Rule of 72 Calculator
Estimate how long money takes to double at a given return — and check the shortcut against the exact maths.
Your details
Details
This calculator runs entirely on your device. Nothing you enter is uploaded, stored, or sold. How this works
Years to double
10.3 yrs
The exact answer is 10.24 years — the shortcut is off by 0.04 years
Includes your inputs, the full breakdown, and every row of the table.
Rule of 72 estimate
10.3 yrs
Exact doubling time
10.24 yrs
Quadruples in
20.5 yrs
10× in
34.0 yrs
| Multiple | Balance | Time |
|---|---|---|
| 2× | $50,000 | 10.2 yrs |
| 4× | $100,000 | 20.5 yrs |
| 8× | $200,000 | 30.7 yrs |
| 16× | $400,000 | 41.0 yrs |
| 32× | $800,000 | 51.2 yrs |
What this means
- Divide 72 by the annual return to estimate doubling time. It works because the natural logarithm of 2 is about 0.693, and 69.3 is close to 72 while being far less convenient to divide by.
- 72 is chosen for its divisors — 2, 3, 4, 6, 8, 9, and 12 all divide cleanly, which is what makes it usable in your head.
How the rule of 72 calculation works
The rule of 72 is the single most useful piece of mental arithmetic in personal finance. Divide 72 by an annual percentage return and you get a close estimate of how many years it takes to double your money. At 8%, that is nine years; at 6%, twelve.
It also runs in reverse, and that is where it becomes uncomfortable. Divide 72 by an inflation rate to see how fast prices double, or by a credit card's interest rate to see how fast a balance you never pay grows.
The shortcut is most accurate in the 6% to 10% range and drifts at the extremes. At very high rates it understates the time required, which this page shows by putting the exact logarithmic answer alongside the estimate.
Frequently asked questions
Why 72 and not 69.3?
69.3 is mathematically correct but awkward. 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12, which is the entire point of a mental shortcut.
When does the rule break down?
Above roughly 15% or below 3% the error grows noticeably. This calculator shows the exact figure alongside the estimate so you can see the gap.
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Disclaimer. This calculator is provided for general information and educational purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Results are estimates based on the inputs you provide and the assumptions described above. Confirm any figure with a qualified professional before acting on it.