How accurate is the rule of 72?

Very, in the range that matters. It is most accurate around eight percent and drifts at the extremes: at seven percent it gives 10.29 years against an exact 10.24, an error of a few weeks. At very low rates the gap widens — at two and a half percent the shortcut says 28.8 years and the exact answer is 28.1. The table always uses the exact formula, so the approximation never leaks into the numbers.

Why does it use 72 rather than 69 or 70?

Because the mathematically exact numerator for continuous compounding is about 69.3, and 72 was chosen instead for being divisible by 2, 3, 4, 6, 8, 9 and 12, which makes the division doable in your head. The small upward adjustment also happens to compensate for annual rather than continuous compounding at moderate rates, which is why it is more accurate than the exact constant would be for this use.

What is the practical point of a doubling time?

It converts a rate into a unit people reason about, which is time. A deposit at two and a half percent doubles in about 28 years and a long-run equity return doubles in about 10, and that comparison lands harder than the difference between two percentages does. It is the same argument the emergency fund and purchasing power pages make with euros instead of years.

Rule of 72 — doubling time at any rate of return

The rule of 72 is the one piece of compounding arithmetic worth carrying in your head: divide 72 by the annual return and you have the years to double. It is an approximation, and this page shows you both it and the exact answer so you can see how good it is. At seven percent the shortcut says 10.29 years and the exact calculation says 10.24 — close enough to settle most arguments without a spreadsheet.

The calculator

How it works

Every figure in the table is the exact formula, the logarithm of the multiple divided by the logarithm of one plus the rate, rather than the shortcut. The 72 approximation appears only in the callout, where it is shown against the exact number so the error is visible rather than inherited. The multiples go beyond doubling deliberately: tripling and tenfold growth are the horizons that actually correspond to a working life, and the years between them are not intuitive from the doubling time alone.

What it assumes

A single constant rate applied without interruption, no contributions, no withdrawals, no costs and no tax. It is arithmetic about compounding rather than a projection of a portfolio, which is precisely what makes it useful as a mental model — and precisely why it should not be used as a plan. Nothing is adjusted for inflation, so a doubling in nominal terms is a considerably smaller gain in what the money will buy.

Common questions

How accurate is the rule of 72?: Very, in the range that matters. It is most accurate around eight percent and drifts at the extremes: at seven percent it gives 10.29 years against an exact 10.24, an error of a few weeks. At very low rates the gap widens — at two and a half percent the shortcut says 28.8 years and the exact answer is 28.1. The table always uses the exact formula, so the approximation never leaks into the numbers.
Why does it use 72 rather than 69 or 70?: Because the mathematically exact numerator for continuous compounding is about 69.3, and 72 was chosen instead for being divisible by 2, 3, 4, 6, 8, 9 and 12, which makes the division doable in your head. The small upward adjustment also happens to compensate for annual rather than continuous compounding at moderate rates, which is why it is more accurate than the exact constant would be for this use.
What is the practical point of a doubling time?: It converts a rate into a unit people reason about, which is time. A deposit at two and a half percent doubles in about 28 years and a long-run equity return doubles in about 10, and that comparison lands harder than the difference between two percentages does. It is the same argument the emergency fund and purchasing power pages make with euros instead of years.

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Rule of 72 — doubling time at any rate of return