⏳ Rule of 72 Calculator
Enter an annual rate and the Rule of 72 estimates the doubling time, shown alongside the Rule of 70 and the exact figure.
Rule of 72
9 yrs
to double
Rule of 70
8.75 yrs
Exact
9.01 yrs
ln2 ÷ ln(1+r)
The Rule of 72 estimates the doubling time: years ≈ 72 ÷ rate. It’s most accurate near 8%; the exact figure is ln2 ÷ ln(1+rate). Educational, not advice. 🔒 In your browser.
How the rule of 72 calculator works
The Rule of 72 is a mental-math shortcut: divide 72 by the annual percentage rate to estimate the years to double your money. It works because the exact doubling time is ln(2) ÷ ln(1 + rate), and near typical rates ln(2) ≈ 0.693 combined with the rate approximation lands close to 72/rate, the slightly rounded-up 72 is chosen because it divides cleanly by many whole numbers. The tool also shows the Rule of 70 (often used for continuous growth) and the exact doubling time. Worked example: at 6%, the Rule of 72 gives 72 ÷ 6 = 12 years, while the exact figure ln(2) ÷ ln(1.06) is about 11.9 years.
The Rule of 72 is most accurate around 6-10%; far from that range the exact figure diverges. Educational, not financial advice.
Frequently asked questions
What is the Rule of 72?
A shortcut for estimating how long an investment takes to double: years ≈ 72 ÷ annual percentage rate. At 8%, money doubles in about 72 ÷ 8 = 9 years.
How accurate is the Rule of 72?
Very close around 6-10%. Outside that range, use the Rule of 70 or 69.3, or the exact formula ln(2) ÷ ln(1 + rate), which the tool also shows.
Why 72 and not 70?
72 has many small divisors (2, 3, 4, 6, 8, 9, 12), making the mental division easy, and it’s a good approximation for annual compounding. 70 is closer for continuous compounding.
Can I use it for inflation?
Yes, dividing 72 by an inflation rate estimates how long until prices double (or your money’s purchasing power halves).
What is the exact doubling time?
ln(2) ÷ ln(1 + rate). At 8% that’s about 9.01 years, very close to the Rule of 72’s estimate of 9.
Can I use the Rule of 72 to find a required rate?
Yes, rearrange it to rate ≈ 72 ÷ years. To double your money in 8 years you need roughly a 9% annual return (72 ÷ 8), a quick way to sanity-check a savings or investment target.
How long to triple or quadruple money?
Tripling uses a rule of about 114 (114 ÷ rate) and quadrupling is simply two doublings, so about 144 ÷ rate. At 8%, money roughly doubles in 9 years, triples in about 14, and quadruples in about 18.
Educational information, not financial advice. These calculators use standard formulas with the figures you enter; results are illustrations, not guarantees. For decisions about your money, consult a qualified, regulated financial professional.