Rule of 72 Calculator
A mental shortcut accurate enough for most purposes: divide 72 by the rate and you have the doubling time in years.
Why 72
The exact doubling time comes from logarithms:
Since ln(2) ≈ 0.693, the theoretically correct numerator for continuous compounding is 69.3. The reason 72 is used instead is entirely practical: it has far more whole-number divisors — 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 — which makes the division doable in your head. 72÷8 = 9 is easy; 69.3÷8 is not.
The substitution also happens to compensate for the difference between continuous and annual compounding, which is why 72 is most accurate in the 6–10 % range where most long-run investment returns sit.
How accurate is it
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2 % | 36.0 yrs | 35.0 yrs | +2.9 % |
| 4 % | 18.0 yrs | 17.7 yrs | +1.7 % |
| 8 % | 9.0 yrs | 9.0 yrs | <0.1 % |
| 12 % | 6.0 yrs | 6.1 yrs | −1.8 % |
| 20 % | 3.6 yrs | 3.8 yrs | −5.4 % |
Between 4 and 12 % the error stays under 2 %, which is far smaller than the uncertainty in any real return forecast. Outside that range, use 70 for low rates and 78 for high ones if you want to stay in your head, or just use the exact figure this calculator gives.
What it is good for
- Judging a return claim instantly. An investment promising to double in three years implies a 24 % annual return. Sustained returns at that level are exceptionally rare, so the claim deserves hard scrutiny.
- Understanding inflation. The same arithmetic applies to prices. At 3 % inflation the cost of living doubles in 24 years; at 6 % it doubles in 12.
- Seeing what fees cost. A fund returning 7 % gross with a 1 % annual charge returns 6 % net. Doubling time goes from 10.3 years to 12 years — over 40 years, that one percentage point costs you roughly a quarter of the final balance.
- Debt in reverse. At 24 % APR, an unpaid credit card balance doubles in about three years.
Frequently asked questions
Does it work for debt as well as investments?
Yes, identically. Unpaid debt compounding at 18 % doubles in about four years. The mathematics does not care which direction the money is flowing.
What about the rule of 114 and 144?
Same principle for different multiples: 114 divided by the rate gives the years to triple, and 144 gives the years to quadruple. They derive from ln(3) ≈ 1.10 and ln(4) ≈ 1.39 with the same practical adjustment applied.
Is 7% a realistic return assumption?
It is a common long-run planning figure for a diversified equity portfolio before inflation, based on historical averages. It is not a guarantee, it says nothing about any particular decade, and after 2.5 % inflation the real return is closer to 4.5 % — which doubles purchasing power in about 16 years rather than 10.