Rule of 72 Calculator
Divide 72 by your return to get the years to double your money. This calculator runs the famous rule and the exact compounding answer side by side — in both directions.
The banker's napkin rule, audited
Divide 72 by the annual return and you get the years for money to double — a rule known since Renaissance ledgers. This page runs the rule and, beside it, the exact answer from compounding, so you can see where the rule is trustworthy and where it drifts.
Years to double ≈ 72 ÷ rate · exact = ln 2 ÷ ln(1 + rate)
Example: at 8%, the rule says 9 years; the exact figure is 9.01 years — the rule is nearly perfect in its home territory. At 2% it says 36 against an exact 35.0; at 24% it says 3 against an exact 3.22. Its sweet spot is roughly 5–12%, the range of most real portfolios.
Run it backwards, too
The rule inverts: years available divided into 72 gives the return a doubling requires. Want to double in a decade? You need about 7.2% a year — a sentence that has ended many unrealistic plans and started some realistic ones.
How this is calculated
The exact figure compounds annually: years = ln(2) ÷ ln(1 + r). The estimate is 72 ÷ r (percent). In reverse mode, the rule gives 72 ÷ years and the exact rate is 2^(1/years) − 1. The constant 72 works because it approximates 69.3 (100 × ln 2) nudged upward to cancel compounding error in the mid-range — and because 72 divides by 2, 3, 4, 6, 8, 9 and 12, which is why bankers adopted it over more accurate rivals.
Frequently asked questions
Why 72 and not 69.3?
69.3 is exact for continuous compounding. 72 corrects better for the yearly compounding people actually face at common rates — and it divides cleanly by most small numbers, which mattered in a pre-calculator world.
Does the rule work for inflation (halving)?
Yes, mirrored: at 4% inflation, money's purchasing power halves in about 18 years (72 ÷ 4). The inflation calculator produces the exact version.
What about tripling?
The informal 'rule of 114' (72's sibling) approximates tripling time; quadrupling is simply two doublings. The exact answers come from ln(3) and ln(4) in place of ln(2) — the same machinery as this page.
How wrong can the rule be?
Within 5–12% returns, within a few percent of the truth. At extreme rates it degrades — at 72% it claims one year; the truth is about 1.28. Treat it as a first estimate and let the exact line beside it arbitrate.
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