Rule of 72 Calculator
A mental shortcut for how long compounding takes to double your money. It is an approximation, so this page always shows the exact answer next to the estimate and tells you how far apart they are.
Add an amount to see the first three doublings. No extra contributions are assumed.
Your doubling time will appear here
Enter a rate to find the years, or a number of years to find the rate you would need.
A deliberate overlap with compound interest
Rule of 72 vs. our Compound Interest Calculator: the Rule of 72 is a stripped-down version of the full compound interest calculation. One input, one output, and an answer you can work out in your head. That is why this page always shows both the estimate and the exact result from t = ln(2)/ln(1+r), so the gap between them is never hidden. Want a precise closing balance with regular contributions? The Compound Interest Calculator is the tool for that.
Against our Inflation Calculator: the Rule of 72 only gives you the doubling point. It has no price index behind it, so for real historical purchasing power use the inflation tool.
Against our 401(k) Calculator: the retirement example further down this page is an illustration with no extra contributions in it. For a full projection with contributions, employer match and IRS limits, use the 401(k) tool.
Quick Answer
The Rule of 72 says R x t = 72, so years to double = 72 / rate, and the rate you need = 72 / years. At 6% that is 12 years. The exact answer comes from t = ln(2)/ln(1+r), which gives 11.90 years for the same 6%. The rule is most accurate between 6% and 10%, where the error is typically under 1%.
How It Works: Formula & Variables
The rule itself
R × t = 72
t = 72 / R (years to double)
R = 72 / t (rate needed)
- R
- The annual rate as a whole number. 8% is 8, not 0.08.
- t
- Time in years.
The exact version
t = ln(2) / ln(1 + r)
This falls straight out of A = P(1+r)t when you set A = 2P. The P cancels, leaving 2 = (1+r)t, and taking logs of both sides gives the formula above. Our calculator shows this answer alongside the estimate every time.
Where the rule holds up, and where it does not
“It works best for rates between 2% and 18%... It is most accurate for rates between 6% and 10%, with error typically under 1%... At 2%, the Rule of 69.3 is more precise... Above 20%: accuracy degrades significantly.”
| Rate | Rule of 72 | Exact | Deviation |
|---|---|---|---|
| 2% | 36.0 yr | 35.00 yr | +2.85% |
| 6% | 12.0 yr | 11.90 yr | +0.88% |
| 8% | 9.0 yr | 9.01 yr | -0.07% |
| 10% | 7.2 yr | 7.27 yr | -1.00% |
| 20% | 3.6 yr | 3.80 yr | -5.31% |
The shaded rows are the band where the rule earns its keep. Outside it, read the exact column.
Worked Examples
Example 1: the arithmetic at 6% and 8%
At 6% a year, t = 72 / 6 = 12 years. At 8%, 72 / 8 ≈ 9 years, against an exact answer of 9.006 years. That is a gap of well under 0.1%, which is about as good as a mental shortcut gets.
Example 2: retirement and inflation
A 401(k) averaging 7% doubles in 72 / 7 = 10.29 years. So $50,000 at age 30 becomes approximately $100,000 by age 40 and $200,000 by age 50 through compounding alone, before additional contributions.
The same rule runs in the other direction. At 3% inflation, 72 / 3 = 24 years until prices double, which means $100 of purchasing power today will buy only $50 worth of goods in 24 years. Same arithmetic, considerably less cheerful.
Key Concepts
It is a shortcut, and it knows it: the value of the Rule of 72 is that you can run it without a calculator. Once you have opened one, use the exact formula.
It only describes compound growth: simple interest does not double on this schedule, because nothing is being earned on the earnings.
It works on anything that compounds: portfolio returns, inflation, revenue, a subscriber count. The maths does not care what the number represents.
Doublings stack: two doublings is four times your money, three is eight times. That stacking is what makes long horizons behave so differently from short ones.
Common Mistakes
Using it above 20% without checking the exact figure: at 20% the rule is already off by more than 5%, and it keeps getting worse from there.
Treating the estimate as the answer: 72 divided by anything is an approximation. Handy, but not the number to put in a spreadsheet.
Applying it to simple interest: the rule is built on compound growth. On a simple-interest product it will tell you the wrong thing entirely.
Frequently Asked Questions
Divide 72 by the annual rate of return. At 6% that is about 12 years, at 8% about 9 years, and at 12% about 6 years. The arithmetic is simple enough to do in your head, which is the whole point of the rule.
It approximates the natural log of 2, which is roughly 0.693, and 72 happens to divide cleanly by 2, 3, 4, 6, 8, 9 and 12. That combination of being close enough and easy to divide is what made it stick.
No. It is most accurate between 6% and 10%. At 2% the Rule of 69.3 gives a closer answer, and by 20% the Rule of 72 is off by roughly 5%. This calculator always shows the exact figure next to the estimate so you can see the gap.
Both approximate the same underlying formula. Seventy is slightly more accurate at low rates, somewhere in the 1% to 4% range, while 72 is easier to divide in your head. Pick whichever suits the numbers in front of you.
Yes, and it is one of the more useful applications. At 3% inflation, prices double in about 24 years, so $100 of purchasing power today will buy only $50 worth of goods in 24 years.
Yes. R = 72/t gives the return you would need. Doubling your money in six years asks for about 12% a year, which is a useful reality check on any plan that promises it.
Related Calculators
Compound Interest Calculator
The full calculation: exact balances, contributions and any compounding frequency.
Inflation Calculator
Actual US price index data between two years, not just a doubling point.
401(k) Calculator
A real retirement projection with contributions, employer match and IRS limits.
Investment Calculator
Growth from a starting amount plus ongoing monthly contributions.
CAGR Calculator
The annual growth rate between a beginning and an ending value.
Future Value Calculator
Project a lump sum plus optional contributions at any rate and frequency.
Sources
- CalculatorSoup, Rule of 72 Calculator (R x t = 72, t = 72/R, R = 72/t, and the exact doubling formula): https://www.calculatorsoup.com/calculators/financial/rule-of-72-calculator.php
- AJ Designer, Rule of 72 (accuracy limits, why 72, the Rule of 70 comparison, and the retirement and inflation examples): https://www.ajdesigner.com/rule-of-72/