Rule of 72 Calculator
Estimate how long an investment takes to double or the annual return needed for a chosen doubling time. Compare the Rule of 72 with exact annual compounding, the Rule of 70 and the Rule of 69.3.
Doubling results
| Method | Result | Difference from exact |
|---|
Rule of 72 formula
The Rule of 72 is a mental-math shortcut for compound growth. Divide 72 by an annual percentage return to estimate the years required to double:
Estimated years to double = 72 ÷ annual return (%)
To work backward, divide 72 by the desired doubling time:
Estimated annual return (%) = 72 ÷ years to double
For annual compounding, the exact formulas are years = ln(2) ÷ ln(1 + r) and r = 2^(1 ÷ years) − 1, where r is written as a decimal. The Rule of 70 uses 70 instead of 72. The Rule of 69.3 is closely related to continuous compounding, where exact doubling time is ln(2) ÷ r.
Verified examples
| Inputs | Result |
|---|---|
| US$10,000 at 8% effective annual return | Rule of 72: 9 years; exact annual-compounding time: 9.0065 years; doubled amount: US$20,000 |
| US$25,000 with a 10-year doubling target | Rule of 72: 7.2%; exact effective annual return: 7.1773%; doubled amount: US$50,000 |
| US$5,000 at 1% effective annual return | Rule of 72: 72 years; exact annual-compounding time: 69.6607 years; Rule of 70: 70 years |
How to interpret the comparison
The Rule of 72 is an approximation, not a separate compounding method. The calculator reports its difference from exact annual compounding so you can see when the shortcut is close enough for planning. The Rule of 70 and Rule of 69.3 are included on the same page because they answer the same doubling-time intent; they do not need separate calculators.
At 8%, the Rule of 72 is especially close: 9 years versus approximately 9.0065 years with exact annual compounding. At very low or very high rates, the approximation error can be more noticeable.
Limits and assumptions
- The annual return must be greater than 0% and no more than 1,000%, with up to six decimal places.
- The target doubling time must be from 0.01 through 10,000 years, with up to six decimal places.
- The starting amount must be greater than zero and no more than 1,000,000,000,000 monetary units, with up to two decimal places.
- The exact result assumes a constant effective annual return compounded once per year. Continuous, monthly and daily compounding use different exact relationships.
- Contributions and withdrawals are excluded because they change when an account balance reaches twice its starting value.
- Taxes, fees, inflation, volatility and sequence of returns are not modeled. A stated return is not guaranteed.
- Results are educational estimates, not investment advice.
Use the exact result for precise planning. Use the Rule of 72 only as a quick shortcut when the constant-return assumption is reasonable.
Frequently asked questions
Why does the Rule of 72 use 72?
Seventy-two is easy to divide by many common rates and gives a useful approximation across ordinary investment-return ranges. It is not a universal constant.
Does the Rule of 72 include inflation?
No. You may enter a nominal return to estimate nominal doubling or a separately calculated real return to estimate purchasing-power doubling. Do not mix the two.
Can I use the Rule of 72 for debt?
It can illustrate how a balance might double under a constant compound rate with no payments, fees or new charges. Real loans and credit cards usually include payments and other terms, so use a debt-specific calculator for payoff planning.
Related calculators
- Compound Interest Calculator — model balances with compounding and contributions.
- CAGR Calculator — derive a compound annual growth rate between two values.
- Time Value of Money Calculator — solve present value, future value, rate, periods or payment.
- Inflation Calculator — compare nominal amounts and purchasing power.