Rule of 72 Calculator
Approximate how long a balance takes to double at a constant effective annual growth rate, or the approximate rate needed to double in a chosen number of years. Rule of 72 is a mental shortcut. Exact compounding math is shown alongside for comparison.
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Enter your assumptions and calculate to see the estimated result and supporting details.
How this calculator works
Choose Rate known (estimate doubling time) or Doubling time known (estimate required rate).
Primary results show the Rule-of-72 approximation. Secondary results show the exact mathematical comparison and the difference.
Formula / methodology
Rule of 72 doubling years ≈ 72 ÷ ratePercent Exact doubling years = ln(2) ÷ ln(1 + annualRate) Rule of 72 rate% ≈ 72 ÷ years Exact required rate = 2^(1 ÷ years) − 1
- Rate is treated as an effective annual growth rate for comparison with exact compounding.
- Rule of 72 is an approximation — most useful as a mental shortcut, not an exact prediction.
Worked example
At 8%: Rule of 72 ≈ 9.00 years; exact doubling time ≈ 9.0065 years.
At 6%: Rule of 72 = 12.00 years; exact ≈ 11.8957 years.
To double in 10 years: Rule of 72 ≈ 7.20%; exact effective annual rate ≈ 7.1773%.
Important assumptions
- If a balance grew at a constant effective annual rate, these formulas estimate doubling time or required rate.
- Rule of 72 does not predict actual investment performance.
- Exact results assume continuous application of the effective annual compounding identity shown above.
Common questions
No. These results are mathematical comparisons under a constant-rate assumption. Actual returns vary.
Rule of 72 is a quick estimate. Exact compounding differs slightly and is shown so the approximation is transparent.
An effective annual growth rate assumption for comparison — not a guarantee of future returns.