Rule of 72 Calculator
The oldest shortcut in finance: divide 72 by your rate and you get the years to double your money. Check the estimate against the exact answer — and see the doublings stack up on a chart.
▸ Rule vs. exact, rate by rate
| Rate | Rule of 72 | Exact | Error |
|---|
Estimates are for illustration and education only — not financial advice. A constant annual rate is assumed.
Why 72, and how accurate is it?
The exact doubling time is ln(2) ÷ ln(1 + r) — not something you do in your head. The rule of 72 replaces it with 72 ÷ rate, and it works because ln(2) ≈ 0.693, scaled slightly upward to correct for compounding. 72 is also conveniently divisible by 2, 3, 4, 6, 8, 9 and 12, which is why it beat the technically-closer "rule of 69.3" in popularity.
Where it's sharp — and where it drifts
The rule is remarkably accurate between about 4% and 12% — within a couple of months of the true answer. At very low rates it slightly overestimates the time; at high rates it underestimates. The table above shows the error rate by rate; for everyday planning the rule is more than good enough.
Doublings are what matter
The powerful reframe: a 40-year investing life at 7% contains about four doublings — $10,000 becomes $160,000 without a single extra deposit. Each extra doubling doubles the final result, which is why starting one doubling-period earlier (about 10 years at 7%) matters more than almost any other decision.
It works for inflation too
Divide 72 by the inflation rate to see how fast prices double — or purchasing power halves. At 3% inflation that's every ~24 years. See it in detail in our inflation calculator, or model the full growth picture in the compound interest calculator.
Doubling times worth memorizing
Five numbers that make you faster than a calculator in most money conversations.
| Rate | Doubles in | Typical of |
|---|---|---|
| 2% | 36 years | Inflation target / cautious bonds |
| 3% | 24 years | Long-run US inflation |
| 4% | 18 years | High-yield savings, good years |
| 7% | 10 years | Stock market, real long-run average |
| 10% | 7 years | Stock market, nominal long-run average |
Rounded rule-of-72 figures; historical averages are not guarantees of future returns.
Why 72 works
The Rule of 72 is a mental shortcut for how long money takes to double. Divide 72 by the annual return and you get the doubling time — remarkably close to the exact logarithmic answer.