Case 1
- Annual rate of return
- 8%
- Grow to
- Double (×2)
9.00
Open with these valuesRule of 72 Calculator
9.00years
Result: 9.00 yearsDivide 72 by the annual rate and you have roughly the years it takes money to double. The 72 is a convention, not a derivation: the exact constant is 69.3, and 72 is used because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12. Tripling and quadrupling use 114 and 144 the same way.
Worked examples
Case 2
- Annual rate of return
- 6%
- Grow to
- Double (×2)
12.00
Open with these valuesCase 3
- Annual rate of return
- 8%
- Grow to
- Triple (×3)
14.25
Open with these valuesHow it's calculated
Years ≈ Rule number ÷ Rate · exact: ln(target) ÷ ln(1 + rate)
- StepEnter the annual rate as a whole number: 8 for 8 %, not 0.08.
- StepPick whether you want the money to double, triple or quadruple.
- StepDivide the rule number by the rate to get the estimate in years.
- ResultCompare it with the exact figure in the table below before relying on it.
What this number means
The Rule of 72 answers the compound interest question that is meant to need no calculator: how long until the money doubles. It is the same equation solved for time, with a logarithm swapped for one division you can do in your head — which is the whole point, since a figure you can produce during a conversation gets used and a formula you have to look up does not. At the default 8 % the rule gives 72 ÷ 8, so 9.00 years, against an exact ln 2 ÷ ln 1.08 of 9.006: about two days out. Switch the target and the same trick runs on 114 and 144, giving 14.25 and 18.00 years where the exact figures are 14.27 and 18.01. Notice what never appears in any of it: the amount. Doubling time depends on the rate alone, so 100 and 100000 both take those nine years, and that is what makes the rule portable. It is also nominal. For the time in which purchasing power doubles, enter the rate after inflation rather than before. The weakest assumption is not the rounded constant but the rate: the division quietly holds one rate steady across all nine years, and it will return a tidy answer for any rate you type, including rates nobody earns steadily for that long.
An estimate with a known error
The rule is closest around 8 %, where it is off by only a few days. At 18 % it says four years against an exact 4.19, and at 2 % it says 36 against an exact 35.
72 is a convention, not a derivation
The exact constant is about 69.3, which is 100 times the natural logarithm of 2. The 72 is used because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the arithmetic doable in your head.
114 and 144 do the same job
Divide 114 by the rate for the tripling time and 144 by the rate for the quadrupling time. Both are conventions in exactly the way 72 is; the exact constants are 109.9 and 138.6.
It works on inflation too
Dividing 72 by an inflation rate estimates how long prices take to double. That is the same span in which money's purchasing power halves.
Commonly misread
Enter 0.08 for a rate of 8 %.
Enter the rate as a whole number, so 8 for 8 %. The rule number is divided by that figure directly.
The Rule of 72 gives the exact doubling time.
It approximates the exact logarithmic doubling time, ln(2) ÷ ln(1 + rate). Compare it with the exact column in the table before relying on it.
Reference table
| Annual rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 2 % | 36.0 years | 35.0 years |
| 4 % | 18.0 years | 17.7 years |
| 6 % | 12.0 years | 11.9 years |
| 8 % | 9.0 years | 9.0 years |
| 10 % | 7.2 years | 7.3 years |
| 12 % | 6.0 years | 6.1 years |
| 18 % | 4.0 years | 4.2 years |
Questions
What is the Rule of 72?
The Rule of 72 estimates how many years money takes to double at a fixed annual rate: divide 72 by the rate. At 9 % a year that is 72 ÷ 9, so about eight years. It approximates the exact logarithmic doubling time and is closest for rates between roughly 6 % and 10 %.
Why 72 and not another number?
The mathematically exact constant is about 69.3, which is 100 times the natural logarithm of 2. The 72 is a convention chosen because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes the arithmetic doable in your head. The small loss of precision is the price of a number you can actually divide.
How accurate is it?
It is closest around 8 %, where the estimate is off by only a few days. Further from 8 % the error grows: at 18 % the rule says four years while the exact figure is 4.19, and at 2 % it says 36 years against an exact 35. The table above shows the gap at each rate.
What are the Rule of 114 and the Rule of 144?
They apply the same trick to bigger targets: 114 divided by the rate estimates the tripling time, and 144 divided by the rate the quadrupling time. Both numbers are conventions in exactly the way 72 is — the exact constants are 109.9 and 138.6. Pick the target above and the calculator uses the matching rule number.
Can I use it for inflation?
Yes. Dividing 72 by an inflation rate estimates how long prices take to double, which is the same as the time for money's purchasing power to halve. At 6 % inflation that is roughly twelve years.
Sources and last check
Information, not financial advice.