Home › Calculators › Rule of 72 Calculator
Rule of 72 Calculator
Estimate how long it takes an investment, a debt or prices to double. Enter a rate to get the years, or enter the years to get the rate you need, and compare the quick rule of 72 with the rules of 70 and 69.3 and the exact answer.
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%
years
Enter your values to see the result.
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How to use the Rule of 72 Calculator
- Choose what to solve for: years to double or the rate needed.
- Enter the annual rate (or the number of years).
- Pick the compounding used for the exact answer.
- Press Calculate to compare the rules with the exact doubling time and see the reference table.
Rule of 72 formula
- Years to double ≈ 72 ÷ annual rate (%)
- Rate needed ≈ 72 ÷ years
- Exact, annual compounding: years = ln 2 ÷ ln(1 + r)
- Exact, continuous compounding: years = ln 2 ÷ r ≈ 69.3 ÷ rate
The rule works because ln 2 ≈ 0.693 and ln(1 + r) is a little less than r. Rounding 69.3 up to 72 compensates for annual compounding at typical rates and gives a number that is easy to divide in your head.
Rule of 72 vs. exact doubling time
Exact values assume annual compounding.
| Rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact years |
|---|---|---|---|---|
| 2% | 36.00 | 35.00 | 34.65 | 35.00 |
| 3% | 24.00 | 23.33 | 23.10 | 23.45 |
| 4% | 18.00 | 17.50 | 17.32 | 17.67 |
| 5% | 14.40 | 14.00 | 13.86 | 14.21 |
| 6% | 12.00 | 11.67 | 11.55 | 11.90 |
| 7% | 10.29 | 10.00 | 9.90 | 10.24 |
| 8% | 9.00 | 8.75 | 8.66 | 9.01 |
| 9% | 8.00 | 7.78 | 7.70 | 8.04 |
| 10% | 7.20 | 7.00 | 6.93 | 7.27 |
| 12% | 6.00 | 5.83 | 5.77 | 6.12 |
| 15% | 4.80 | 4.67 | 4.62 | 4.96 |
| 20% | 3.60 | 3.50 | 3.46 | 3.80 |
The rule of 72 is almost exact around 8%; at 2% the rule of 70 is closer, and at 20% the rule of 72 underestimates the time slightly.
Frequently asked questions
What is the rule of 72?
The rule of 72 is a shortcut to estimate how long money takes to double: divide 72 by the annual percentage rate. At 8% a year, 72 ÷ 8 = 9 years. The exact answer with annual compounding is 9.01 years.
How accurate is the rule of 72?
It is very close for rates between about 6% and 10% with annual compounding. At low rates it slightly overestimates the time and at high rates it underestimates it. The table on this page shows the error at common rates.
What is the difference between the rule of 72, 70 and 69.3?
They use different numerators. 69.3 (from ln 2 ≈ 0.693) is exact for continuous compounding, 70 works well for low rates such as inflation or GDP growth, and 72 is popular because it divides evenly by 2, 3, 4, 6, 8, 9 and 12 and fits annual compounding at typical rates.
What is the exact formula for doubling time?
With annual compounding, years = ln(2) ÷ ln(1 + r). With m compounding periods per year it is ln(2) ÷ (m × ln(1 + r/m)), and with continuous compounding ln(2) ÷ r.
Can I use the rule of 72 for inflation or debt?
Yes. At 3% inflation prices double in about 24 years, so money loses half its buying power in that time. A credit card balance at 24% interest doubles in about 3 years if nothing is paid.
What are the rules of 114 and 144?
They are the same idea for tripling and quadrupling: divide 114 by the rate to estimate the years to triple, and 144 to quadruple.
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