Rule of 72 Calculator
How long money takes to double at a given rate — the mental shortcut, and the exact answer beside it.
Divide 72 by the annual percentage rate and you get the doubling time in years.
How the rule of 72 calculator works
Divide 72 by the annual percentage rate and you get the doubling time in years. At 8%, money doubles in about nine years. It is the most useful piece of mental arithmetic in finance.
It works because ln(2) is 0.693, and dividing by ln(1+r) rather than r introduces an error that 72 happens to cancel neatly over the range that matters. The approximation is at its best between 6% and 10%, where it is accurate to under a tenth of a year. Below 3% and above 20% it drifts, and this page shows the exact figure so you can see by how much.
72 is chosen partly because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12. Purists use 69.3 for continuous compounding and 70 for a general approximation.
Formula: years ≈ 72 / rate%; exact: ln(2) / ln(1 + r)
Worked examples
| Inputs | Doubling time (rule of 72) | Note |
|---|---|---|
| 8% a year | 9 years | about 9 years, exactly 9.01 |
| 2% — where the rule drifts | 36 years | 36 years by the rule, 35.0 exactly |
| 24% — drifts the other way | 3 years | 3 years by the rule, 3.22 exactly |
FAQFrequently asked questions
What is the rule of 72?
Divide 72 by the annual percentage rate to get the number of years for money to double. At 8%, about nine years.
How accurate is it?
Within a tenth of a year between about 6% and 10%. It drifts at very low and very high rates, which is why the exact figure is shown beside it.
Why 72 and not 69?
69.3 is the mathematically correct constant for continuous compounding, but 72 divides cleanly by more numbers and is more accurate for annual compounding at ordinary rates.
What is the rule for tripling?
Divide 114 by the rate. The same idea, with ln(3) in place of ln(2).
Does it work for inflation?
Yes — 72 divided by the inflation rate gives roughly how long until prices double, which is the same arithmetic in reverse.
Where these figures come from
- CFA Institute — Quantitative Methods: The Time Value of Money — the discounting, annuity and IRR conventions used here
- US Federal Reserve — Regulation Z (Truth in Lending), APR calculation — why APR includes fees where a nominal rate does not
- MoneyHelper (UK Government-backed) — the UK's free money guidance service
Last checked: September 2026. These are the standard textbook formulas; the conventions named are those of the CFA Institute curriculum and ISO 80000 usage.