Rule of 72 Calculator

The Rule of 72 is a mental-math shortcut that estimates how long money takes to double at a steady compound interest rate. You divide 72 by the annual rate, and the answer is roughly the number of years to double. No logarithms and no spreadsheet, just one division you can do in your head.

At 8% a year, the rule says 72 ÷ 8 = 9 years. The exact answer is 9.01 years, so the shortcut lands within days of the truth. It works in reverse too: divide 72 by the number of years you have to find the rate you would need, so doubling in 10 years calls for about 7.2% a year.

1. Choose what you want to find: the years to double at a given rate, or the annual rate needed to double in a set time.
2. Enter the annual rate in percent (for example 8) or the number of years (for example 10).
3. Press Calculate to see the Rule of 72 estimate next to the exact answer, the difference between them, and the tripling and quadrupling times.

Years to double = 72 ÷ annual rate (%). The rate goes in as a whole number, not a decimal, so you write 8 and not 0.08. At 6%, the rule gives 72 ÷ 6 = 12 years.

The exact doubling time is ln(2) ÷ ln(1 + r), where r is the rate as a decimal and ln is the natural logarithm. The calculator shows both figures side by side so you can see how close the shortcut is at your rate.

The Reverse: Finding the Rate You Need

To find the rate, flip the division: required annual rate (%) = 72 ÷ years. Want to double in 10 years? Then 72 ÷ 10 = 7.2% a year. The exact answer is 7.18%, and the calculator shows it beside the rule's answer.

Two reasons make 72 the chosen number. First, it divides evenly by 2, 3, 4, 6, 8, 9, and 12, so the mental math stays easy for the rates people actually meet. Second, the small error from rounding the true numerator up from 69.3 cancels the approximation error in the band where the rule gets used most, roughly 6% to 10%. Near 8%, the rule is almost exact.

The number 69.3 is the mathematically pure choice because ln(2) equals 0.693, and it is the right numerator for continuous compounding. But 69.3 is awkward to divide in your head, and ordinary savings compound in steps rather than continuously, which stretches doubling times slightly. The number 72 trades a little accuracy for arithmetic you can do anywhere, and the trade pays off best around 8%.

The shortcut is most accurate around 6% to 10%. Below that band it runs a little slow, and above it a little fast. The table compares the rule with the exact doubling time, ln(2) ÷ ln(1 + r).

At 2% the rule says 36 years while the truth is 35.0, a full year off. At 8% the two differ by a hundredth of a year. At 20% the rule promises 3.6 years when the truth is 3.8, a gap of about two months. The error is always predictable, never a surprise.

The same idea works with different numerators for different jobs.

Rule of 70 for low rates

When rates are low, 70 beats 72. At 2%, 70 ÷ 2 = 35 years, which matches the exact answer of 35.0, while 72 gives 36. Inflation is the classic low-rate case: at 3% inflation, the rule of 70 says buying power halves in 70 ÷ 3 = 23.3 years.

Rule of 69.3 for continuous compounding

With continuous compounding, the exact doubling time is ln(2) ÷ r, which equals 69.3 ÷ rate (%). Economists use 69.3 when growth compounds constantly, for example in textbook models. For everyday accounts that compound monthly or yearly, 72 is the handier number.

Rule of 115 for tripling

To estimate tripling instead of doubling, divide 114 or 115 by the rate. At 8%, 114 ÷ 8 = 14.25 years to triple, against an exact answer of 14.27. Quadrupling is simply two doublings, so 144 ÷ 8 = 18 years at 8%, against 18.01 exact. The calculator reports the tripling and quadrupling times for every rate you enter.

Doubling investments

An 8% average return doubles money roughly every 9 years. Over 36 years that is four doublings, so $10,000 becomes about $20,000, then $40,000, then $80,000, then $160,000. The last doubling adds more than the first three combined, which is why starting early matters so much. To see how repeated doubling plays out across decades of saving, the retirement calculator projects the complete picture.

Inflation quietly halving your money

Run the rule on an inflation rate instead of a return and it tells you how fast buying power halves. At 3% inflation, money loses half its value in about 24 years by the rule of 72, or 23.3 years by the rule of 70. The exact answer is 22.8 years. This is the quiet cost of cash sitting still.

Debt compounding against you

Unpaid compounding debt doubles the same way investments do. A balance growing at 18% a year doubles in about 4 years, since 72 ÷ 18 = 4. Minimum payments that barely cover interest let the rule run against you, which is why clearing high-rate debt usually beats chasing returns.

Start with compound growth: A = P(1 + r)^t, where A is the final amount, P is the starting amount, r is the rate per period as a decimal, and t is the number of periods. Set A to twice P and divide both sides by P to get (1 + r)^t = 2. Taking the natural log of both sides gives t = ln(2) ÷ ln(1 + r), the exact doubling formula. For the rates people meet most, that expression simplifies to about 72 ÷ rate (%), which is the rule.

The rule is old. It appears in Luca Pacioli's 1494 mathematics text Summa de arithmetica, where he states it plainly for doubling at a given yearly percentage, using 6% and 12 years as his example. For exact growth projections with contributions and compounding frequency, the compound interest calculator runs the full math.

The rule assumes one constant rate with compound growth, so it is not for simple interest, where money grows by the same dollar amount each year. It assumes returns are reinvested and ignores fees, taxes, contributions and withdrawals, all of which shift the real doubling time. Real returns also vary year to year, and a bumpy path to the same average can double money slower than the smooth math suggests. Treat the answer as a planning estimate, not a promise.

This calculator gives an estimate for planning and education. It is not financial advice, and actual results depend on your account's terms, fees and timing. Read our full disclaimer for the details.

• CalculatorSoup, Rule of 72 calculator: formula and full derivation. calculatorsoup.com
• Wikipedia, Rule of 72: variations, halving and history. wikipedia.org
• OnlyCalculators, Rule of 72 calculator: divisor switching and doubling projections. onlycalculators.com
• CalculatorPark, Rule of 72 calculator: compounding frequency and tripling. calculatorpark.com