Rule of 72 calculator
Enter an annual return to see how many years it takes to double using the rule of 72, 70 and 69.3, next to the exact figure. Or enter a number of years to see the rate you need.
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How to use it
- Choose whether you want the years to double or the rate needed.
- Enter the rate, or the number of years.
- Compare the three rules with the exact value.
- Exact years to double = ln 2 ÷ ln(1 + r), with r the rate as a fraction
- Exact rate needed = (2^(1 ÷ years) − 1) × 100
- Rules: 72 ÷ r, 70 ÷ r and 69.3 ÷ r (and the same divided by years for the rate)
Worked example
At 8%: exact 9.006 years; rule of 72 gives 9; rule of 70 gives 8.75; rule of 69.3 gives 8.6625. To double in 10 years you need 2^0.1 − 1 = 7.177%; the rule of 72 says 7.2%.
Good to know
The rule assumes the rate stays the same and returns are reinvested. It says nothing about taxes or fees, which lower the real rate.
Frequently asked questions
What is the rule of 72?
A shortcut: divide 72 by the yearly return in percent to get the years it takes to double. At 8% that is 72 ÷ 8 = 9 years. The exact answer, ln 2 ÷ ln(1.08), is 9.006 years.
Why 72 and not 70 or 69.3?
The exact doubling time is ln 2 ÷ ln(1 + r). For small rates, 69.3 ÷ r is closest (ln 2 = 0.693). 72 has many divisors, so it is easy to use in your head and is accurate around 8%. 70 is a compromise at lower rates.
How accurate is it at high or low rates?
Very accurate between about 6% and 10%. At 1% the exact time is 69.66 years, so 72 overstates it by 2.3 years; at 30% the exact time is 2.64 years but 72 ÷ 30 gives 2.4.
Does it work for inflation and debt?
Yes. At 3% inflation prices double in about 24 years (72 ÷ 3), and a debt growing at 18% doubles in about 4 years. It assumes steady annual compounding.