Rule of 72 Calculator: How Long to Double
Use this Rule of 72 calculator for the classic shortcut: 72 divided by your annual return = years to double. Quick mental math for any investment rate.
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Years to double (Rule of 72)0.00
Exact answer (compound math)0.00
Years to triple0.00
Years to 10×0.00
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How this calculator works
The Rule of 72 says: divide 72 by your annual return percentage and you get a quick estimate of years to double. The exact answer comes from solving the compound-interest equation:
rule: years ≈ 72 / rate%
exact: years = log(2) / log(1 + rate)
exact: years = log(2) / log(1 + rate)
The rule is most accurate at returns of 6–10%. At 7% it predicts 10.29 years; the exact answer is 10.24. At 1%, the rule says 72 years; the exact is 69.7. Use Rule of 72 for napkin math; use the exact column for anything material.
Source: Rule of 72 dates to Luca Pacioli's 1494 Summa de Arithmetica. Long-term real equity returns ~7% per Federal Reserve research.
FAQ
Why 72 specifically?
Because 72 has a lot of small divisors (1, 2, 3, 4, 6, 8, 9, 12) which makes the mental math clean — 72/6=12, 72/8=9, 72/12=6 are all integer answers. Mathematically, ln(2) × 100 ≈ 69.3 would be more accurate, and the 'Rule of 70' is sometimes used in academic settings.
Can I use this for inflation?
Yes — and it's chilling. At 3% inflation, your dollar's purchasing power halves in 24 years. At 6% inflation, it halves in 12 years. Run your real (inflation-adjusted) investment return, not the nominal one, when planning long-term goals.
What is the Rule of 72?
A mental shortcut: divide 72 by your annual return % to estimate years until your money doubles. At 6% → 12 years. At 8% → 9 years. At 4% → 18 years. The rule is most accurate at returns between 6-10%.
Why does the Rule of 72 work?
Compound math: the exact answer is years = ln(2) / ln(1 + r), where ln(2) ≈ 0.693. At small rates, ln(1+r) ≈ r, so years ≈ 0.693 / r ≈ 69.3 / r%. The rule rounds 69.3 to 72 because 72 has more clean divisors (2, 3, 4, 6, 8, 9, 12).
How accurate is the Rule of 72 vs the exact formula?
Very accurate at 6-10%: at 8% rule says 9 years, exact says 9.0 years. At 4% rule says 18, exact says 17.7. At 18% rule says 4, exact says 4.2. For any practical decision, the rule is within a few months — close enough for napkin math.
Does the Rule of 72 work for inflation too?
Yes — and it is chilling. At 3% inflation, your dollar's buying power halves in 24 years. At 6% inflation, 12 years. This is why parking cash in a 0% account is silently destructive long-term. Always calculate purchasing power AFTER inflation.
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