Rule of 72 Calculator
How long money takes to double, and how far the shortcut is off.
About
Rule of 72 Calculator
The rule of 72 is mental arithmetic that answers a real question: how long until this doubles? Divide 72 by the annual rate and you have the number of years, close enough to be useful and quick enough to do in a conversation.
How it works
years to double = 72 ÷ annual rate
At 8% a year, 72 ÷ 8 = 9 years. At 6%, 12 years. At 12%, 6 years. Run it backwards to find the rate a deadline demands: doubling in five years needs 72 ÷ 5 = 14.4% a year.
Note that the rate goes in as a plain number, not a decimal. It is 72 ÷ 8, not 72 ÷ 0.08.
Where 72 comes from
The exact answer uses logarithms: ln(2) ÷ ln(1 + rate). Since ln(2) is 0.693, the mathematically pure version of the shortcut would be 69.3 divided by the rate, and that is exact only under continuous compounding.
Two things push the number up to 72. Annual compounding, which is how most things actually pay, needs a slightly larger numerator to compensate. And 72 divides evenly by 2, 3, 4, 6, 8, 9 and 12, which matters enormously for a rule meant to be done in your head. 69.3 is more accurate and useless without a calculator, which defeats the purpose.
How accurate is it?
Very, in the middle of the range, and it drifts at the edges.
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2% | 36.0 years | 35.0 years | +2.8% |
| 6% | 12.0 years | 11.9 years | +0.9% |
| 8% | 9.0 years | 9.01 years | -0.1% |
| 10% | 7.2 years | 7.27 years | -1.0% |
| 15% | 4.8 years | 4.96 years | -3.2% |
| 20% | 3.6 years | 3.80 years | -5.3% |
The shortcut is essentially perfect around 8%, which is no accident: that is roughly where the annual-compounding correction and the 72-for-69.3 substitution cancel out. Below 3% the rule of 70 is closer, and above 20% neither shortcut is worth using.
Doublings stack up
The real value of the rule is seeing several doublings in a row, which is where compounding stops being intuitive.
$10,000 at 8% doubles in 9 years. Four doublings take 36 years and turn $10,000 into $160,000. The exact figure is $159,682, so the shortcut is off by two-tenths of a percent across nearly four decades.
| Years at 8% | Doublings | Value of $10,000 |
|---|---|---|
| 9 | 1 | $20,000 |
| 18 | 2 | $40,000 |
| 27 | 3 | $80,000 |
| 36 | 4 | $160,000 |
The last nine years add $80,000, more than the first twenty-seven combined. That asymmetry is the argument for starting early, and it lands harder as a table than as a sentence about compound interest.
Running it on inflation
The rule works on anything growing at a steady percentage, including prices. At 3% inflation, 72 ÷ 3 = 24 years for prices to double, which is the same as money losing half its purchasing power.
That reframes a cash savings account. Money sitting at 1% while prices rise 3% is losing about 2% a year in real terms, and 72 ÷ 2 = 36 years to lose half its value. It also explains why a pension pot that looks generous today buys noticeably less at the end of a long retirement.
Running it on fees
Fees compound the same way returns do, in the wrong direction. A fund charging 1% a year against one charging 0.1% gives up 0.9% annually. Over 40 years that gap alone consumes roughly a third of the final balance, and the rule of 72 gets you close to that intuition quickly: the fee difference is doubling someone else's money at your expense.
Beyond money
Anything compounding at a steady percentage obeys the same arithmetic. A population growing 2% a year doubles in 72 ÷ 2 = 36 years, against an exact 35.0. Demographers usually use 70 here, since the rates involved are low enough for 70 to be closer.
It works on a user base, a subscriber count, an energy demand curve and a bacterial culture. The rule has nothing to do with finance in particular; it is a property of exponential growth, and money is simply where most people meet it.
Debt doubles too
A credit card at 24% doubles an untouched balance in 72 ÷ 24 = 3 years, and the exact answer is 3.22. That is the same compounding that grows a pension, working against you and at a rate no investment reliably matches.
