ReviewedEducational article · Updated Oct 2026
Key takeaways
- Years to double ≈ 72 ÷ annual percentage rate.
- It is a mental shortcut for compound growth, not an exact law.
- Accuracy is best for mid-range rates; very high or low rates drift more.
- You can also solve for the rate: rate ≈ 72 ÷ years.
The Rule of 72 is a back-of-the-envelope way to estimate how long money takes to double at a given compound rate — or what rate you need to double in a given number of years. It is popular because the division is easy and the answer is usually close enough for conversation.
How to use it
- Doubling time: years ≈ 72 ÷ rate(%). At 8%, about 9 years. At 6%, about 12 years.
- Required rate: rate(%) ≈ 72 ÷ years. To double in 10 years, you need about 7.2%.
The entire rule in one expression: divide 72 by the annual percentage rate to estimate years to double.
It is a napkin, not a spreadsheet — and that is exactly why it is useful.
Where it comes from
Exact doubling under continuous compounding involves the natural log of 2 (about 0.693). For annual compounding, the exact years to double are ln(2) / ln(1+r). The Rule of 72 is a convenient approximation that stays tidy with whole percentages. Variants like the Rule of 69.3 are closer for continuous compounding; 72 is friendlier for mental math.
When it drifts
Compare the rule with the exact annual-compounding answer:
- At 6%: rule ≈ 12.0 years; exact ≈ 11.9 — excellent.
- At 9%: rule ≈ 8.0; exact ≈ 8.0 — excellent.
- At 2%: rule ≈ 36; exact ≈ 35.0 — still fine for intuition.
- At 18%: rule ≈ 4.0; exact ≈ 4.2 — the gap grows.
For typical mid-single-digit to low-double-digit rates, the rule is surprisingly good. For very high rates, use the exact formula or a calculator.
Inflation twin: the same rule estimates how long it takes prices to double at a given inflation rate. At 3% inflation, purchasing power of a cash pile halves in roughly 24 years.
What the model leaves out
Taxes, fees and volatile returns all change real-world doubling paths. The Rule of 72 assumes a steady rate — perfect for teaching compounding, incomplete as a forecast.
Comparing the shortcuts with the exact answer
Several variations of the rule exist. The table compares them with the exact doubling time for annual compounding:
| Rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact |
|---|---|---|---|---|
| 3% | 24.0 | 23.3 | 23.1 | 23.45 |
| 5% | 14.4 | 14.0 | 13.9 | 14.21 |
| 7% | 10.3 | 10.0 | 9.9 | 10.24 |
| 10% | 7.2 | 7.0 | 6.9 | 7.27 |
| 12% | 6.0 | 5.8 | 5.8 | 6.12 |
For annually compounded rates between roughly 6% and 10%, the Rule of 72 is the closest to the exact figure. At very low rates the Rule of 70 or 69.3 can be slightly closer. The differences are small enough that any of them works for a quick estimate.
Solving for the rate you need
The rule can be turned around. To double in a given time, you need roughly 72 divided by the number of years:
- Double in 10 years: about 7.2% (exact: 7.18%).
- Double in 5 years: about 14.4% (exact: 14.87%).
- Double in 7 years: about 10.3% (exact: 10.41%).
The shortcut slightly understates the rate needed over short horizons. If you are planning around a target, use the exact formula or a calculator.
Related rules
- Tripling: a Rule of 114 gives roughly 114 ÷ rate years to triple. At 6%, that is 19 years; the exact answer is about 18.9.
- Quadrupling: a Rule of 144 gives 144 ÷ rate. At 6% that is 24 years, versus an exact 23.8.
A sanity check, not a plan
The rule is useful for checking whether a projection looks plausible. If someone promises to double your money in two years, 72 ÷ 2 implies 36% a year, which should make you ask questions. It is also a good reminder of how powerful compounding is; see how compound interest works for the mechanism behind it.
Common questions
Does the rule work with monthly compounding?
It still gives a good estimate. Monthly compounding doubles money slightly faster than annual compounding at the same stated rate.
Where can I check my own numbers?
Use the Rule of 72 estimator and compare its output with the exact formula.
Further reading from official sources
These are general educational resources. Rules and figures differ by country, so look for your own country’s equivalent.
Related reading
This article is for general educational purposes only and is not financial advice. Examples use simplified, hypothetical numbers and ignore taxes, fees and personal circumstances. Consider speaking with a qualified professional before making financial decisions. See our full disclaimer.