How to use the Rule of 72 calculator
There are three tools.
- Years to double. Enter an annual rate of return or interest rate to see the exact doubling time and the estimates from the Rules of 72, 70 and 69.3, with the error of each. The table covers every whole rate from 1% to 20%.
- Rate needed. Enter the number of years in which you want your money to double, and see the annual return that achieves it, by each rule and exactly.
- Triple or more. Choose a target of 2×, 3×, 4× or any other multiple to see how long it takes, using the Rule of 114 for tripling and the Rule of 144 for quadrupling.
All results assume a constant rate compounded once a year.
The formulas
Exact: years to double = ln(2) ÷ ln(1 + r)
Rate to double in Y years = 21/Y − 1R is the annual rate in percent (8 for 8%), r the same rate as a decimal (0.08) and ln the natural logarithm.
For any multiple k, the exact time is ln(k) ÷ ln(1 + r). The matching rule replaces 72 with 72 × log2(k): about 114 for tripling and 144 for quadrupling.
A worked example
Years to double. At 8% a year, the Rule of 72 says money doubles in 9.00 years. The exact answer is 9.01 years, so the rule is off by just a couple of days. The Rule of 70 gives 8.75 and the Rule of 69.3 gives 8.66, both too short at this rate.
Rate needed. To double your money in 10 years, you need 7.18% a year. The Rule of 72 suggests 7.20%, a fraction of a point too high.
Tripling. At 8%, money triples in 14.27 years; the Rule of 114 says 14.25.
Why 72 works best around 6% to 10%
With annual compounding, the exact constant is not fixed: it is R × ln(2) ÷ ln(1 + r), which rises slowly with the rate. At 2% it is about 70.0, at 8% about 72.05 and at 20% about 76.0. A useful approximation is 69.3 + R ÷ 3, so the constant crosses 72 at roughly 8%, and 72 is exact at about 7.85%.
That makes the Rule of 72 most accurate across the returns people most often plan with. It also helps that 72 divides evenly by 2, 3, 4, 6, 8, 9 and 12, so the arithmetic is easy in your head.
| Rate | Exact years | Rule of 72 | Rule of 70 |
|---|---|---|---|
| 2% | 35.00 | 36.00 | 35.00 |
| 4% | 17.67 | 18.00 | 17.50 |
| 8% | 9.01 | 9.00 | 8.75 |
| 12% | 6.12 | 6.00 | 5.83 |
| 20% | 3.80 | 3.60 | 3.50 |
At 2% the Rule of 70 is almost exact while 72 is a year too long. At 20% every rule underestimates: the Rule of 72 says 3.60 years against an exact 3.80. For continuous compounding, the Rule of 69.3 is exact at every rate.
Using the rule the other way
The rule also turns a time horizon into a required return. Doubling in 6 years takes 12.25% a year; doubling in 20 years needs only 3.53%. That makes it a quick sanity check on any promise: an investment that claims to double your money in three years is claiming about 26% a year, far above long-run stock market returns. To find the rate behind any start and end value, use the CAGR calculator.
The rule applies to costs too. Inflation of 3% halves the buying power of cash in about 24 years, and fees compound against you in the same way, which is why the compound interest calculator is worth running with a realistic net return.
Limitations
- Constant rates only. Real returns vary from year to year, so a doubling time based on an average return is a rough guide, not a schedule. Volatile returns compound to less than their simple average.
- Annual compounding. The exact figures assume interest is added once a year. More frequent compounding shortens the doubling time slightly, toward the Rule of 69.3.
- No deposits, withdrawals, taxes or fees, each of which changes how fast a real balance grows.