Rule of 72 Calculator
How long money takes to double.
Reviewed by the Calculation Machine team · Updated 24 October 2026 · How we check our maths
Your values
ⓘ Live results
- Years to double (rule of 72)
- 9
- Exact years
- 9.01
- Value after doubling
- $20,000.00
- Value in 20 years
- $46,609.57
- Doublings in 30 years
- 3.33
Quick answer
The rule of 72 says money doubles in roughly 72 ÷ annual rate years. At 8% a year, 72 ÷ 8 = 9 years; the exact compound-interest answer is 9.01 years. It works in reverse too: to double in 6 years you need about 72 ÷ 6 = 12% a year. The shortcut is most accurate between about 6% and 10%.
What the Rule of 72 calculator does
This calculator applies the rule of 72 to your rate of return and puts the exact doubling time beside it, worked out with logarithms. Add a starting amount to see what it doubles to, what it grows to in 20 years, and how many doublings fit into 30 years.
Investors use the rule to sanity-check growth assumptions, compare savings rates, and see the effect of fees or inflation. It also works for anything that grows at a steady percentage: prices under inflation, debt left unpaid, or a population. At 3% inflation, prices double in about 24 years; on a credit card at 24%, an unpaid balance doubles in about 3 years.
The rule assumes a constant rate compounded once a year. Real investment returns vary year to year, so treat the result as a guide. For contributions over time or an exact balance, use the compound interest calculator or the future value calculator.
The formula
Years to double ≈ 72 ÷ R (exact: t = ln 2 ÷ ln(1 + R/100))
| Symbol | Meaning | Unit |
|---|---|---|
| R | Annual rate of return or growth, entered as a whole-number percentage (8 for 8%) | % |
| t | Exact number of years to double with annual compounding | years |
| ln 2 | Natural logarithm of 2, about 0.693 | — |
The rule comes from the exact doubling formula: ln 2 ≈ 0.693, so continuous compounding gives 69.3 ÷ R. The number 72 is used instead because it corrects for annual compounding at typical rates and divides evenly by 2, 3, 4, 6, 8, 9 and 12. The idea appears in Luca Pacioli's 1494 *Summa de arithmetica*. This page also covers searches for a doubling time calculator — the 'exact years' result is the precise doubling time for any growth rate.
Worked examples
Long-run stock market return
$10,000 invested in a diversified fund assumed to return 8% a year.
Inputs
- Annual return8 %
- Starting amount10000 $
Result
- Years to double (rule of 72)9
- Exact years9.01
- Value after doubling$20,000.00
- Value in 20 years$46,609.57
- Doublings in 30 years3.33
The rule gives 9 years and the exact answer is 9.01, so the shortcut is almost perfect here. The $10,000 grows to about $46,600 in 20 years, which is a little over two doublings.
High-yield savings or bond return
$25,000 in savings or bonds earning 4% a year.
Inputs
- Annual return4 %
- Starting amount25000 $
Result
- Years to double (rule of 72)18
- Exact years17.67
- Value after doubling$50,000.00
- Value in 20 years$54,778.08
- Doublings in 30 years1.7
About 18 years to double (17.67 exact). In 30 years the money doubles only 1.7 times, so low-risk savings alone rarely build long-term wealth after inflation.
Inflation at 2.5%
Using the rule to see how long prices take to double if inflation averages 2.5%. The starting amount stands for $10,000 of today's prices.
Inputs
- Annual return2.5 %
- Starting amount10000 $
Result
- Years to double (rule of 72)28.8
- Exact years28.07
- Value after doubling$20,000.00
- Value in 20 years$16,386.16
- Doublings in 30 years1.07
Prices double in roughly 28 years at 2.5% inflation, so $10,000 of spending today would cost about $20,000 by then. The inflation calculator gives the exact purchasing-power figures.
Rule of 72 accuracy at different rates
The rule is almost exact near 8% and drifts at the extremes. At low rates, 69 or 70 is closer; at high rates, the rule underestimates.
| Annual rate | Rule of 72 | Rule of 70 | Exact |
|---|---|---|---|
| 2% | 36.0 | 35.0 | 35.00 |
| 3% | 24.0 | 23.3 | 23.45 |
| 4% | 18.0 | 17.5 | 17.67 |
| 6% | 12.0 | 11.7 | 11.90 |
| 8% | 9.0 | 8.8 | 9.01 |
| 10% | 7.2 | 7.0 | 7.27 |
| 12% | 6.0 | 5.8 | 6.12 |
| 20% | 3.6 | 3.5 | 3.80 |
Rule of 69, 70 and 72: which to use
- Rule of 72: the standard for annual returns between about 6% and 10% — stock returns, mortgage rates, long-run savings.
- Rule of 70: slightly better below about 4%, which is why economists use it for GDP and population growth.
- Rule of 69.3: exact for continuous compounding at any rate.
- High rates: above about 15%, add 1 to the numerator for every 3 points above 8% (for 20%, use 76 ÷ 20 = 3.8).
For halving rather than doubling — the effect of inflation on cash or a falling asset — the same rule applies: at 3% inflation, purchasing power halves in about 24 years.
Using the rule backwards
Divide 72 by the number of years to find the rate you need. To double a down-payment fund in 5 years you would need about 14.4% a year — a sign that the goal needs higher savings, not just higher returns.
The same trick shows the cost of fees. A fund returning 7% doubles in about 10.3 years; after a 1% fee, 72 ÷ 6 = 12 years. Over 36 years that is roughly 3 doublings instead of 3.5, a meaningful gap in the final balance.
How to use the Rule of 72 Calculator
- 1Enter the expected annual return or growth rate as a percentage — 7 for 7%, not 0.07.
- 2Optionally enter a starting amount to see the doubled value and the value after 20 years.
- 3Compare 'Years to double (rule of 72)' with 'Exact years' — a large gap means your rate is outside the rule's sweet spot.
- 4Use 'Doublings in 30 years' to see long-term growth at a glance: 3 doublings multiply the money by 8.
Frequently asked questions
How long does it take to double money at 7%?
About 10.3 years by the rule of 72 (72 ÷ 7), and 10.24 years exactly with annual compounding.
Why is it 72 and not 70?
72 gives closer answers at typical investment rates of 6–10% with annual compounding, and it divides evenly by many small numbers. The rule of 70 is slightly better at low rates such as inflation or economic growth.
Does the rule of 72 work for debt?
Yes. An unpaid credit card balance at 24% interest doubles in about 3 years (72 ÷ 24), which shows why carrying high-rate debt is so costly.
Does the rule of 72 account for contributions?
No. It describes a single lump sum growing at a fixed rate. Regular deposits make a balance grow faster than the rule suggests; use a future value or compound interest calculator for that.
What return do I need to double my money in 10 years?
About 7.2% a year (72 ÷ 10). The exact figure with annual compounding is about 7.18%.
References
- Investor.gov – saving and investing basics — US Securities and Exchange Commission, Office of Investor Education and Advocacy
- Summa de arithmetica, geometria, proportioni et proportionalità (1494) — Luca Pacioli
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Last reviewed: October 24, 2026
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