Rule of 72 vs Rule of 70 vs Rule of 69
All three estimate how long money takes to double — divide the number by your growth rate. Use the Rule of 72 for everyday mental math and typical rates; it divides cleanly and is closest for annual compounding at 6 to 10 percent. Use the Rule of 69.3 when compounding is continuous, where it is mathematically exact. The Rule of 70 sits in between and edges ahead at lower rates. At 8 percent they give 9.0, 8.75 and 8.66 years respectively — close enough that the easiest one usually wins.
The short answer
Each rule estimates a doubling time the same way — divide the number by your annual growth rate as a percentage. The only difference is the number:
- Rule of 72 — the everyday default. Easy mental math and closest of the three for annual compounding at typical rates of 6 to 10 percent.
- Rule of 70 — a slightly closer estimate at lower rates, and common in economics for growth and inflation.
- Rule of 69.3 — the mathematically exact version for continuous compounding.
Skip the arithmetic: the Rule of 72 calculator gives the doubling time for any rate instantly.
The three rules at a glance
| Rule | Doubling time | Best suited to |
|---|---|---|
| Rule of 72 | 72 ÷ rate | Everyday mental math; annual compounding at 6–10% |
| Rule of 70 | 70 ÷ rate | Lower rates; economics, inflation and population growth |
| Rule of 69.3 | 69.3 ÷ rate | Continuous compounding; maximum precision |
The smaller the divisor, the shorter the estimate. Because they sit so close together, the practical choice usually comes down to which is easiest to divide in your head.
Doubling times compared
Here is what each rule produces across common rates, next to the true doubling time with annual compounding:
| Rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Actual (annual) |
|---|---|---|---|---|
| 4% | 18.0 | 17.5 | 17.3 | 17.7 |
| 6% | 12.0 | 11.7 | 11.6 | 11.9 |
| 8% | 9.0 | 8.8 | 8.7 | 9.0 |
| 10% | 7.2 | 7.0 | 6.9 | 7.3 |
All figures are in years. Notice how the Rule of 72 tracks the actual annual doubling time most closely from 6 percent upward — and at 8 percent it is almost exact, 9.0 versus 9.01. At 4 percent the Rule of 70 pulls slightly ahead. The gaps are small enough that for a quick estimate any of them works.
Why 72 is the popular default
Given that 69.3 is the exact figure, why did 72 become the household name? Divisibility. The number 72 splits evenly into 1, 2, 3, 4, 6, 8, 9 and 12 — most of the growth rates people actually use. That makes the arithmetic instant: 72 ÷ 6 = 12, 72 ÷ 8 = 9, 72 ÷ 9 = 8, all whole numbers.
A rule of thumb only earns its keep if you can run it in your head, and 72 wins on that front. It trades a sliver of precision for arithmetic anyone can do without a calculator, which is exactly what a mental shortcut is for. The Rule of 72 explainer covers how to use it day to day.
When to use 70 or 69.3
The other two have their place:
- Reach for 69.3 when interest compounds continuously, as in some finance and physics contexts. There it is not an approximation at all — it is the exact answer.
- Reach for 70 at low growth rates, or in economics and demography where it is the traditional choice for how fast prices, GDP or a population double. At 2 percent inflation, 70 ÷ 2 = 35 years is the standard estimate.
- Stick with 72 for everyday investing questions at normal return rates, where it is both the easiest and, for annual compounding, the most accurate of the three.
The math behind the numbers
The exact doubling time comes from logarithms. For continuous compounding:
Multiply the top by 100 to work in whole percentages and you get 69.3 ÷ rate — the Rule of 69.3. For annual compounding the exact figure is ln(2) ÷ ln(1 + rate), which curves slightly away from a fixed number as the rate rises. That curvature is why a divisor a little above 69.3 fits ordinary compounding better, and why 72 — easy to divide and close across common rates — became the rule everyone remembers. See how compound interest works for the growth these rules approximate.
Assumptions
- A constant growth rate. All three rules assume your rate of return stays fixed; real returns vary year to year.
- Compounding basis matters. 69.3 is exact for continuous compounding; 72 fits annual compounding best at typical rates. The comparison table uses annual compounding.
- They estimate time to double only. These are shortcuts for one specific question, not a full projection of a balance.
- Best in the mid-range. Every version drifts at very high rates; for those, calculate the exact figure instead.
Frequently asked questions
The bottom line
All three rules answer the same question and land within months of each other. Use the Rule of 72 for everyday investing math — it is the easiest to divide and the closest for annual compounding at normal rates. Switch to 69.3 for continuous compounding, where it is exact, and to 70 for low rates or economic growth. At 8 percent, all three agree money doubles in roughly 8.7 to 9 years.
Run any rate through the Rule of 72 calculator, or read what the Rule of 72 is for the basics.
Disclaimer: This page is for general educational purposes only and is not financial advice. Doubling-time rules are approximations that assume a constant rate of return; actual results vary with markets, inflation, taxes and fees. Consider speaking with a qualified financial professional before making decisions about your own money.