Rule of 72 Calculator
How long to double your money? Divide 72 by your annual return rate. Find the doubling time, the rate needed to double by a target date, or compare the Rule of 72 against the exact formula.
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How to Use This Calculator
Tab "Years to Double"
Enter an annual interest or growth rate (e.g., 8%). The calculator divides 72 by that rate to estimate the number of years until your money doubles. It also shows the exact answer using the compound-interest formula and the Rule of 69.3 for comparison.
Tab "Rate to Double By"
Enter a target number of years (e.g., 6 years). The calculator divides 72 by that number to tell you the annual return you need. Useful for setting investment goals: "I want to double my savings in 5 years — what return do I need?"
Tab "Exact vs Rule of 72"
Enter any rate and see a side-by-side comparison of the Rule of 72 estimate, the exact compound-interest answer, and the Rule of 69.3. A full accuracy table shows how the approximation performs at rates from 1% to 72%, highlighting where it is most and least accurate.
The Formulas
Years ≈ 72 / Rate%
Exact doubling time (annual compounding):
Years = ln(2) / ln(1 + r/100)
Reverse — required rate:
Rate% ≈ 72 / Years
Rule of 69.3 (continuous compounding):
Years ≈ 69.3 / Rate%
Why 72?
ln(2) ≈ 0.6931, which rounds to 69.3. But 72 has more divisors (1, 2, 3, 4, 6, 8, 9, 12) making mental math far easier, and the slight upward adjustment compensates for the discrete compounding effect.
All calculations assume a fixed annual compound rate. No taxes, fees, or inflation are applied. The Rule of 72 is most accurate between 6% and 10%.
Worked Examples
Example 1 — Stock market at 8% return
You invest in an index fund earning 8% per year. How long until your investment doubles?
At 8%, the Rule of 72 is almost perfectly accurate. $10,000 invested today becomes $20,000 in about 9 years.
Example 2 — Double in 6 years: what rate?
You want to double your savings in 6 years. What annual return do you need?
You need roughly a 12% annual return. That is achievable historically with aggressive equity investing but above average for balanced portfolios.
Example 3 — Accuracy at various rates
How does the Rule of 72 compare to the exact formula across different rates?
The sweet spot is 6–10%. At very low or very high rates, the approximation drifts further from the exact answer. For rates above 20%, use the exact formula.
Understanding the Rule of 72
What Is the Rule of 72?
The Rule of 72 is a shortcut for estimating how long it takes for an investment to double in value at a given fixed annual rate of return. Divide 72 by the interest rate, and you get the approximate number of years. It works because of the mathematics of compound growth.
When to Use It
Use the Rule of 72 whenever you need a quick mental estimate. Common scenarios include: evaluating investment options, understanding the impact of inflation on purchasing power, comparing savings accounts, or setting financial goals. It is fast enough to do in your head during a conversation.
Beyond Investments
The rule applies to any exponential growth: population growth, GDP growth, inflation erosion, bacteria reproduction, or even credit card debt accumulation. At 3% inflation, your purchasing power halves in about 72 / 3 = 24 years.
Limitations
The Rule of 72 assumes: (1) a fixed, constant rate of return, (2) annual compounding, (3) no withdrawals or additional deposits. Real investments fluctuate. It also becomes less accurate at extreme rates — below 2% or above 20%. For precise planning, use the exact formula or the "Exact vs Rule of 72" tab.