Home / Financial / Rule of 72 Calculator
Rule of 72 Calculator: How Long Does Money Take to Double?
Divide 72 by the yearly rate to estimate the years it takes to double. This calculator does that and shows the exact answer beside it, for doubling or any other growth multiple.
What the rule says
The rule of 72 states that money growing at r percent a year doubles in roughly 72 ÷ r years. At 6% it suggests 12 years, at 8% it suggests 9 and at 12% it suggests 6. Run in reverse, the rate needed to double in t years is about 72 ÷ t percent. For other multiples, scale by the number of doublings: tripling needs about 1.585 doublings, since log2(3) ≈ 1.585, so the estimate is 72 × 1.585 ÷ r. The calculator applies this scaling for any multiple you enter.
The exact formula behind it
With yearly compounding, money doubles when (1 + r)t = 2. Taking natural logarithms gives t = ln 2 ÷ ln(1 + r). For small rates ln(1 + r) is close to r, so t ≈ 0.693 ÷ r, which is where the "69.3" version of the rule comes from; it is exact for continuous compounding. The figure 72 is slightly higher because it corrects for yearly compounding at typical rates, and because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes mental arithmetic easy. Some people use 70 for the same reason.
| Rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 | 35.00 |
| 6% | 12.0 | 11.90 |
| 8% | 9.0 | 9.01 |
| 12% | 6.0 | 6.12 |
| 24% | 3.0 | 3.22 |
Practical uses
- Investing: a quick sense of how a return rate translates into time, such as what 5% means over a working life.
- Debt: an unpaid balance at 18% doubles in about four years if nothing is paid and interest compounds yearly.
- Inflation: at 3% inflation, prices double in about 24 years, so purchasing power halves in the same time.
- Growth targets: a business wanting to double revenue in six years needs about 12% a year.
For a precise figure with an end value, use the CAGR calculator, and for balances with regular deposits use the compound interest calculator.
When the shortcut is weak
The rule assumes one fixed rate, annual compounding and no extra deposits. It is least accurate below about 2% and above 20%. Real returns also vary from year to year, so a doubling time worked out from an average rate is only a rough guide to what will happen. Fees and taxes lengthen the doubling time, so use the rate you keep after both. To check an answer by hand, raise 1 plus the rate to the estimated number of years; the result should land close to the growth multiple you chose. If it is far off, the rate is probably outside the range where the shortcut works well. The results are an educational estimate, not a prediction about any investment.
Worked example
How long does an investment take to triple at 6% a year? The rule of 72 gives a quick estimate, and the exact formula checks it.
Inputs
| What do you want to find? | Years needed at a given rate |
|---|---|
| Annual rate of return | 6 % |
| Growth multiple | 3 |
Result
Exact answer: 18.854 years at 6% a year for a growth multiple of 3.
| Rule of 72 estimate | 19.020 years |
|---|---|
| Rule of 70 estimate | 18.491 years |
| Exact time, ln(multiple) ÷ ln(1 + rate) | 18.854 years |
| Rule of 72 error | 0.88% |
Estimate against exact time for the chosen multiple
| Rate | Rule of 72 (years) | Exact (years) |
|---|---|---|
| 1% | 114.12 | 110.41 |
| 2% | 57.06 | 55.48 |
| 3% | 38.04 | 37.17 |
| 4% | 28.53 | 28.01 |
| 5% | 22.82 | 22.52 |
| 6% | 19.02 | 18.85 |
| 7% | 16.30 | 16.24 |
| 8% | 14.26 | 14.27 |
| 9% | 12.68 | 12.75 |
| 10% | 11.41 | 11.53 |
| 12% | 9.51 | 9.69 |
| 15% | 7.61 | 7.86 |
- The rule of 72 is a mental shortcut. It is most accurate for rates of roughly 6% to 10% and drifts at very low or very high rates.
- Growth is assumed to compound once a year with no deposits, fees or taxes. This is arithmetic on a fixed rate and not a forecast.
Financial disclaimer: Results are estimates for planning and education. They are not financial, tax or legal advice. Fees, taxes, rates and rules vary by lender, product and country, so confirm figures with your provider or a qualified adviser before making decisions.
Frequently asked questions
How does the rule of 72 work?
Divide 72 by the annual percentage rate to estimate the years needed for money to double. At 9% the estimate is 8 years.
Why 72 and not 69.3?
The exact figure for continuous compounding is 69.3, but 72 fits yearly compounding at typical rates better and has many whole-number divisors, which makes it easier to use mentally.
How accurate is the rule of 72?
It is typically within a few percent for rates between about 6% and 10%. The table on this page compares the estimate with the exact figure at other rates.
Can I use it for tripling or other growth?
Yes. Multiply the estimate by the number of doublings, which is the base-2 logarithm of the multiple. The calculator does this when you change the growth multiple.
Does it work for inflation or debt?
Yes. Any quantity that grows by a fixed percentage a year follows the same pattern, whether it is prices, a loan balance or revenue.
Related calculators
References and sources
- Standard finance texts: doubling time for compound growth, t = ln 2 ÷ ln(1 + r).
- Investor.gov (U.S. SEC): material on compounding and long-term investing. Link