Rule of 72 Calculator – Type in an annual rate of return and see how long your money takes to double — then check how close that shortcut lands to exact compound math’s. The tool also runs the reverse problem, turning a doubling target into the return you would need.
Your assumptions
How the three rules drift apart
Run the calculation and the curves appear here.
Doubling milestones along the way
| Doubling | Years (rule of 72) | Cumulative years | $1,000 becomes |
|---|---|---|---|
| Run the calculation to fill this table. | |||
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Table of Contents
What the rule of 72 actually says
The rule of 72 is a quick method for compound growth. The annual percentage return divided into 72 gives an approximation to the number of years needed for a sum of money to double. Divide 72 by 8 to find the number of years, which is 9. It yields 12 years at 6 per cent. It gives 6 years of service life at 12 percent. What attracted me to it is the arithmetic does not require a spreadsheet to perform, which means you can sanity-check a fund fact sheet, a savings rate or a loan rate without opening a spreadsheet. It’s useful because it can be used to calculate the doubling time when you give the rate. It is this symmetry that makes the rule of 72 relevant to retirement planning, to the compound interest problems in a classroom, to comparisons of two accounts, etc.
How this rule of 72 calculator works
The tool provides both answers, so that you can view the shortcut next to the true answer.
- The shortcut. The doubling time is 72/annual rate. The inverse of this is the rate required, in this case: 72 / number of years. Both are displayed to one decimal place due to the only about one decimal place accuracy of the rule.
- The exact answer. Real compounding resolves 2 = (1 + r/n) to the power of n×t with r being the nominal rate per year, n the number of compounding periods per year and t the time in years. The rearranged form of the doubling time is ln(2)/(n×ln(1 + r/n)). When compounding is continuous, it reduces to ln(2) / r (about 69.3 / rate in percent).
- The comparison. The tool shows the rule of 72 as a line, and the rule of 70 and the actual curve over a range of rates to see how much the two rules differ. Then it follows the doubling steps and displays what $1000 would become at each doubling, and that’s where the shortcut and exact math’s begins to differ.
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Where 72 comes from, and why 69.3 is the purist’s number
The value of the constant does not come from nowhere. Doubling time is ln(2) divided by ln(1 + r), and ln(2) is 0.6931. For small rates, ln(1 + r) is approximately r, which means that the doubling time is approximately 69.3 / per cent rate. That is the one o’ math purity.
For the same reason 72 is used rather than 70 instead: 72 is divisible by 2, 3, 4, 6, 8, 9 and 12, which are the rates people actually use; and ln(1 + r) is slightly below r at common rates. That leaves the practical constant just a bit higher, from about 69.3 to 72, for rates in the range of about 5 to 12 percent. If it exceeds 20 percent, the rule is an over shooter, if it is less than 3 percent, then it is an under shooter.
The rule of 72 comes into play.
Investors use it to compare funds whose expense ratios vary, as a 0.5 percent cost sneaks up a couple of months per doubling. A saver will compare the promotional rate to determine if a move is worthwhile. On debt, it works the other way around and it hurts: a credit card at 24 percent will double an unpaid debt in about three years—quite a dramatic illustration of the power of interest as compared to an APR figure. It also puts inflation into perspective: If it’s at 3 percent, the value of your purchasing power will be half as much in about 24 years, and halved in 12 years at 6 percent.
Here are some tips to utilize it properly.
- Do the fee and inflation adjustments first. The rule applies to your “actual” rate. A 7 percent gross return, with an additional 1.5 percent in fees and 3 percent in inflation, comes up to just close to 2.5 percent net, more than tripling the doubling time.
- Keep in mind that it’s an approximation. Use the output as a planning estimate, not a projection. If it is a big decision, use the exact number.
- For continuous compounding use 69.3. The constant 72 was adjusted for common rates of annual or periodic compounding.
- Don’t over-extend it to more than 20 percent. At high rates, the error is rapidly increasing, and exact maths will be more helpful.
- Use it in actual results. Double the portfolio after inflation is a much better statement than double the portfolio.
FAQ
Does the Rule of 72 hold true?
It is within a distance where planning can be done at normal speeds. The estimate is typically within a few months of the actual number, between 4% and 12%. The accuracy is not maintained at very low or very high rates, and it does not account for any fees, taxes or inflation unless you change the rate yourself.
Should I use 72, 70 or 69.3?
For quick mental math’s use 72 – this is easily divisible by common rates. Use 70 if you wish to have a slightly better fit over a wide range of rates. For continuous compounding use 69.3 which is the true value of the constant.
Can the rule of 72 be applied to debt?
Yes, and that is the hard part. If no money is repaid, a balance at 18% would double in approximately 4 years. The same rule applies that flattered an investment on how fast an unpaid balance is growing.
At 7 percent what is the doubling time?
The rule of 72 provides approximately 10.3 years. The exact answer (compounding monthly) is approximately 9.9 years, which is about a four month overestimate in this case but close enough for planning purposes, but not for a contract.
What about tripling?
The changes are constant since ln(3) is not 0.6931, but rather 1.0986. If the rule of 72 is used for the tripling time, then the rule of 114 is a suitable companion for the same range of rates, but works less well.
Reviewed by: aFreeTools Editorial Team
Last updated: September 25, 2026
Freshness: The shortcut behavior was checked against periodic and continuous compounding at common rates.
Disclaimer: This rule of 72 calculator is an educational and planning tool. It does not provide financial, investment or tax advice, and its output is a mathematical estimate rather than a forecast. Real returns vary, may be negative, and are reduced by fees, taxes and inflation. Always read the terms of a financial product and consider speaking to a qualified adviser before making decisions about your money.