Rule of 72 Calculator (doubling time / required rate)

What the Rule of 72 says

Years to double ≈ 72 / annual rate. So at 6% return, your money doubles in roughly 12 years; at 8%, in 9 years; at 12%, in 6 years. The same rule works in reverse: if you want to double in 10 years, you need ~7.2% annual return.

It's a mental-math shortcut, not a precise formula. The exact answer is ln(2) / ln(1 + r), which requires a calculator. The Rule of 72 was popularized in 15th-century European arithmetic textbooks because 72 has many divisors (2, 3, 4, 6, 8, 9, 12), making mental division easier.

How accurate is it?

Within ~0.5% for rates between 4% and 12% — which covers most realistic investment returns. At very low rates (1-2%) or very high (15%+) the error grows. Some textbooks use the Rule of 70 or 69.3 for higher accuracy at low rates, but 72 is the practical sweet spot.

Use this calculator to see both the Rule of 72 estimate and the exact compound math side by side. The 'approximation error' shows how off the rule is for your specific rate or period.

Where it's used

Investment planning: 'at my expected 7% return, money doubles every 10 years' — this is the Rule of 72 in action. Useful for back-of-envelope retirement projections.

Inflation analysis: at 3% inflation, prices double every 24 years. At 7%, every 10 years. Quick way to grasp purchasing-power erosion.

Population and growth modeling: any quantity growing at a constant percent rate (population, debt, technology adoption) doubles in 72/r years. Foundation of exponential thinking.