Rule of 72 Calculator
Estimate how long money takes to double at a given annual return, or the rate you need to double in a set time.
Quick answer
The Rule of 72 estimates doubling time: years to double is about 72 divided by the annual return in percent. The exact figure is ln 2 / ln(1 + r), and the rate needed to double in N years is 2^(1/N) - 1.
Rule of 72 Calculator
Rule of 72 (years)
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Rule of 70 (years)
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Rule of 69.3 (years)
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Rule of 72 error
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Exact doubling time (years)
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Rule of 72 rate
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Rule of 70 rate
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Rule of 69.3 rate
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Rule of 72 error
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Exact annual rate needed
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Estimates compared
Rule of 72 vs 70 vs 69.3 vs exact (years to double)
| Rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact | 72 error |
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Assumptions & method
- Exact doubling time with annual compounding = ln 2 ÷ ln(1 + r), where r is the annual rate as a decimal.
- Rule estimates = 72 ÷ r, 70 ÷ r and 69.3 ÷ r with r in percent. Rate needed for a given time uses the same divisions in reverse (72 ÷ years).
- Exact rate needed to double in N years = 2^(1/N) − 1.
- Error is the estimate minus the exact value, as a percent of the exact value. Positive means the rule overestimates.
- Assumes a constant return compounded once a year with no contributions, fees, taxes or inflation. Real returns vary.
Results are estimates based on the figures you enter. They are not guarantees and not financial advice.
How the Rule of 72 works
With compound growth, money doubles when (1 + r) raised to the number of years equals 2, which gives years = ln 2 ÷ ln(1 + r). Because ln(1 + r) is close to r for small rates and ln 2 is about 0.693, the answer is roughly 69.3 ÷ r. People round to 72 because it is easy to divide and compensates for compounding at typical rates. This calculator shows the quick estimates from 72, 70 and 69.3 next to the exact figure, so you can see the error. You can also reverse the question and ask which rate doubles your money in a chosen number of years.