Rule of 72 Calculator
Rule of 72 Calculator
Estimate Doubling Time or Required Rate
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Years to Double
Enter a rate or timeframe to see the estimate.
Understanding the Rule of 72
The Rule of 72 is a mental-math shortcut for estimating how long it takes an investment to double at a fixed annual rate of return, without needing a calculator or logarithms -- just divide 72 by the rate.
The Formula
Years to double ≈ 72 ÷ annual rate (%). At 8% growth, money roughly doubles in 72 ÷ 8 = 9 years.
72, 114, and 144
The same shortcut extends further: divide by 114 to estimate tripling time, and by 144 to estimate quadrupling time.
An Approximation
72 is a convenient round number chosen because it divides evenly by many common rates (6, 8, 9, 12). The true exact answer is ln(2) / ln(1 + rate), which the Rule of 72 approximates closely for rates between roughly 6% and 10%.
Works in Reverse Too
If you instead know how many years you have and want to double your money, divide 72 by the years to find the annual rate you'd need.
Worked Example
Suppose your investments grow at an average of 8% per year:
- Time to double: 72 / 8 = 9 years.
- Time to triple: 114 / 8 ≈ 14.25 years.
- Time to quadruple: 144 / 8 = 18 years (simply double the doubling time).
At 8% Annual Growth
- Double: 9.0 years
- Triple: 14.25 years
- Quadruple: 18.0 years
Want the Exact Future Value Instead?
The Rule of 72 is a fast mental estimate, not an exact projection -- for a precise future balance from a starting amount, rate, and contribution schedule, use the Compound Interest Calculator or Investment Calculator.
Key Takeaways
- Quick Mental Math: No calculator needed -- just divide 72 by the rate.
- Most Accurate Near 8%: The approximation is closest for rates roughly between 6% and 10%.
- Works Both Ways: Solve for doubling time given a rate, or the required rate given a timeframe.
- An Estimate, Not a Guarantee: Real investment returns vary year to year -- this assumes a constant average rate.