Rule of 72 Calculator

The rule of 72 is the mental-maths shortcut every investor should know: divide 72 by the annual return and you get the years needed to double your money. This calculator applies it and compares it against the exact logarithmic answer, so you can see where the shortcut is reliable and where it drifts.

Inputs

Annual return(%)

Result

9 years

Approximate doubling time

How it works

Years ≈ 72 / rate

How the rule of 72 calculator works

Years to double ≈ 72 ÷ r, where r is the annual percentage return. At 9%, that is 8 years.

The exact answer is ln(2) ÷ ln(1 + r/100). At 9% that gives 8.04 years, so the shortcut is off by half a week.

Accuracy is best between roughly 5% and 12%. Below that, 69.3 divided by the rate is closer; well above it, the rule increasingly overestimates the time needed.

Worked example: shortcut versus exact

At 6%: 72 ÷ 6 = 12 years. Exact: 11.90 years.
At 8%: 72 ÷ 8 = 9 years. Exact: 9.01 years.
At 12%: 72 ÷ 12 = 6 years. Exact: 6.12 years.
At 24%: 72 ÷ 24 = 3 years. Exact: 3.22 years — the shortcut is now clearly optimistic.
Run it in reverse for inflation: at 6% inflation, prices double in about 12 years.

Common mistakes to avoid

Applying it to volatile returns

The rule assumes a steady rate. With a portfolio that swings, use the compound annual growth rate rather than the average of yearly returns.

Forgetting it works on inflation too

The same arithmetic tells you how fast your costs double. A 7% nominal return against 3.5% inflation means real doubling takes about 20 years, not 10.

Using it for very high rates

Above roughly 20%, switch to the logarithmic formula. Credit card debt at 36% doubles in about 2.2 years, not the 2.0 the rule suggests.

Frequently asked questions

Why 72 and not 70?

72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which makes it far easier for mental maths, and it happens to be most accurate in the 6–10% range investors care about.