Rule of 72 Calculator

What the Rule of 72 is

The Rule of 72 is a mental shortcut for compound growth: divide 72 by an annual percentage return and you get, near enough, the number of years it takes for money to double. At 8% a year, money doubles in roughly nine years. Its value is that it turns an exponential relationship most people find unintuitive into a single division you can do while someone is still talking.

Why it works

Exact doubling time is ln(2) ÷ ln(1 + r). Since ln(2) ≈ 0.693, the true numerator is about 69.3 for continuous compounding — but 72 is used instead because it has far more whole divisors (2, 3, 4, 6, 8, 9, 12) and it corrects slightly for annual rather than continuous compounding. The approximation is at its most accurate between 6% and 10%, where it is within a few months of the exact answer, and drifts at the extremes.

How to use this calculator

Enter the annual return you expect. The result shows both the Rule of 72 estimate and the mathematically exact doubling time, so you can see how close the shortcut is at your particular rate.

Where else to point it

The rule works just as well against you. At 6% inflation, prices double in twelve years — which is another way of saying money loses half its value in that time. Applied to a credit card at 24%, an untouched balance doubles in three years. It also inverts usefully: if you need to double a sum in ten years, divide 72 by 10 and you have the return you must find, which is about 7.2% a year.