Rule of 72 Calculator — Years to Double (or Required Rate)

Rule of 72: A Friendly Guide

The Rule of 72 is a quick mental shortcut for estimating how long an investment will take to double. Divide 72 by your annual interest rate (in percent) to get the approximate number of years to double: \[ \text{Years} \approx \frac{72}{\text{rate\%}}. \] You can also flip it around: if you want to double your money in a certain number of years, divide 72 by the years to estimate the required annual rate: \[ \text{Rate\%} \approx \frac{72}{\text{years}}. \]

Why 72?

The number 72 is convenient because it divides evenly by many small integers (2, 3, 4, 6, 8, 9, 12). That makes mental math fast: at 8% you get \(\,72 ÷ 8 = 9\,\) years; at 6% it’s \(\,12\,\) years. Behind the scenes, the exact doubling time for annual compounding is \[ t_{\text{exact}} = \frac{\ln 2}{\ln(1+r)}, \] where \(r\) is the rate as a decimal (e.g., 0.08 for 8%). The Rule of 72 is a smooth approximation to this logarithmic relationship.

How Accurate Is It?

Around mid–single-digit to low–double-digit rates (roughly 6%–10%), the Rule of 72 is typically within a few months of the exact value. Accuracy drifts at very low or very high rates because compounding is non-linear. If you want the precise number, this calculator shows the Rule of 72 estimate alongside the exact compounding result.

When to Prefer 69.3 or 70

You might see references to a “Rule of 69.3” or “Rule of 70.” These are alternate heuristics. 69.3 lines up with continuous compounding because \(\ln 2 \approx 0.693\). 70 is a rounder number that some people find easier to remember. For most everyday uses, 72 is friendlier for mental math, and the difference is small.

Practical Examples

• Rate → Years: At 8% per year, \(\,72 ÷ 8 = 9\,\) years (exact ≈ 9.01 years).
• Years → Rate: To double in 12 years, you need about \(\,72 ÷ 12 = 6\%\) (exact ≈ 5.95%).

Limitations to Keep in Mind

• Compounding assumptions: The exact comparison here assumes annual compounding. Different compounding frequencies shift the exact result, though the 72 shortcut remains useful.
• Fees and taxes: The rule ignores friction like fund fees, spreads, or taxes. Real-world returns after costs may be lower.
• Volatility and sequence risk: Markets don’t move in a straight line. Averages can hide year-to-year swings that affect actual outcomes.

Going Beyond Doubling

You can adapt the idea for other targets. Tripling time is often estimated with the “Rule of 114,” and quadrupling time with “Rule of 144.” The exact formulas are \[ t_{3\times} = \frac{\ln 3}{\ln(1+r)}, \qquad t_{4\times} = \frac{\ln 4}{\ln(1+r)}. \]

Tips for Using This Tool

• Use the Rule of 72 for a fast sense-check, then glance at the exact value for precision.
• Try a few rates to build intuition: how much faster does doubling get as the rate rises?
• If you have a time goal (e.g., double in 10 years), switch to “Years → Rate” and compare the 72-estimate to the exact rate.

Bottom line: the Rule of 72 is a friendly compass for growth, not a contract. It’s perfect for back-of-the-envelope planning—and this calculator shows you exactly how close that envelope is.

FAQ

Why “72”?

It’s a convenient constant that divides cleanly by many small integers (2,3,4,6,8,9,12). It approximates the natural-log math behind doubling.

What about 69.3 or 70?

You may see the “Rule of 69.3/70” for continuous or more precise compounding. This tool uses 72 for quick intuition and shows the exact value separately.

Does it assume annual compounding?

Yes for the “exact” comparison shown here. If your product compounds differently, the exact value will shift slightly—but the 72 shortcut stays handy.