The rule of 72: formula, examples and a calculator
How to estimate when money doubles in your head, how close the shortcut is to the exact answer, and where it stops working.
Checked October 22, 2026
The rule of 72 formula
Investor.gov, the SEC's site for investors, describes the rule of 72 as a quick estimate of growth. With a rate in hand, it gives a rough time to double: divide 72 by the rate. Its example is 9%, which doubles about every 8 years, since 72 divided by 9 equals 8.
Years to double = 72 / rate
Use the rate as a whole number: 8 for 8%, not 0.08. The rule is for compound interest, where each year's growth earns growth of its own.
Where the rule of 72 comes from
Investor.gov does not say who came up with it, and we found no source that does, so we do not credit anyone. What we can show is why it works. Money that grows at rate r a year doubles when (1 + r) to the power of the years equals 2. Solving gives the exact answer:
Years to double = ln(2) / ln(1 + r)
For small rates that comes to about 69.3 divided by the rate in percent. 72 is a little bigger, but it divides evenly by 2, 3, 4, 6, 8, 9 and 12, so the mental math is easy.
Rule of 72 vs the exact answer
| Rate | Rule of 72 | Exact | Off by |
|---|---|---|---|
| 2% | 36.00 years | 35.00 years | +2.8% |
| 4% | 18.00 years | 17.67 years | +1.9% |
| 6% | 12.00 years | 11.90 years | +0.9% |
| 8% | 9.00 years | 9.01 years | -0.1% |
| 9% | 8.00 years | 8.04 years | -0.5% |
| 10% | 7.20 years | 7.27 years | -1.0% |
| 12% | 6.00 years | 6.12 years | -1.9% |
The shortcut is within 3% of the exact answer across this range. It runs a little long below about 8% and a little short above it.
A worked example
You put $10,000 in something you expect to grow 8% a year. 72 / 8 = 9, so about 9 years to $20,000 and 18 years to $40,000. The exact answer for one doubling is 9.01 years. The 8% is a number you choose to test an idea. It is not a promise about what any investment will earn.
Rule of 72 calculator
The exact answer sits beside the shortcut.
The rate is one you pick, not a promise of what an investment will earn. Nothing you type here leaves this page.
- Rule of 7272 / rate9.00 years
- Exact answerln 2 / ln(1 + rate)9.01 years
- The shortcut is off by-0.1%
- $10,000 becomes $20,000 in about9.01 years
The rule of 72 for a couple
The rule is about one amount at one rate, so it does not care how many people own it. Two things help a pair. Running it on the household's total gives one shared picture. And you can run it on each person's account at its own rate. Say you have $20,000 and your partner has $10,000, both at 8%. Both double in about 9 years, to $40,000 and $20,000. The gap in dollars doubles too, from $10,000 to $20,000, even though the two accounts grew at the same pace. If you hold money separately, that is worth knowing before you decide whose goes toward what. Our guide on splitting bills by income covers the monthly side.
When the rule of 72 doesn't fit
- Simple interest. It is for compound growth, not for a flat amount added each year.
- Added money. It tracks one amount with nothing deposited or withdrawn.
- Rates that move. Investor.gov calls the rate "expected". Real returns change from year to year and are not guaranteed.
- Very low or very high rates. See the table: the shortcut drifts at the edges.
- Fees, tax and inflation. The rule uses the rate you give it. Use the rate you actually keep.
Questions people ask
What is the rule of 72?
A shortcut for how long money takes to double. Divide 72 by the yearly rate of return. Investor.gov's example: at 9%, 72 / 9 = 8, so an investment doubles about every 8 years.
What is the rule of 72 formula?
Years to double = 72 / rate, where the rate is the yearly percent as a plain number (8 for 8%). The exact version is ln(2) / ln(1 + r), with r as a decimal (0.08 for 8%).
How accurate is the rule of 72?
Close at ordinary rates. At 8% it gives 9.00 years against an exact 9.01. At 2% it says 36 years against an exact 35.00, and at 12% it says 6 years against 6.12. The table on this page has the rest.
Why 72 and not 70 or 69?
The exact doubling time is about 69.3 divided by the rate, for small rates. People round up to 72 because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, so the mental math is easy, and it fits rates near 8% best.
Does the rule of 72 work with monthly contributions?
No. It describes one amount growing at one rate with nothing added. Regular deposits get you to double faster than the rule says.
Can the rule of 72 be used for debt?
The math is the same. A balance that grows at 24% a year with no payments doubles in about 3 years (72 / 24 = 3). That is arithmetic about a balance, not a prediction about yours.
Sources
1 source · read October 22, 2026
Every number on this page comes from investor.gov. If a source has changed since, the source is right.
Wonderful gives general information. It isn't a financial or tax advisor.