Rule of 72 Doubling Calculator

The first written record is Luca Pacioli's Suma de Arithmetica, published in Venice in 1494. Pacioli describes the rule as a merchant's shortcut for estimating how long money at compound interest takes to double, though he does not derive it. The math underneath only got cleaned up centuries later: the rule is a first-order approximation to ln(2) divided by your interest rate, where 0.72 happens to fit common merchant rates better than 0.693 because it stays close at 6 to 10 percent and is much easier to divide in your head.

All three estimate the same thing: years to double equals the rule number divided by the rate in percent. The Rule of 69.3 is mathematically exact for infinitesimal rates under continuous compounding because ln(2) is 0.6931. The Rule of 70 is cleaner for slow growth like inflation. The Rule of 72 wins for mental math because 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12, which covers most realistic investment returns. Pick 72 when the rate is 6 to 10 percent, pick 70 below that, and pull up the exact answer when precision matters.

Within roughly 1 percent of the exact answer for annual rates between 6 and 10 percent. At 8 percent the rule gives 9.00 years versus the exact 9.006, so the error is about 0.07 percent. At 2 percent the Rule of 72 gives 36 years versus the exact 35.0, an error around 2.8 percent, which is why the Rule of 70 (giving 35 years) is preferred for low rates. At 20 percent the rule gives 3.6 years versus the exact 3.80, a 5 percent error. The calculator shows the exact answer next to all three rules so you can see the gap.

Yes. The Rule of 114 estimates years to triple (ln(3) is about 1.0986, and 1.0986 divided by typical merchant rates lands near 114). The Rule of 144 estimates years to quadruple, which is simply two doublings stacked. So at 8 percent your money doubles in about 9 years, triples in about 114 / 8 = 14.25 years, and quadruples in about 144 / 8 = 18 years.

Yes. The same shortcut tells you how fast purchasing power halves. At 3 percent inflation, the cost of a basket of goods doubles in roughly 72 / 3 = 24 years, which means today's dollar buys half as much. At 6 percent inflation it doubles in 12 years. To convert a nominal investment return into a real (inflation-adjusted) doubling time, subtract the inflation rate from the nominal return first, then divide. A 7 percent nominal return with 3 percent inflation gives a real return of 4 percent, so real purchasing power doubles in about 18 years rather than the nominal 10 years.