What Is the Rule of 72?
The Rule of 72 is a quick way to estimate how long money takes to double at a yearly rate: divide 72 by the rate. At 8%, that's about 9 years. It works for anything growing at a steady rate, so it can show how fast savings grow, how fast a debt with unpaid interest grows, or how fast inflation halves what money buys.
It also works backward: 72 divided by a number of years gives the rate needed to double in that time. To double in 6 years, you'd need about 12% a year.
How accurate is it?
The rule is very close near 8%, and less so at very low or very high rates:
| Rate | Rule of 72 | Exact | Off by |
|---|---|---|---|
| 1% | 72.00 years | 69.66 years | +3.4% |
| 4% | 18.00 years | 17.67 years | +1.9% |
| 8% | 9.00 years | 9.01 years | -0.1% |
| 12% | 6.00 years | 6.12 years | -1.9% |
| 25% | 2.88 years | 3.11 years | -7.3% |
| 50% | 1.44 years | 1.71 years | -15.8% |
| 99% | 0.73 years | 1.01 years | -27.8% |
Which calculator should I use?
- This calculator: for a quick estimate of how long money takes to double.
- Investment Growth calculator: to see what an amount becomes over a set number of years, at two rates.
- Time Value of Money calculator: for the exact time to reach any amount, not only double, with other compounding.
- Compound Interest calculator: when you also add regular deposits.
How to Calculate the Rule of 72
The estimate, with the rate as a whole number (7 for 7%):
The exact time comes from the time value of money. Doubling means:
The amount cancels out, so the time to double doesn't depend on how much you start with. Solving for n:
- PV: the amount you start with.
- r: the yearly rate as a decimal (6% = 0.06), with the return added once a year.
- n: the number of years.
Example
$3,500 at 6% a year:
- Rule of 72: 72 ÷ 6 = 12.00 years
- Exact: ln(2) ÷ ln(1.06) = 11.90 years, when the $3,500 becomes $7,000.00
- The rule is 0.10 years too long, or 0.9%
How to Use the Rule of 72 Calculator
"If my $1,000 earns 7% a year, about how long will it take to double, and how good is that estimate?" This calculator answers that.
Let's enter the numbers for this example in each box. They are already filled in when the calculator opens, so you can follow along and then change any box to match your own numbers.
- Interest Rate: Enter 7, which is the yearly rate in percent. It must be from 0.1 to 99.99.
- Investment Amount: Enter 1,000, which is the amount you start with. It must be greater than 0 and less than $1 billion. It changes the dollars in the table, but not the time.
Calculate and Reset
Click Calculate to see your results. If a box has a problem, such as a rate of 0, a message pops up under that box instead. With the default numbers you get:
- Your Results: a short summary in words: the estimate, the exact time and how close the rule is at your rate.
- Rule of 72 estimate: the headline number, 10.29 years.
- Exact Years, Difference, Value When Doubled and Total Interest: 10.24, +0.04 years, $2,000.00 and $1,000.00.
- How your money doubles: your investment and its interest up to the exact time, with a dashed line at the rule's estimate. Links under it open the Investment Growth and Time Value of Money calculators with your numbers filled in.
- How accurate the rule is: how far off the rule is at rates from 1% to 30%, with a dot at your rate. Where the line crosses zero, the rule is exactly right.
- Yearly table: each year's beginning balance, interest and end balance. The last row is the part of a year that reaches double.
- Share Results: a link that opens this calculator with your numbers filled in. Copy it, or share it on Facebook or X.
Amounts of $1 million or more are shortened, for example $1.25M. Click Reset to put every box back to its default and show the default results again.