The rule in one line, with the maths
The Rule of 72 says that to find how many years an investment takes to double, you divide 72 by the annual rate of return written as a whole number. If your money grows at 6 percent a year, it doubles in about 72 divided by 6, or 12 years. At 9 percent it doubles in roughly 8 years, and at 4 percent in about 18 years. You can run the same sum backwards: to double in a set number of years, divide 72 by that number of years to get the return you need. The whole appeal is that it works in your head, with no calculator and no compound interest formula.
It works because compounding is exponential, and the time to double under steady growth depends on the natural logarithm of 2, which is about 0.693. Expressed as a percentage that is 69.3, so the purest version of the rule would be the Rule of 69.3. The number 72 is used instead because it is close enough and far friendlier to divide.
Why 72 and not 69.3 or 70
If 69.3 is more exact, why has 72 won out? Two reasons. First, 72 divides evenly by a long list of numbers: 2, 3, 4, 6, 8, 9 and 12. Those happen to be the return rates people most often want to estimate, so the division stays tidy. Dividing 69.3 by 7 in your head is awkward, while 72 divided by an exact factor is instant.
Second, 72 quietly corrects for a detail the simplest formula misses. The pure 69.3 figure assumes growth is compounded continuously, smeared evenly across the year. Most real investments compound once a year, or once a quarter, which nudges the true doubling time slightly higher. Bumping the divisor up from 69.3 toward 72 happens to offset that for the mid range rates most people use, which is why 72 is often more accurate in practice than the technically purer 69.3 for everyday annual compounding.
So when should you reach for 69.3 or 70 instead? Use a lower divisor when you are dealing with low rates or continuous compounding. At 2 to 3 percent, 69.3 or 70 gives a closer answer than 72. For the typical investing range of roughly 6 to 10 percent compounded annually, 72 is the sweet spot and the one worth memorising.
A mental-maths table for common rates
Because 72 divides so cleanly, a handful of cases are worth keeping in your head. Here is the doubling time the rule gives for rates you are likely to meet:
- 2 percent: about 36 years to double
- 3 percent: about 24 years
- 4 percent: about 18 years
- 6 percent: about 12 years
- 8 percent: about 9 years
- 9 percent: about 8 years
- 12 percent: about 6 years
Notice how steep the effect is at the low end. The jump from 2 percent to 4 percent halves the doubling time from 36 years to 18, because the rule is dividing a fixed number by your rate. That is the same reason a small difference in fees or interest can matter so much over a long horizon: a platform charging 1 percent more is not shaving a sliver off your return, it is meaningfully stretching the time your money needs to grow.
A worked example at 7 percent
Say you invest 10,000 pounds and expect a long run return of 7 percent a year. The Rule of 72 says it doubles in about 72 divided by 7, which is roughly 10.3 years. So after about a decade you would expect around 20,000 pounds, after another decade around 40,000, and after a third around 80,000, each doubling stacking on the last. That stacking is the whole point of compounding: the same growth rate produces ever larger jumps because it is working on a bigger base each time.
How good is the estimate? The exact answer for a 7 percent annual return is about 10.24 years, so the rule lands within a few weeks of the truth. That is plenty accurate for a back of the envelope decision about whether a savings plan will get you where you want in time. When you want the precise figure rather than the shortcut, run the numbers through our compound interest calculator, which applies the full formula and lets you change the contribution and compounding frequency. To pressure test the doubling logic at different rates, the Rule of 72 calculator does the division for you and shows the exact result alongside it.
Where the rule fits, and where it does not
The Rule of 72 is a shortcut for steady, constant growth. Real investment returns are anything but steady: markets rise and fall, and a 7 percent average over a decade hides good years and bad ones. The rule tells you what a smooth 7 percent would do, not what a bumpy 7 percent will do, so treat its answer as the calm midpoint of a much wider range of possible outcomes.
It also assumes you reinvest everything and add nothing. If you are making regular contributions, your pot will pass each double sooner than the rule suggests, because new money is doing some of the work that growth alone would otherwise have to. And the rule says nothing about what a return should be, only what a given return does. Picking a realistic rate in the first place is the harder question, and it is worth being conservative. When you want to compare a single multi year return against an average, our CAGR calculator works out the smoothed annual growth rate, which is exactly the number the Rule of 72 expects you to feed it.
Used with those limits in mind, the Rule of 72 earns its place. It turns an abstract percentage into a human timescale in seconds, which makes it a brilliant sanity check before you commit to a savings goal or compare two products. This is general educational information, not financial advice; for decisions with a lot riding on them, model the full numbers or speak to a qualified, regulated adviser.