What the rule of 72 is
The rule of 72 is a mental shortcut for figuring out — without a calculator — how many years it takes an investment to double at a fixed growth rate. The trick is simple: divide 72 by the annual interest rate (as a percentage), and the answer is the number of years. If a savings certificate pays 8% a year, then 72 ÷ 8 = 9: your money doubles in nine years.
Investors love it because it turns a logarithm problem into head-math. It isn’t exact, but it lands remarkably close across the range of rates you meet in real life (roughly 6% to 10%). This calculator runs entirely in your browser — nothing you type is stored or sent anywhere.
How to use the calculator
There are two modes, switched with the buttons at the top:
- I know my rate — how many years? Type the annual rate (say
8) and you’ll see how long your capital takes to double. - I know the years — what rate? Type your target time frame (say
10years) and you’ll see the annual rate you need to double in that window:72 ÷ 10 = 7.2%.
In both modes we show the rule-of-72 answer next to the exact value, so you can see at a glance how close the shortcut gets.
The formula
The rule of 72 rests on these two expressions:
Years to double ≈ 72 ÷ annual rate (%)
Annual rate needed (%) ≈ 72 ÷ years
The exact value comes from the math of compound interest. Since we want (1 + r)^years = 2, we solve with logarithms:
Exact years = ln(2) ÷ ln(1 + r)
where r is the rate written as a decimal (8% → 0.08). The number 72 is used instead of the more precise 69.3 because it has so many whole-number divisors (2, 3, 4, 6, 8, 9, 12…), which keeps the division easy to do in your head.
Worked example
You invest at an annual rate of 8%.
- Rule of 72:
72 ÷ 8 = 9years. - Exact value:
ln(2) ÷ ln(1.08) = 0.6931 ÷ 0.07696 = 9.006years.
The gap is just 0.006 years (about two days) — which is exactly why 8% is the case where the rule of 72 nearly nails it. Now in reverse: to double in 10 years, you need 72 ÷ 10 = 7.2% a year; the exact figure is 2^(1/10) − 1 = 7.177%. Again, almost identical.
Common rates table
| Annual rate | Rule of 72 | Exact years |
|---|---|---|
| 2% | 36 years | 35.003 years |
| 4% | 18 years | 17.673 years |
| 6% | 12 years | 11.896 years |
| 8% | 9 years | 9.006 years |
| 10% | 7.2 years | 7.273 years |
| 12% | 6 years | 6.116 years |
Notice the pattern: the approximation is sharpest around 8% and drifts a little at the extremes. At very low rates (2%) the rule overstates the time; at high rates (12%) it comes up slightly short — but for a back-of-the-envelope answer it stays genuinely useful.
Frequently asked questions
Why 72 and not some other number?
Mathematically, the number that gives exact doubling is ln(2) × 100 ≈ 69.3. But 69.3 is awkward to divide in your head. 72 was chosen as a compromise: it’s very close and divisible by 2, 3, 4, 6, 8, 9, and 12, so it almost always yields round answers. For rates near 8%, 72 is actually more accurate than 69.3.
Does it work for inflation too?
Yes, and it’s one of its most eye-opening uses. If inflation runs at 6% a year, prices double — and your money loses half its buying power — in about 72 ÷ 6 = 12 years. It’s a fast way to see why cash stuffed under the mattress erodes your wealth over time.
When does the rule of 72 stop being accurate?
When the rate strays far from 8%. Below 3% or above 15%, the error grows and you’re better off using the exact logarithm formula. Some analysts switch to 70 for low rates and 78 for high rates, nudging the numerator to shrink the error.
Does it apply to debt and credit cards?
Absolutely. If a card charges 36% a year, an unpaid balance doubles in 72 ÷ 36 = 2 years. Framing it that way makes it clear why compound interest works for you when you invest and against you when you owe.
Does the rule of 72 assume compound interest?
Yes. The formula assumes gains are reinvested and go on to earn further gains (annual compounding). With simple interest, where only the original principal earns, money doesn’t double along this rule — it grows in a straight line instead.