Rule of 72 calculator
How long money takes to double, and how far the shortcut is off.
Fill in the fields and the result will appear here automatically.
Seventy-two divided by the rate gives the doubling time in years — an approximation you can do in your head. The exact figure from logarithms sits beside it along with the gap between them, not to replace the rule but to show where it starts to mislead. At eight percent the gap is under a week; at half a percent the rule is five years out.
How it works
Formula and logic
Estimated years = 72/r, where r is a positive annual return in percent. Logarithmic time = ln(2)/ln(1+r/100); the gap is the absolute difference between the two times. The model assumes a constant annual growth factor and reinvested interest without contributions. A fractional exact time extends the growth curve mathematically: if interest is credited only at whole-year ends, doubling is first observed at the next whole-year date. The optional starting amount only controls the doubled-amount row.
Example
At 8 percent the rule gives 72 ÷ 8 = 9 years, and the exact answer is 9.01. At 0.5%, the 144-year estimate differs from 138.98 logarithmic years by 5.02 years; a zero rate cannot produce finite doubling.
Fields and units
- Annual rate, % — unitless
- Starting amount — $
How to use
- — Enter the annual rate.
- — Read the rule-of-72 estimate.
- — Compare it with the exact figure beside it.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- Investor.gov, United States: reinvested interest and the approximate rule of 72
- Limitation
- A shortcut for a constant positive annual return. Contributions, withdrawals, fees, taxes and rate changes are excluded. Fractional time does not promise a contractual interest-crediting date or a guaranteed return.
FAQ
Why 72 and not 70?
Seventy-two divides evenly by many common rates — 2, 3, 4, 6, 8, 9, 12 — which is what makes the shortcut usable in your head.
When does the rule stop working?
There is no universal acceptable error. At 6%, 12 years differs from 11.8957 by 0.1043 years; at 10%, 7.2 differs from 7.2725 by 0.0725 years. Compare the displayed gap with the precision your task needs.
Is this the same as a compound interest calculator?
No. A compound interest calculator grows a balance over a period you choose; this one answers a single question — when does it double.
What compounding does it assume?
The model uses the effective annual factor 1+r/100. Convert a nominal rate with more frequent compounding to its effective annual rate first. The same effective annual growth gives the same curve here.