Rule of 70

The Rule of 70 is a quick way to estimate how many years it takes for a quantity to double given a constant annual growth rate. It’s widely used for investments, population growth, GDP, and other exponential-growth situations.

Formula

If the annual growth rate is expressed as a percent:
Years to double ≈ 70 ÷ (annual growth rate in percent)

Examples:
* 3% growth → 70 ÷ 3 = 23.3 years
8% growth → 70 ÷ 8 = 8.75 years
12% growth → 70 ÷ 12 = 5.8 years

How it works

The Rule of 70 is an approximation based on the natural logarithm of 2 (ln 2 ≈ 0.693). It’s simple to use and gives a quick intuition about exponential growth without complex math.

For more precise results:
* Exact discrete doubling time: t = ln(2) / ln(1 + r) (r as a decimal)
* Continuous compounding doubling time: t = ln(2) / r

When to use it

• Comparing investment returns or estimating how long savings will double at a given annual return.
• Estimating the doubling time of population, GDP, or other steady growth measures.

Limitations

• Assumes a constant growth rate. If rates fluctuate, the estimate can be misleading.
• Less accurate for very high or very low rates; the exact formulas above are preferable when precision matters.
• Does not account for changes in contributions, withdrawals, taxes, fees, or changing compounding frequency unless those are incorporated into the effective growth rate used.

Rule of 70 vs. Rules of 69 and 72

• Rule of 69 (or 69.3) is closer to the exact value when growth compounds continuously (derived from ln 2).
• Rule of 72 is often used because 72 has many divisors, making mental math easier; it can be slightly more accurate for common interest rates and discrete compounding intervals.

Practical tip

Treat the Rule of 70 as a fast mental check. For planning, reporting, or situations where accuracy matters, use the exact logarithmic formulas or a financial calculator.

Key takeaways

• The Rule of 70 estimates doubling time: 70 ÷ growth rate (%).
• It’s a convenient, intuitive tool for quick comparisons and rough forecasts.
• Use exact formulas or calculators when rates are volatile or precision is required.