you switch the divisor to 70 or 69.3 for sharper estimates, and can project a starting amount through its first few doublings.
Formula
Worked example
At an 8% annual return: 72 ÷ 8 = 9 years to double (the exact figure is 9.01 years). Quadrupling takes two doublings, about 18 years. Reversing it, to double in 6 years you would need 72 ÷ 6 = 12% per year (exact: 12.25%).
What the Rule of 72 is
The Rule of 72 is a back-of-the-envelope shortcut for compound growth. Divide 72 by the annual percentage rate of return and the result is roughly the number of years it takes an investment to double in value. Because it needs no calculator or logarithms, it is a favourite for sizing up savings rates, inflation, and investment returns in your head. The same division works in reverse: divide 72 by a target number of years to find the rate you would need to double in that time. This calculator does both, and also shows the mathematically exact answer next to the estimate so you can see how close the shortcut really is.
Why 72, and choosing 70 or 69.3 instead
The exact time to double is ln(2) divided by ln(1 + r), and ln(2) is about 0.693, so the precise numerator near typical rates is closer to 69.3. The number 72 is used instead because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12, making mental arithmetic easy while staying very close to the true answer. The approximation is most accurate for rates around 6 to 10%. For very low rates, such as estimating how fast inflation erodes purchasing power, the Rule of 70 or the Rule of 69.3 is sharper, so you can switch the divisor here. For high rates the rule slightly overestimates the doubling time, and again a smaller divisor closes the gap.
Tripling, quadrupling and projecting a balance
Doubling is only the start. Two doublings is a quadrupling, so the time to grow 4x is simply twice the doubling time, and the calculator reports it directly. Tripling sits between the two and is found by scaling the divisor by log(3) over log(2), about 1.585. Turn on the starting-amount option to project a real balance: the tool shows the value after one and two doublings, draws a growth curve, and lists each doubling milestone in a table. Treat these as a sanity check that assumes a single fixed rate with everything reinvested, and switch to a full compound-interest or investment calculator once you add contributions, taxes, or fees.
Years to double at common rates
| Annual return | Rule of 72 (years) | Exact (years) |
|---|---|---|
| 2% | 36.0 | 35.0 |
| 4% | 18.0 | 17.7 |
| 6% | 12.0 | 11.9 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
| 15% | 4.8 | 5.0 |
Rule-of-72 estimate (72 ÷ rate) versus the exact doubling time.
Frequently asked questions
How do I use the Rule of 72?
Divide 72 by your annual rate of return to estimate the years to double. At 9% per year, 72 ÷ 9 = 8 years. To find the rate needed to double in a set time, divide 72 by the number of years instead. This calculator solves either direction and shows the exact answer alongside the estimate.
How accurate is the Rule of 72?
It is very close for rates between about 6% and 10%, where the true doubling time is within a few percent. At very high rates it slightly overstates the time, and at low rates using 70 or 69.3 gives a sharper estimate. You can switch the divisor here and compare the rule directly against the exact figure.
Why is the number 72 used instead of 69.3?
The mathematically exact numerator near typical rates is about 69.3 (from ln 2), but 72 divides evenly by many common rates such as 2, 3, 4, 6, 8, 9, and 12. That makes the mental math far easier while keeping the answer almost as accurate. Pick 69.3 in the divisor dropdown when you want the most precise estimate.
How long does it take to triple or quadruple my money?
Quadrupling is just two doublings, so it takes twice the doubling time: at 8% that is about 18 years. Tripling falls in between and is found by multiplying the doubling time by about 1.585 (log 3 ÷ log 2). The calculator reports both the tripling and quadrupling times for your rate.