Running the rule on a debt before taking it on is a fast reality check. At 24%, a $4,000 balance ignored for six years is roughly $16,000, and nothing about the original purchase changes that arithmetic.
What a small fee difference costs
Fees compound in the same direction as debt. Take $10,000 invested for 40 years: at a 7% net return it reaches $149,745, and at 6% it reaches $102,857. One percentage point of annual fee has taken 31% of the final balance.
The rule of 72 gets you to that intuition without the arithmetic. At 7% the money doubles every 10.3 years, and at 6% every 12 years. Over 40 years that is roughly four doublings against three and a third, and each missing doubling is enormous at the end.
Where the rule quietly fails
It needs a steady rate, and real returns are not steady. A portfolio averaging 8% through violent swings does not double in nine years, because a 50% loss requires a 100% gain to recover from. The order the returns arrive in matters too, particularly for someone drawing money out, and no shortcut of this kind captures that.
Use it for what it is: a way to size a problem in your head during a conversation. When the decision actually depends on the number, use the exact formula.
Sanity-checking a claim
The rule works well in the other direction, as a filter on whatever someone is promising. An investment that will double your money in two years is claiming 72 ÷ 2 = 36% a year, and the exact figure is 41.4%.
Stated as a doubling it sounds like a good opportunity. Stated as a sustained annual return of 41%, it sounds like what it is, since almost nothing delivers that reliably and the ones that briefly do carry risk to match. Converting a doubling claim into an annual rate takes three seconds and is the fastest filter available.
The same check works on a plan of your own. Doubling a business in five years needs 72 ÷ 5 = 14.4% a year, exactly 14.87%, which is demanding but ordinary. Doubling it in two is a different proposition entirely.
Rules for tripling and quadrupling
The same trick extends to other multiples by changing the numerator. Divide 114 by the rate for a tripling and 144 for a quadrupling, which is simply two doublings stacked.
At 8% those give 14.25 years to triple and 18 years to quadruple, against exact answers of 14.27 and 18.01. The accuracy holds up because the correction that makes 72 work at annual compounding scales with the numerator.
Common mistakes
Entering the rate as a decimal. 72 ÷ 0.08 is 900 years. It is 72 ÷ 8.
Using it on volatile returns. The rule needs a steady rate. An average of 8% built from wild swings does not double money in nine years, because losses compound too.
Applying it above 20%. The error passes 5% and keeps growing. Use the exact formula for high rates.
Forgetting tax. A taxable account growing at 8% before tax grows more slowly after it, and the doubling time should use the after-tax rate.
Common questions
Frequently asked questions
Because 72 divides cleanly by more numbers, which is the whole point of a mental shortcut. It also happens to correct for annual rather than continuous compounding, making it most accurate right around the 8% mark where a lot of long-term return assumptions sit.
At low rates, particularly below 3%, where 70 is closer to the exact answer. It is standard in demography and economics for population and inflation growth, which typically run in low single digits.
Yes, divide 114 by the rate. At 8% that gives 14.25 years against an exact 14.27. For quadrupling, use 144, which is simply two doublings.
It works for halving, which is the mirror image. At a 6% annual decline, 72 ÷ 6 = 12 years to lose half the value. It is commonly used this way for inflation and for depreciating assets.
Convert to an effective annual rate first. A 12% nominal rate compounded monthly is an effective 12.68%, so the doubling time is 72 ÷ 12.68 = 5.7 years rather than 6.
It gives 7.2 years against an exact 7.27, so it is short by about a percent, or roughly three weeks. That is comfortably inside the error of any assumption about what a 10% return will actually be.
It appears in the Summa de Arithmetica of Luca Pacioli, published in 1494, presented as something already known rather than as a discovery, so the rule is older than that. Pacioli gave no derivation, which fits its nature as a practical tool for merchants.
Yes, and it is sobering there. A credit card at 24% doubles the balance in about three years if nothing is paid. The same arithmetic that grows an investment grows a debt, and card rates sit high enough that the exact formula is worth using.