Rule of 72 Calculator
Divide 72 by your rate of return and you get, roughly, the number of years it takes to double your money. This calculator runs that shortcut alongside the exact logarithmic answer so you can see precisely where it holds up and where it drifts.
Why 72
Doubling time is exactly ln(2) ÷ ln(1 + r). At small rates, ln(1 + r) is very close to r, so the expression collapses to ln(2) ÷ r ≈ 0.693 ÷ r — which would make it the Rule of 69.3.
Seventy-two is used instead for two reasons. It slightly overshoots, which happens to correct for the approximation error in the range of rates people actually care about. And it divides cleanly by 2, 3, 4, 6, 8, 9, and 12, which is what makes it usable in your head.
The "better numerator" output shows what the exact multiplier would be at the rate you entered. Near 8% it lands almost exactly on 72. At 2% it drifts toward 70; at 20% it wants to be closer to 76.
Where it breaks
The shortcut is within about 1% of the true answer between roughly 4% and 12%. Outside that band the error grows quickly — at 25% the Rule of 72 says 2.88 years while the real answer is 3.11, an 8% miss.
For low rates like savings account yields or inflation figures, the Rule of 70 is more accurate, which is why economists reach for 70 rather than 72 when discussing inflation or population growth.
The output most people miss
Look at "doublings over your horizon," not just the doubling time.
Doubling time is linear in your patience but the result is exponential. At 8%, money doubles about every nine years. Over 36 years that is four doublings — sixteen times your money, not four times. Push the horizon to 45 years and you get five doublings, or thirty-two times.
That gap between the fourth and fifth doubling is larger than everything that came before it combined. It is the clearest single argument for starting early that arithmetic can make, and it is why the horizon field moves the final value far more than the rate field does.
Using it in reverse
Divide 72 by the years you have instead of the rate. Need to double in 6 years? You need roughly 12% a year. This is a fast sanity check on any investment pitch: if someone promises to double your money in three years, they are claiming 24% annually, and you now know to ask exactly how.
Frequently asked questions
How accurate is the Rule of 72?
It is within roughly 1% of the exact answer for rates between about 4% and 12%, which covers most investment scenarios. Outside that range the error grows — at 25% it is off by about 8%. This calculator shows both the shortcut and the exact figure so you can see the gap for your specific rate.
What is the exact formula for doubling time?
Years to double equals ln(2) divided by ln(1 + r), where r is the rate expressed as a decimal. The Rule of 72 is a mental-math approximation of this, useful because 72 divides evenly by so many common rates.
When should I use the Rule of 70 instead of 72?
At low rates. The mathematically pure numerator is 69.3, so 70 is more accurate for figures under about 4% — savings yields, inflation, population growth. Economists conventionally use 70 for exactly this reason. At 8% and above, 72 is both more accurate and easier to divide.
Can I use the Rule of 72 for inflation?
Yes, in reverse. Dividing 72 by the inflation rate gives roughly how long it takes your purchasing power to halve. At 3% inflation that is about 24 years. Enter an inflation rate above to see the exact figure.
What rate of return should I assume?
There is no correct answer, only historical reference points. US large-cap stocks have averaged roughly 10% nominally and about 7% after inflation over the long run, with large swings in any given decade. Bonds and savings accounts are far lower. Using an after-inflation rate gives you a doubling time in real purchasing power, which is usually the more meaningful number.