Last updated October 4, 2026 · Report an error
When something grows at a steady percentage rate each period — savings, population, an investment — it eventually doubles. This tool calculates exactly how many periods that takes, and compares it to the well-known Rule of 72 mental-math shortcut.
How it works
The exact doubling time is t = ln(2) / ln(1 + r), where r is the growth rate as a decimal. The Rule of 72 approximates this as 72 divided by the growth rate percentage — a quick mental estimate that is close but not exact, especially at higher growth rates.
- Enter growth rate per period (%).
- Click Calculate to see your results.
Examples
A 5% annual growth rate
At 5% per year, the exact doubling time is about 14.2 years, while the Rule of 72 approximates it as 72 ÷ 5 = 14.4 years — close, but not identical.
Who should use it
- Estimating how long an investment takes to double at a given annual return.
- Estimating population or resource doubling time given a growth rate.
Industry applications
- Personal finance and investing
- Demography and biology
- Economics
Advantages
- Shows both the exact answer and the well-known Rule of 72 approximation side by side.
- Works for any positive growth rate.
Limitations
- Assumes a constant growth rate every period — real-world growth rates often vary over time.
Common mistakes to avoid
- Treating the Rule of 72 as an exact answer rather than a quick approximation.
Best practices
- Use the exact formula for any calculation where precision matters, and reserve the Rule of 72 for quick mental estimates.
Tips
- For growth rates far from 6-10%, prefer the exact formula — the Rule of 72 approximation error grows at the extremes.
Frequently asked questions
The Rule of 72 is a mental-math approximation of the exact logarithmic formula. It's most accurate for growth rates roughly between 6% and 10%, and drifts further from the exact answer at very low or very high rates.
Yes — the formula applies to any quantity growing at a fixed percentage rate per period, whether that's money, population, bacteria, or any other exponentially growing value.