Rule of 72 calculator
Divide 72 by the rate of return and you get the years it takes to double. Shows the shortcut and the real figure side by side.
Divide 72 by an annual rate of return and you get roughly how many years it takes to double: 12 years at 6%, 9 years at 8%. It is a shortcut meant for doing in your head, so it is a little off. This calculator shows the exact figure alongside it, and how far apart they are.
Your numbers
What you enter is saved in this browser, so it is still here next time
Works backwards to the return you would need
Time to double
What the rule of 72 says
12.0 yrs
How long it actually takes
11.9 yrs
- Difference from the shortcut
- +0.10 yrs
Time to reach 2×
11.9 yrs
- To double it in 10 years
- 7.18% a year
The rule of 72 is closest around 8% a year, and drifts the further you get from that — at these settings it is off by 0.10 yrs. Use it for a quick mental estimate and read the exact figure beside it.
Each doubling
| Multiple | Years taken | Amount then |
|---|---|---|
| 2× | 11.9 yrs | ₩20M |
| 4× | 23.8 yrs | ₩40M |
| 8× | 35.7 yrs | ₩80M |
| 16× | 47.6 yrs | ₩160M |
| 32× | 59.5 yrs | ₩320M |
| 64× | 71.4 yrs | ₩640M |
This assumes the same return every year. Tax, fees and inflation are not included. For what the money is worth after inflation, use the compound interest calculator.
Make a link with these numbers
Opening the link fills this screen with the same values. Useful for going through it with a partner, or for comparing two sets of conditions.
At 6% a year the shortcut says 12 years; the exact figure is 11.9
The rule is 72 ÷ rate, so 12 years at 6%. The exact figure is ln2 ÷ ln(1 + rate): 0.6931 ÷ 0.0583 = 11.9 years. The "difference from the shortcut" is the shortcut minus the exact figure, so +0.10 years means the shortcut overstates by that much. Put 10 in the multiple field and you get ln10 ÷ ln1.06 = 39.5 years; the years field works backwards, 2^(1/10) − 1 = 7.18% a year to double in ten. The principal feeds only the "amount then" column, never the years.
Almost exact at 8%, more than two years out at 1%
At 8% the shortcut gives 9.0 years and the exact figure is 9.0 — under 0.01 years apart. At 1% it is 72 against 69.7, so +2.3 years, and even 3% is +0.5. Go the other way and the sign flips: 20% is 3.6 against 3.8, so −0.2, with the shortcut now understating. Low rates run long, high rates run short.
Tax, fees and inflation are left out
The calculation assumes the same return every single year. Real returns swing and tax and fees leak out, so doubling usually takes longer than shown. Inflation is not deducted either — 6% growth with 2% inflation is roughly 4% real, and doubling then takes 17.7 years, not 11.9.
Common questions
QIs the rule of 72 accurate?
It is an approximation. The exact answer is ln2 divided by ln(1 + rate), and the rule of 72 lines up best around 8% a year. The further the rate is from there the wider the gap — at 1% a year it is off by more than two years. That is why the exact figure is shown too.
QWhy 72 in particular?
The mathematically correct number is 69.3 (ln2 × 100), but 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which makes it easy to do in your head. It trades a little accuracy for convenience.
QDoes it account for inflation?
No — it works on nominal returns. To see when the money doubles in real terms, put the real rate (return minus inflation) in the rate field.
QIf the difference shows as +, which one is longer?
The shortcut. The difference is the rule-of-72 years minus the exact years, so +0.10 at 6% means the shortcut's 12 years is 0.1 longer than the exact 11.9. Above 8% the sign turns negative.
QCan it give the years to triple, or to reach 10×?
Enter it in the multiple field. It uses ln(multiple) ÷ ln(1 + rate), so at 6% tripling takes 18.9 years and 10× takes 39.5.