Rule of 72 Calculator

At 5% a year, money doubles in about 14.4 years: that is 72 divided by 5. The exact answer is 14.21, so the shortcut is off by roughly ten weeks.

Currency and number format for

Years to double (rule of 72)

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Years to double (rule of 72)—

Exact calculation—

Error of the shortcut—

Years to triple—

How this was worked out

The formula

years to double ≈ 72 ÷ annual interest rate

Where it comes from

The rule of 72 is a mental shortcut for how long compounding takes to double an amount. It works because the logarithm behind the exact answer happens to be very close to 72 divided by the rate for the range of rates people actually deal with.

How to work it out by hand

Take the annual rate as a whole number, not a decimal
Divide 72 by it
The result is roughly the number of years to double
For tripling, use 114 instead of 72

What is worth knowing

The shortcut is at its most accurate around 8%, and drifts at the extremes: at 1% it is off by about half a year, and above 20% it starts to overstate noticeably. Its real value is not precision but speed, because it makes the cost of a percentage point obvious without a calculator. At 5% money doubles in 14.4 years; at 8% it takes 9. That gap is why fund fees matter so much: a 1% annual fee does not cost you 1%, it costs you years.

Frequently asked questions

Why 72 and not another number?

Because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, and it happens to sit very close to the exact answer for typical rates. 69.3 is mathematically more accurate but useless for mental arithmetic.

How accurate is it?

Within a couple of months for rates between 4% and 12%. Outside that range the error grows, and this calculator shows you the exact figure alongside it.

Does it work for inflation?

Yes, and it is sobering: at 3% inflation, prices double in 24 years. It works for anything that compounds.

What is the rule of 114?

The same shortcut for tripling instead of doubling. There is also 144 for quadrupling.