Rule of 72 calculator
How many years does it take to double your money at a given annual return? A 300-year-old mental shortcut, in one click.
Cheat sheet — years to double by rate
| Annual return | Years to double | Exact (compound) |
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What the rule of 72 is
A back-of-the-envelope estimate that says: at an annual return r %, your money roughly doubles in 72 / r years. At 6 % it doubles in 12 years; at 8 %, in 9 years; at 12 %, in 6 years. The trick comes from Luca Pacioli in 1494 and is still the fastest way to feel the power of compounding without opening a spreadsheet.
Why 72 and not 70 or 69
The exact value is ln(2) ÷ r ≈ 0.693 ÷ r. With percentages: 69.3 / r %. 72 is preferred in practice because it is divisible by 2, 3, 4, 6, 8, 9 and 12 — perfect for mental arithmetic. The error against the exact formula is below 1 % for rates between 4 % and 12 %, which covers most reasonable investment scenarios.
When the rule does NOT work well
- Very high or very low rates. Below 2 % or above 20 % the approximation drifts more than ~5 %.
- Variable returns. Markets do not yield 7 % every year on the dot. The rule gives an average estimate, not a guaranteed schedule.
- It ignores inflation, fees and taxes. To know what you can actually buy with that doubled capital, use the inflation calculator; to compare two return scenarios after fees, our compound interest calculator is more precise.
How to use it well
Estimate orders of magnitude, not exact figures. "Is it worth getting 1 % more annually? That is two years less to double the capital." Useful for comparing alternatives quickly: a bond fund at 3 % doubles in 24 years; an index fund at 8 % doubles in 9. The full guide on compound interest covers the formal math.
FAQ — Rule of 72
Why use 72 instead of the exact formula?
Because 72 is divisible by 2, 3, 4, 6, 8 and 9, which makes the calculation possible without paper. The exact value, ln(2) ÷ r ≈ 0.693 / r, gives almost the same number for typical rates but is not friendly for mental arithmetic.
Does it work for negative returns or losses?
No. The rule of 72 only makes sense for positive returns (it estimates how long it takes to double the money). For losses, you would look at how long it takes to halve, using a similar idea: years to halve ≈ 72 / annual loss %.
Should I use a real or nominal return?
Depends on what you want to know. With a nominal return you get how long it takes to double the number of euros. With a real return (subtracting inflation) you get how long it takes to double your purchasing power. For long-term planning the real one usually makes more sense.
Is there a more accurate version?
Yes. The "rule of 70" uses 70 instead of 72 (closer to ln(2) × 100 = 69.3) and works slightly better for low rates. There is also the Eckart-McHale rule (E-M): years = (69.3 / r) × (200 / (200 − r)), which is more accurate above 10 %. For 99 % of personal-investment cases, plain 72 is enough.