How the Rule of 72 works
The Rule of 72 answers a single question — how many years until my money doubles? — without a calculator. You take the number 72 and divide it by the percentage rate of return. At 6% the result is 12 years; at 9% it is 8 years; at 12% it is just 6 years. Because it is pure division by a friendly number, it is the kind of estimate you can run in your head while someone is still pulling up a spreadsheet. The same logic works backward too: if you want your savings to double in a set number of years, divide 72 by that target to find the return you need.
The Rule of 72 formula
Years to double ≈ 72 ÷ rate (%)
Exact years = ln(2) ÷ ln(1 + rate)
where rate is the annual rate of return expressed as a whole percent. The first line is the shortcut; the second is the precise answer from compound growth, which this calculator computes alongside it so you can judge the gap.
Worked example
Take an investment expected to return 8% a year — here is how the Rule of 72 shortcut stacks up against the exact compound-growth answer:
| Step | Amount |
|---|---|
| Annual rate of return | 8.00% |
| Exact doubling timeln(2) ÷ ln(1 + 8%), from compound growth | 9.01 yrs |
| A $1,000 stake after 9 yearsfrom the calculator’s growth series — essentially doubled | $1,999.00 |
| = Years to double (Rule of 72: 72 ÷ 8)just 0.01 years off the exact answer — the rule is at its best in the 6–10% range | 9.00 yrs |
These figures match the calculator's default settings — open the tool above and you'll see the same numbers, then try your own expected return.
Why it works and where it is accurate
Doubling time is fundamentally a logarithm problem. The exact answer divides the natural log of 2 — about 0.693 — by the natural log of one plus the rate. For the modest rates typical of investing, that math rearranges into something very close to dividing 100 times 0.693, or roughly 69, by the rate. The number 72 is chosen instead of 69 because it divides cleanly by so many small numbers and nudges the estimate to be most accurate right in the 6% to 10% range where most real returns sit. Step outside that band and the approximation drifts: it slightly overshoots at low rates and undershoots at high ones, which is exactly why the exact figure is worth checking. To see the actual compounding play out year by year, use ourcompound interest calculator, and to work out the implied annual growth rate behind a known doubling, try theCAGR calculator.
Variants: the Rule of 70 and Rule of 69.3
The Rule of 72 has cousins suited to different assumptions. The Rule of 70 swaps in an even rounder numerator and is popular for quick demographic and inflation estimates. The Rule of 69.3 comes directly from the exact mathematics — since the natural log of 2 is 0.693 — and is the most precise choice when growth compounds continuously rather than once a year. In practice, 72 wins for everyday use because its many divisors make the arithmetic painless, while 69.3 wins when you need theoretical accuracy under continuous compounding. All three describe the same underlying curve; they simply pick different trade-offs between mental ease and precision.
Frequently asked questions
What is the Rule of 72?
The Rule of 72 is a mental-math shortcut for estimating how long an investment takes to double at a fixed annual rate of return. You divide 72 by the percentage rate and the answer is the approximate number of years. At an 8% return, for example, 72 divided by 8 gives 9, so money roughly doubles every nine years. It trades a little precision for the convenience of being something you can work out in your head.
Why does dividing by 72 work?
Doubling time is really governed by logarithms — the exact answer is the natural log of 2 divided by the natural log of one plus the rate. The natural log of 2 is about 0.693, and for the small rates typical of investing the math works out so that multiplying by 100 and rounding gives a numerator close to 72. The number 72 is also convenient because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the arithmetic easy.
How accurate is the Rule of 72?
It is most accurate for rates in the 6% to 10% range, where it lands within a fraction of a year of the exact figure. Outside that band the approximation drifts: at very low rates it tends to overstate the doubling time slightly, and at very high rates it understates it. For everyday planning the error is usually small enough to ignore, but the exact logarithmic figure shown alongside it is the one to trust when precision matters.
What are the Rule of 70 and Rule of 69.3?
They are variants tuned for different compounding assumptions. The Rule of 70 is sometimes preferred for its easy division and works well for continuous-style growth, while 69.3 comes straight from the exact math because the natural log of 2 is 0.693 — making it the most accurate choice for continuous compounding. The Rule of 72 splits the difference and is favored for annual compounding because 72 has so many convenient divisors.
Does the Rule of 72 work for things other than investments?
Yes. Any quantity growing at a steady percentage rate doubles on the same schedule, so the rule applies to inflation eroding purchasing power, populations expanding, or debt compounding against you. If prices rise 3% a year, the Rule of 72 says the cost of living roughly doubles in 24 years. The same shortcut even runs in reverse to estimate how long it takes a value to halve under a steady rate of decline.
Disclaimer: This calculator is foreducation and illustration only. The Rule of 72 is an approximation that assumes a single, constant rate of return, which real investments rarely deliver, and the figures it produces are not a forecast of any specific outcome. Nothing here is investment, tax, or trading advice.