Rule of 72 Calculator

Divide 72 by the annual interest rate, expressed as a whole number, and you get the approximate number of years it takes for money to double at that rate - assuming the return compounds annually and is reinvested in full.

At 8% the rule is almost exact. At 2% and 12% it is within a few percent. At 20% it starts to drift noticeably - the error grows as the rate moves away from the middle of the range.

Note. The rule works in both directions. To find the rate needed to double your money in a given number of years, divide 72 by the years. To double in 8 years you need about 9% a year.

The exact doubling time under compound growth is ln(2) / ln(1 + r). Since ln(2) is approximately 0.693, the precise answer for small rates is close to 69.3 divided by the rate.

• 69.3 is the accurate constant for continuous compounding and for low rates.
• 70 is a common slightly better everyday approximation at low rates.
• 72 was chosen because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12 - the rates people actually encounter - making mental arithmetic easy. It also happens to compensate for compounding by nudging the result upward, which keeps it close across a practical middle range.

The rule is therefore a deliberate compromise between accuracy and divisibility, not a mathematical identity. It should be treated as a fast estimate for rates between roughly 2% and 14%, not as a formula.

Investment growth. At 7% a year, 72 / 7 gives about 10.3 years to double. The actual figure is 10.24 years. On a $25,000 balance that reaches $50,000 in a little over a decade, $100,000 in about twenty, and $400,000 in about forty - the doubling effect compounding on itself.

Erosion from inflation. The same arithmetic runs in reverse. At 3% inflation, 72 / 3 = 24 years for your money to lose half its purchasing power. The exact figure is 23.4 years. This is the single most useful application of the rule, because it applies to money you are holding rather than growing.

Debt. A balance compounding at 18% - typical of a credit card - doubles in 72 / 18 = 4 years if nothing is paid. The exact figure is 4.19 years. On an $8,000 balance left untouched, that is $16,000 in four years.

• Very high rates. Above about 15-20% the estimate increasingly understates the time required. At 50% the rule says 1.44 years; the actual figure is 1.71 years.
• Very low rates. Below about 1% the arithmetic becomes misleading, and at 0% the concept does not apply at all - money never doubles without growth.
• Non-compounding returns. Simple interest does not compound, so a linear rule is a poor fit. Money at 5% simple interest doubles in 20 years, not the 14.4 the rule suggests.
• Irregular returns. The rule assumes a constant rate every year. Investment returns arrive unevenly - three good years followed by two bad ones does not behave like a flat rate, even if the average matches.
• Fees, tax and withdrawals. None of these are in the arithmetic. A 1% annual fee on an 8% investment does not reduce the doubling time by one-eighth; it changes the effective rate to 7%, which changes it more than proportionally.

Note. For a quick sanity check on rates between 2% and 14% the rule is reliable. Outside that range, use the calculator, which computes the exact figure rather than an approximation.

The practical value of the rule is that it converts an abstract percentage into a number of years you can picture.

1. Test a rate. Enter the return you have been quoted. If doubling takes 40 years, a modest-looking rate is doing very little.
2. Check a goal against a timeline. If you need to triple your money in 15 years, the rule tells you quickly whether that is in the region of possibility - tripling is roughly a little under two doublings, so you would need roughly two doublings in 15 years, about 36 years at 2%. That is nowhere near. The calculation rules out unrealistic targets before you plan around them.
3. Weigh it against inflation. Run the same rule at your expected return and at expected inflation. The gap between the two doubling times is how quickly your real purchasing power is actually improving.
4. Revisit annually. A change of one percentage point in expected return changes the doubling time by years, not months.