Rule of 72 Calculator
Last verified · Methodology
Find your doubling time, check it against the exact answer, and see where the shortcut stops being reliable.
What do you want to find?
The rule is most accurate between about 6% and 10%.
Optional. Only used to show what the doublings look like in dollars.
Years to double at 7%
10.3
72 divided by 7 is 10.3 years. The exact answer is 10.24 years, so the rule is off by 0.04 years here.
Rule of 72 estimate
10.3 yr
The mental shortcut
Exact answer
10.24 yr
Using logarithms
What $25,000 becomes at 7.0%
| Doublings | Years | Value |
|---|---|---|
| Start | 0 | $25,000 |
| 1x doubled | 10.3 | $50,000 |
| 2x doubled | 20.6 | $100,000 |
| 3x doubled | 30.9 | $200,000 |
| 4x doubled | 41.1 | $400,000 |
| 5x doubled | 51.4 | $800,000 |
How accurate is the rule?
The approximation is tuned for mid single-digit rates and drifts at the extremes.
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 1% | 72.0 | 69.66 | +2.34 yr |
| 2% | 36.0 | 35.00 | +1.00 yr |
| 4% | 18.0 | 17.67 | +0.33 yr |
| 6% | 12.0 | 11.90 | +0.10 yr |
| 8% | 9.0 | 9.01 | -0.01 yr |
| 10% | 7.2 | 7.27 | -0.07 yr |
| 15% | 4.8 | 4.96 | -0.16 yr |
| 20% | 3.6 | 3.80 | -0.20 yr |
| 25% | 2.9 | 3.11 | -0.23 yr |
What is the Rule of 72?
The Rule of 72 is the most useful piece of mental arithmetic in personal finance. Divide 72 by an annual growth rate and you get the number of years it takes for the amount to double.
72 ÷ 8 = 9 years
rate needed ≈ 72 ÷ years available
72 ÷ 10 = 7.2%
It works because compound growth is exponential, and the logarithm of 2 multiplied by 100 is 69.3. The number 72 is close enough while being far easier to divide, since it splits cleanly by 2, 3, 4, 6, 8, 9, and 12.
Where it is accurate and where it is not
The rule is calibrated for mid single-digit to low double-digit rates. Inside that band it is accurate to a rounding error. Outside it, the approximation drifts in a predictable direction: it overestimates the time at very low rates and underestimates it at very high ones.
| Rate | Rule of 72 | Exact | Verdict |
|---|---|---|---|
| 2% | 36.0 yr | 35.0 yr | Slightly pessimistic |
| 6% | 12.0 yr | 11.9 yr | Excellent |
| 8% | 9.0 yr | 9.0 yr | Essentially exact |
| 10% | 7.2 yr | 7.3 yr | Excellent |
| 25% | 2.9 yr | 3.1 yr | Noticeably optimistic |
Three ways to use it
Investment growth
At a 7% real return, money doubles in purchasing power roughly every 10 years. A 30 year old with $100,000 invested reaches about $800,000 in today's dollars by 60 through three doublings, with no further contributions at all. This is the arithmetic behind Coast FIRE.
Inflation
At 3% inflation, prices double every 24 years. That reframes retirement planning: a $60,000 annual budget at 40 becomes a $120,000 budget by 64 for the identical lifestyle. It is the clearest argument for planning in real rather than nominal terms.
Fees and debt
A 1% expense ratio does not sound like much until you notice it consumes an entire doubling every 72 years of your investing life. On the debt side, a 24% credit card doubles the balance in three years if you stop paying, which is why high-interest debt usually comes before investing in any sensible order of operations.
When you need a real projection
For actual projections rather than mental shortcuts, use the compound interest calculator, which handles contributions and variable timelines. To see doubling applied to a retirement target, try the Coast FIRE calculator or the investment calculator.
The Rule of 72 is a mental shortcut for finding how long an investment takes to double. Divide 72 by the annual return rate and the answer is the number of years. At 8% a year, money doubles in about 9 years. At 6%, about 12 years. It works in reverse too: divide 72 by the years you have and you get the rate you need.
Very accurate between about 6% and 10%, where the error is under a tenth of a year. It drifts at the extremes. At 2% the rule says 36 years while the exact answer is 35.0, and at 25% it says 2.88 years while the true figure is 3.11. For mental arithmetic in the range most portfolios actually return, the error is not large enough to matter.
The mathematically exact numerator is 69.3, which comes from the natural logarithm of 2 multiplied by 100. But 72 is chosen because it divides evenly by 1, 2, 3, 4, 6, 8, 9, and 12, which makes the mental arithmetic far easier. Some practitioners use the Rule of 70 for continuous compounding and the Rule of 69.3 when precision matters more than convenience.
Yes, and it is arguably more useful there. At 3% inflation, prices double in about 24 years, meaning something costing $100 today costs $200 by then. Apply it to fees the same way: a 1% annual expense ratio consumes a doubling of your money every 72 years, which sounds harmless until you compare it against a 0.03% index fund.
Yes, and it is sobering. A credit card at 24% APR doubles the balance in about 3 years if you make no payments. At 18% it takes about 4 years. The same compounding that builds wealth on the investing side works against you here, which is why high-interest debt usually outranks investing in the order of operations.
Use a real return, meaning after inflation, if you want the answer in today's purchasing power. The S&P 500 has returned roughly 10% nominally and about 7% after inflation over the long run. At 7% real, money doubles in purchasing power roughly every 10 years. At 10% nominal it doubles in about 7 years, but those dollars buy less.
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