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Finance Calc Kit
Investments

Rule of 72 Calculator

Calculate how long it takes for your investment to double using the Rule of 72.

%

Approximate years to double

9.0 years

At 8.0% annual return using the Rule of 72

Exact doubling time

9.01 years

Using ln(2) / ln(1 + r) with annual compounding

Formula summary

Rule of 72: 72 / 8 = 9.0 years. Exact: ln(2) / ln(1 + 0.0800) = 9.01 years.

How the Rule of 72 works

Compare the quick mental math shortcut with the exact compound growth formula.

  1. Rule of 72 approximation

    Years to double≈728=9.00 years\text{Years to double} \approx \frac{72}{8} = 9.00\text{ years}

    At 8.0% annual return, the Rule of 72 estimates your investment doubles in about 9.0 years.

  2. Exact logarithmic calculation

    T=ln⁡(2)ln⁡(1+r)=9.01 yearsT = \frac{\ln(2)}{\ln(1 + r)} = 9.01\text{ years}

    The exact formula uses natural logarithms and annual compounding at the stated rate.

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What is the Rule of 72?

The Rule of 72 is a quick mental math shortcut that estimates how long an investment takes to double at a fixed annual return, or what return is needed to double in a given number of years. It is widely taught in personal finance because it turns compound growth into a simple division problem.

Use rate-to-years mode when you know your expected return and want a doubling timeline. Use years-to-rate mode when you have a savings goal and need the required growth rate. For exact logarithmic doubling time with additional compounding options, try the doubling time calculator and the compound interest calculator.

Rule of 72 formulas

To estimate years to double from an annual percentage return RR:

Years to double≈72R\text{Years to double} \approx \frac{72}{R}

To estimate the required return to double in YY years:

Required return≈72Y\text{Required return} \approx \frac{72}{Y}

The exact doubling time with annual compounding uses natural logarithms:

T=ln⁡(2)ln⁡(1+r)T = \frac{\ln(2)}{\ln(1 + r)}

Solving for the exact rate when you know the doubling period uses:

r=21/Y−1r = 2^{1/Y} - 1

Worked example

At 8% annual return, the Rule of 72 gives 72 / 8 = 9 years to double. The exact formula produces about 9.01 years. The shortcut is close enough for quick planning at typical stock-market return assumptions.

When the Rule of 72 is most accurate

  • Best for annual returns between about 6% and 10%, where the approximation error is usually under 1%.
  • Less accurate for very low or very high rates, where the exact logarithmic formula is better.
  • Assumes a constant rate and annual compounding. Real portfolios fluctuate year to year.

Frequently asked questions

Why use 72 instead of 70 or 69.3?
72 is a convenient composite number that divides evenly by many common return rates. The Rule of 70 works better for low inflation rates, while 69.3 is the continuous-compounding approximation.
Does the Rule of 72 include additional contributions?
No. It estimates doubling time for a lump sum at a fixed rate. Recurring contributions require a compound growth calculator instead.
Can I use the Rule of 72 for debt?
Yes. If you carry a 18% credit card balance and make no payments, the balance roughly doubles in 72 / 18 = 4 years because interest compounds against you.
What is the exact calculation shown in the tool?
In rate mode the exact value is ln(2) / ln(1 + r). In years mode the exact rate is (2^(1/y) - 1) × 100.
Are results stored on a server?
No. All calculations run locally in your browser.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.