Rule of 72 Calculator
Enter a yearly growth rate to see roughly how many years it takes an investment to double.
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Formula
- Rule of 72:
years to double ≈ 72 ÷ yearly rate (%) - Exact:
years = ln(2) ÷ ln(1 + rate ÷ 100)
The rule assumes the growth compounds once a year and nothing is added or taken out. It is an estimate, and the gap to the exact figure grows at very high or very low rates.
Worked example
At 8% a year:
- Rule of 72: 72 ÷ 8 = 9 years
- Exact: ln(2) ÷ ln(1.08) = 0.693147 ÷ 0.076961 = 9.01 years
- The difference is 0.01 years.
Frequently asked questions
What is the rule of 72?
It is a shortcut: divide 72 by the yearly growth rate in percent to estimate the years needed to double your money. At 8% that is 72 ÷ 8 = 9 years.
How accurate is it?
It is closest for rates between about 6% and 10%. The exact time is ln(2) ÷ ln(1 + rate). At 8% that is 9.01 years, and at 6% it is 11.9 years against 12 by the rule.
Can I use it for inflation or debt?
Yes. Any quantity growing at a fixed percentage doubles on the same schedule. At 3% inflation prices double in about 72 ÷ 3 = 24 years, and a debt growing at 18% doubles in about 4 years.
Why 72 and not 70 or 69?
72 has many whole-number divisors (2, 3, 4, 6, 8, 9, 12), so the mental maths is easy, and it fits typical rates well. 69.3 is more exact for very small rates, and 70 is a common alternative.