— Investment
Rule of 72 Calculator
A fast way to estimate how long money takes to double — divide 72 by the return — or the return you’d need to double in a set time.
Years to double
9
- At this annual return
- 8%
- Exact (log-based) years
- 9.01
- Approximation error
- -0.07%
— Doubling time by return rate
| Annual return | Rule-of-72 years | Exact years |
|---|---|---|
| 2% | 36 | 35 |
| 4% | 18 | 17.67 |
| 6% | 12 | 11.9 |
| 8% | 9 | 9.01 |
| 10% | 7.2 | 7.27 |
| 12% | 6 | 6.12 |
| 15% | 4.8 | 4.96 |
— How it works
Years to double ≈ 72 ÷ rate. Exact: years = ln(2) ÷ ln(1 + rate). Reverse: rate ≈ 72 ÷ years.
What the Rule of 72 is
The Rule of 72 is the most useful piece of mental maths in investing: divide 72 by your annual return and you get, near enough, the number of years it takes your money to double. At 8% a year, 72 ÷ 8 = 9 years; at 6%, twelve years; at 12%, six. Run it backwards and 72 divided by the years you have gives the return you would need to double in that time.
It works because doubling is about compounding, and the maths of compounding involves logarithms — but 72 is a friendly, highly divisible number (by 2, 3, 4, 6, 8, 9, 12) that lands remarkably close to the exact answer across the rates people actually earn. This calculator gives you the shortcut and the exact figure side by side, so you can see just how close the rule is.
Worked example — 8% a year: Rule of 72: 72 ÷ 8 = 9 years to double. Exact: ln(2) ÷ ln(1.08) ≈ 9.01 years. The shortcut is off by less than a week over nine years.
Why 72, and the other constants
The mathematically exact constant for continuously compounded returns is ln(2) × 100 ≈ 69.3, and some people use 70 for the same reason. But 72 is the popular choice because it divides cleanly by so many common rates, and because for ordinary annual compounding it is actually more accurate than 69.3 around the 6–10% range most investors care about. Switch the variant constant under Advanced options to compare 72, 70 and 69.3 against the exact answer.
The approximation is at its best near 8%. At very low or very high returns the gap widens a little — the calculator shows the error so you know when to trust the shortcut and when to reach for the exact figure.
Beyond doubling: tripling and the Rule of 114
The same trick scales to other multiples. To quadruple your money is simply to double it twice, so it takes about twice as long as doubling; to grow eightfold, three doublings. Choose a target multiple under Advanced options and the calculator works out the time (or rate) for 2×, 4× or 8×.
Tripling has its own constant: because tripling takes about 1.58 doublings, the rule becomes roughly 114 ÷ rate — the “Rule of 114”. Pick the triple option and the calculator handles it for you.
— Reader questions
How accurate is the Rule of 72?
Very, across normal investment returns. Around 6–10% it is within a fraction of a year of the exact answer. The error grows at extreme rates — well below 4% or above about 20% — where the exact figure shown beside it is worth using instead.
Why 72 and not 70 or 69.3?
69.3 is the mathematically exact constant for continuous compounding, and 70 is a rounder version of it. But 72 divides evenly by many common rates (and for annual compounding is more accurate near 8%), which makes it the easiest to do in your head — hence its popularity.
How do I use it to find the return I need?
Switch to “Return needed” mode and enter the years you have. The rule divides the constant by the time: to double in 9 years you need about 72 ÷ 9 = 8% a year. The exact required rate is shown alongside.
What is the Rule of 114?
It is the tripling version of the Rule of 72. Because tripling takes about 1.58 doublings, dividing roughly 114 by your return estimates the years to triple. Choose the triple (3×) target and the calculator applies it.
Does it account for inflation, fees or tax?
No — it is a pure rate-and-time relationship. To double your real spending power, use your inflation-adjusted (real) return as the input; for fees, use the return net of the expense ratio.
Can I see the actual doubled amount?
Yes. Enter an initial amount under Advanced options and the calculator shows the resulting figure for your chosen multiple — for example, 100,000 doubling to 200,000 — purely as an illustration.