Rule of 72 Calculator
Key takeaways
- 72 ÷ 12% gives 6.00 years; the exact compound-growth answer is 6.12 years — the shortcut lands within 1.9% (about 42 days) of it.
- The rule under-estimates here: at 12% a year an amount actually doubles in 6.12 years, and doubling again — 4× the start — takes the same span over, 12.23 years in all.
- At 8% the shortcut is nearly exact: 72 ÷ 8 gives 9.00 years against a true 9.01 years — an error of −0.07%.
How far the shortcut sits from the exact answer
A negative error means the shortcut under-estimates the true doubling time; a positive one means it over-estimates. The exact year figures are in the takeaways above, to two decimals — the result tiles round both to whole years, which is precisely what hides the gap.
About the Rule of 72 Calculator
The Rule of 72 is a mental-arithmetic shortcut: divide 72 by an annual growth rate to estimate how many years it takes an amount to double. At 8% it says nine years; at 12%, six. It trades a small amount of accuracy for being something you can do without a calculator, and 72 was chosen historically because it divides cleanly by many common small numbers — 2, 3, 4, 6, 8, 9 and 12.
Enter the annual return or interest rate you want to test. "Approx. years to double (Rule of 72)" is the shortcut. "Exact years to double" solves the same question precisely from the compound-growth formula, ln(2) ÷ ln(1 + rate ÷ 100). "Approximation error" is how far the shortcut sits from the exact answer at that particular rate — negative means it under-estimates the true doubling time, positive means it over-estimates.
The scale below the result is the page's one chart, and it plots that error rather than the two year figures. The reason is worth stating: across this field's whole range the two doubling times differ by at most about 9%, so a pair of bars would be two near-identical columns whose printed values both round to the same whole number of years. The error is the thing the page is actually about, so the error is what gets the picture, and the exact figures appear to two decimals in the Key takeaways above it.
The shortcut tracks the exact answer most closely for rates roughly in the 6–10% band, which is not a coincidence. The mathematically exact constant for continuous compounding is 69.3, from ln(2) × 100; 72 is the nearby, easier-to-divide number that happens to sit closest to the exact annual-compounding figure around that band. Outside it — at much lower or much higher rates — the gap widens in both directions.
Frequently asked questions
How does the Rule of 72 work?
Divide 72 by the annual percentage rate, taken as a plain number: 72 ÷ 8 = 9 years to double at 8%. It works because ln(2) is about 0.693, and for small rates ln(1 + r) is close to r — so ln(2) ÷ ln(1 + r) is close to 69.3 ÷ (rate as a percentage), and 72 is a more divisible stand-in for 69.3.
How accurate is the Rule of 72?
Very, in the middle of the range: at 8% it is off by about 0.07%, which is a couple of days over nine years. At 12% it under-estimates by roughly 1.9%, and at 24% by about 6.9%. The scale on this page shows exactly where the rate you entered falls, and the error output states it as a number.
Why not the Rule of 69.3, or the Rule of 70?
Both are used. 69.3 is exact for continuous compounding and 70 is a convenient round version of it; 72 sits slightly high, which happens to compensate for the fact that most real-world compounding is annual or monthly rather than continuous. 72 also divides evenly by more small integers, which is the whole point of a mental shortcut.
Does the Rule of 72 work for inflation?
The arithmetic is identical, and it answers the mirror question: at 6% inflation, 72 ÷ 6 = 12 years for prices to double — which is the same as purchasing power halving. Our Purchasing Power Calculator computes that erosion exactly, including the year the halving actually falls in.
Why do both year outputs show the same number?
Because the result tiles round to whole years, and at most rates the two figures differ by well under a year — 6.00 against 6.12 both print as "6 yrs". That rounding is precisely why this calculator carries an explicit error output and states both figures to two decimals in the takeaways.
What happens at a 0% return?
Nothing doubles, and both formulas divide by zero — 72 ÷ 0 and ln(1 + 0), which is ln(1), which is 0. All three outputs show "—" in that case. The field itself starts at 1%, so it is a boundary rather than something you can reach with the slider.
Disclaimer: This calculator is for information and education only. It is not investment advice and not a recommendation. Where a rate or a price is an input, it is an assumption, and actual rates vary. It does not take your personal circumstances into account. Every figure is computed solely by applying the formula and assumptions stated on this page to the inputs you entered.