What this calculator does
Find out roughly how many years it takes your money to double. The rule of 72 is a quick mental-math shortcut for growth that builds on itself (compound growth). Divide 72 by the yearly percentage rate. You get roughly the years it takes for money to double. At 8% a year, 72 ÷ 8 = 9 years. It works in reverse, too. To double in 6 years, you need about 72 ÷ 6 = 12% a year.
This calculator does the shortcut and then checks it. It works out the exact doubling time and shows the two other common versions of the rule, 70 and 69.3. Then it shows how far each one is from the true answer at your rate. You'll see that no single number is best everywhere. That's why all three are still in use.
Where it's used
Why this math matters outside the classroom:
- Doubling time. Money growing at 8% a year doubles in about 72 ÷ 8 = 9 years, and the exact answer is about 9.006 years.
- Inflation. Prices rising 3% a year double in roughly 24 years, which helps put long-run inflation in perspective.
- Population growth. A population growing 2% a year doubles in about 36 years by the same rule.
- Checking an estimate. Students compare the rule with the exact logarithm answer and see it is closest for rates near 8%.
How to use it
- Choose whether you want the doubling time for a rate, or the rate needed to double in a given number of years.
- Enter the yearly rate of return, or the number of years.
- Compare the rule-of-72 estimate with the exact figure and with the rules of 70 and 69.3 in the table.
What the inputs mean
- Annual rate of return
- The yearly growth rate in percent, such as an investment return, an interest rate or an inflation rate. The exact figure assumes growth is added once a year (compounded yearly).
- Years to double
- How soon you want the money to double. Fractions of a year are fine.
Formula and method
Rule of K: years ≈ K ÷ rate% (K = 72, 70 or 69.3) Exact: years = ln 2 ÷ ln(1 + rate ÷ 100) Reverse: rate% ≈ K ÷ years; exact rate = (2^(1 ÷ years) − 1) × 100 Error = estimate − exact
K is the number the rule uses: 72, 70 or 69.3. The rate is your yearly rate in percent, and r is the same rate as a decimal (8% is 0.08). t, or years, is the time to double. ln is the natural logarithm, a button on most calculators that undoes powers. The error is the estimate minus the exact answer.
Money growing at rate r each year doubles when (1 + r)^t = 2. Using logarithms to solve for t gives t = ln 2 ÷ ln(1 + r). For small r, ln(1 + r) is close to r, so t ≈ 0.693 ÷ r. That's 69.3 ÷ the rate in percent, the rule of 69.3. It's exact when growth is added nonstop (continuous compounding).
With yearly compounding, ln(1 + r) is a little smaller than r. So the true doubling time is a little longer than 69.3 ÷ the rate. Using a bigger number on top makes up for it. 72 gives the most accurate results for rates around 8%. 70 does better at low rates of a few percent. 72 is also popular because it divides evenly by 2, 3, 4, 6, 8, 9 and 12.
Worked example
An investment grows at 8% a year, compounded annually. How long until it doubles?
- Rule of 72: 72 ÷ 8 = 9 years.
- Rule of 70: 70 ÷ 8 = 8.75 years. Rule of 69.3: 69.3 ÷ 8 = 8.66 years.
- Exact: ln 2 ÷ ln 1.08 = 0.693147 ÷ 0.076961 = 9.006 years.
- The rule of 72 is off by 9 − 9.006 = −0.006 years, or −0.07%.
Result: The rule of 72 gives 9.00 years, within about two days of the exact 9.006 years. At 8%, it's the closest of the three rules.
Understanding the result
A negative error means the rule says the money doubles sooner than it really does. A positive error means the rule makes the wait sound longer than it is. At ordinary rates of 4% to 12%, all three rules land within a few percent.
The rules get less accurate as rates climb. At 25%, the exact doubling time is about 3.1 years, while 72 ÷ 25 = 2.9. Use the exact figure for high rates.
The same math works for anything that grows on itself, including inflation. At 3% inflation, prices double in about 23.4 years (the rule of 72 says 24). So money loses half its buying power in that time.
Assumptions and limitations
- The rate stays the same every year, and growth is added once a year.
- Nothing is added or withdrawn, and taxes and fees are ignored.
- Real returns vary from year to year. A doubling time from an average return is only a guide.
- With monthly or daily compounding, the true doubling time is slightly shorter than the exact figure shown here. It gets closer to the rule of 69.3.
- Negative rates never double money, so only positive rates are allowed.
Frequently asked questions
Why 72 and not 69.3?
69.3 comes from the natural logarithm of 2. It's exact when growth is added nonstop (continuous compounding). With yearly compounding, the true doubling time is a bit longer, and 72 corrects for that at typical investment rates. It also divides easily by many common rates, which matters for a mental shortcut.
When should I use the rule of 70 instead?
At low rates, roughly 1% to 4%, the rule of 70 is usually closer. That's why economists often use it for population growth and GDP growth (the growth of a country's economy). Those tend to be small percentages. The table shows which rule is closest at your rate.
Can I use the rule of 72 for debt?
Yes. A balance growing at 24% a year with no payments doubles in about 72 ÷ 24 = 3 years. The exact figure is about 3.2 years. It's a quick way to see how fast unpaid interest piles up.
How do I find how long it takes to triple my money?
Use ln 3 instead of ln 2: years = ln 3 ÷ ln(1 + r). The matching shortcut is roughly 114 ÷ the rate in percent. At 8%, that's about 14.3 years.
How this calculator is checked
Method: Doubling condition (1 + r)^t = 2 solved with natural logarithms; rules of 72, 70 and 69.3 as the standard approximations K ÷ R. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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