Find out how long an investment takes to double. The Rule of 72 is a quick mental shortcut — this calculator also shows the exact answer, so you can see how close the shortcut gets.
Dividing 72 by the annual percentage return gives an approximate doubling time.
The exact answer uses logarithms, which is what the comparison figure shows.
The shortcut is closest to correct for rates of roughly 6% to 10%, and drifts further out at very high or very low rates.
Rule of 72: Years ≈ 72 ÷ annual return %
Exact: Years = ln(2) ÷ ln(1 + r)
An investment returning 12% a year.
Annual return: 12%
Apply the rule: 72 ÷ 12 = 6
The exact answer is ln(2) ÷ ln(1.12) = 6.12 years
The shortcut is within about six weeks
Answer: Roughly 6 years to double
The Rule of 72 calculator estimates how many years it takes for money to double at a given annual rate. Divide 72 by the rate, and you have the rough answer. The calculator also shows the exact doubling time using logarithms, the gap between the two, and how long the money takes to triple.
The rule is loved by investors and finance students because it works in your head. If a deposit offers 8%, money doubles in about 9 years. If inflation runs at 6%, prices double in about 12 years. It turns a percentage into a time frame people can feel, which makes it useful for quick comparisons and for sanity-checking a larger calculation.
The calculator assumes the rate is compounded once a year and stays constant.
1. Note the annual rate R as a percentage, for example 9.
2. Estimate the doubling time: years ≈ 72 ÷ R.
3. For the exact doubling time, compute ln(2) ÷ ln(1 + R ÷ 100).
4. For the exact tripling time, compute ln(3) ÷ ln(1 + R ÷ 100).
5. To find the rate needed to double in a target number of years Y, reverse the rule: R ≈ 72 ÷ Y.
Money doubles when (1 + r)ᵗ = 2, so t = ln 2 ÷ ln(1 + r). For small r, ln(1 + r) is close to r, so t ≈ 0.693 ÷ r, or 69.3 ÷ R when R is a percentage. Using 69.3 would be exact for continuous compounding. But for yearly compounding, ln(1 + r) is a little less than r, so the true doubling time is a little longer, and a slightly bigger numerator fits better. 72 works well for rates in the typical range and has the advantage of dividing evenly by 2, 3, 4, 6, 8, 9 and 12.
Around 8%, the rule is almost exact: 72 ÷ 8 = 9 years against an exact 9.01 years. At lower rates, it overestimates. At 2%, it gives 36 years against an exact 35.0. At higher rates, it underestimates. At 24%, it gives 3 years against an exact 3.22. For quick decisions the error rarely matters, but for precise planning at very low or very high rates, use the exact logarithm figure the calculator shows.
The rule applies to anything growing at a steady compound rate, not only investments. At 6% inflation, the cost of living doubles in about 12 years, so a retirement budget must allow for that. At 36% a year, a common effective cost of unpaid credit card balances, a debt doubles in about two years. To see how long it takes your purchasing power to double, use the real return, roughly the investment return minus inflation, in place of the nominal rate.
Geeta is choosing a long-term bond fund that has averaged about 9% a year and wants a quick sense of how long her savings would take to double.
Answer: Years to double (Rule of 72) 8 years; Exact answer 8.04 years; Difference 0.04 years
Entering the rate as a decimal, such as 0.09, instead of 9.
Relying on the rule at very high or very low rates where its error grows.
Using a nominal return to estimate when purchasing power doubles.
Applying it to returns that are not compounded, such as simple interest, where doubling takes 100 ÷ R years.
Quickly comparing the growth of different investment options.
Estimating how fast inflation erodes the value of savings.
Showing the cost of high-interest debt in a memorable way.
Sanity-checking results from compound interest or lumpsum calculators.
Why 72 and not some other number?
The exact number, mathematically, is about 69.3. But 72 is used because it divides neatly by 2, 3, 4, 6, 8, 9, and 12, which makes it easy to work out in your head. It is also a little more accurate for the common return range where people use it most.
How accurate is it?
It is accurate to within a few months, for rates between about 6% and 10%. At very low rates like 2%, or very high rates like 25%, the error grows bigger, so use the exact number when precision matters.
Does it account for inflation?
Only if you use a real return, not a normal (nominal) one. To find out when your buying power doubles, subtract inflation from your return first.