Tools / Investing
Rule of 72 calculator
Divide 72 by the return to get the doubling time, or by the years to get the return you need. Checked against the exact answer either way.
Exact answer: 9.01 years · rule is off by 0.01 years
Assumes a constant annual return compounded yearly, no contributions, taxes, or fees. The exact formula is years = ln 2 / ln(1 + r).
| Annual return | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2% | 36.0 yrs | 35.00 yrs | +1.00 |
| 4% | 18.0 yrs | 17.67 yrs | +0.33 |
| 6% | 12.0 yrs | 11.90 yrs | +0.10 |
| 8% | 9.0 yrs | 9.01 yrs | -0.01 |
| 10% | 7.2 yrs | 7.27 yrs | -0.07 |
| 12% | 6.0 yrs | 6.12 yrs | -0.12 |
What the rule says
Money compounding at r percent a year doubles in roughly 72 divided by r years. At 8%, 72 over 8 gives 9 years; the exact answer, ln 2 divided by ln 1.08, is 9.01 years, so the shortcut lands within a week of the truth. It works in reverse too: to double in 10 years you need about 72 over 10, or 7.2% a year, against an exact 7.18%. The rule earns its keep because it turns an abstract percentage into a length of time you can feel. A fee of 1% is forgettable; hearing that 7% doubles in a decade while 6% takes two extra years is not.
Why 72, and where it bends
The exact doubling time is ln 2 over ln(1 + r), and for small r the denominator is close to r itself, giving roughly 69.3 over r. Seventy-two beats 69.3 as the folk constant because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12, and because the approximation error happens to cancel best near ordinary investment returns. The table above shows the drift: at 2% the rule says 36 years against a true 35.0, at 8% it is nearly exact, and at 12% it says 6 years against a true 6.12. Between about 4% and 12%, the band where most portfolio math lives, the error stays under a few months.
Doublings are the intuition upgrade
The rule's real value is counting doublings instead of percentages. A 30-year horizon at 7% holds about three doublings, since 72 over 7 is roughly 10 years each: $50,000 becomes $100,000, then $200,000, then $400,000. Now shave the return to 5% and each doubling stretches to 14.4 years, so the same 30 years holds barely two: about $200,000. Two points of return, one whole doubling. That is also the honest way to read fees and inflation, each of which quietly subtracts from r and stretches every doubling you have left.
What it cannot tell you
The rule assumes a constant compound rate. Real markets deliver lumpy returns around the average, so "doubles every 9 years" is a statement about the long run, not a schedule; our claim check linked below grades how the rule held up decade by decade. For anything beyond doubling, contributions, or exact figures, use the compound interest calculator, which runs the full month-by-month arithmetic.
The full arithmetic behind the shortcut Compound interest calculator 
The rule, graded against real decades "Your money doubles every 7 years", checked