Rule of 72 Calculator
Estimate how long it takes to double your investment using the Rule of 72. Divide 72 by your annual return rate to get years to double — or work backwards from a target number of years to find the required rate.
Years to Double (Rule of 72)
9.0 yrs
Exact calculation
9.01 yrs
Compound formula
Rule of 72 vs 69.3 (continuous compounding)
Quick Reference
What is the Rule of 72?
The Rule of 72 is a simple mental math shortcut for estimating compound growth. Divide 72 by the annual interest rate to get the approximate number of years it takes for an investment to double. At 6% annual return, money doubles in 72 ÷ 6 = 12 years. At 9%, it doubles in 8 years.
The rule works because 72 is close to 69.3, which is 100 × ln(2) — the mathematically exact divisor for continuous compounding. For periodic compounding (which most investments use), 72 is slightly more accurate than 69.3 in the typical 6–10% range.
How accurate is the Rule of 72?
The rule is most accurate between 6% and 10% annual return. At lower rates (2–3%) it slightly overestimates the doubling time; at higher rates (20%+) it underestimates. The exact calculation uses the formula t = ln(2) / ln(1 + r), where r is the decimal rate. This calculator shows both the Rule of 72 estimate and the exact value.
Can I use it for inflation or debt?
Yes. The Rule of 72 applies to any exponential growth. At 3% inflation, prices double in 24 years. At 20% APR on a credit card with no payments, the debt doubles in 3.6 years. It's a powerful way to make abstract rates of change concrete and intuitive.
Rule of 72 vs Rule of 69.3
The Rule of 69.3 is mathematically exact for continuous compounding. Banks and financial models that compound continuously use 69.3. For everyday investments that compound annually or monthly, 72 is often more accurate and much easier to divide mentally — it's divisible by 2, 3, 4, 6, 8, 9, and 12.
