Rule of 72 Calculator

The Simple Version

The Rule of 72 is a mental math shortcut. Divide 72 by your annual interest rate and the result is the approximate number of years to double your money. At an illustrative 6% rate, 72 divided by 6 equals 12 years. At 4%, it equals 18 years. At 9%, it equals 8 years. No calculator needed, you can do it in your head. The rule works because the natural logarithm of 2 is approximately 0.693, and 0.72 is a conveniently close round number with many small divisors. It was popularized centuries ago as a quick estimation tool and remains useful today for back-of-the-envelope planning. The calculator takes your rate, runs the Rule of 72 division, and displays the result alongside the exact doubling time calculated from the precise formula: t = ln(2) / ln(1 + r). This side-by-side view shows you both the estimate and the mathematically precise answer in one glance.

Where the Rule Drifts From Reality

The Rule of 72 is most accurate at rates near 8%. At that rate, the rule says 9.0 years and the exact answer is 9.01 years, virtually perfect. As you move away from 8% in either direction, the drift grows. At a low illustrative 2% rate, the rule predicts 36 years. The exact answer is 35.0 years. The rule overshoots by roughly one year. At a higher illustrative 12% rate, the rule predicts 6.0 years while the exact answer is 6.1 years, so the rule slightly undershoots. For rates between 4% and 10%, which cover most savings and moderate-return investments, the Rule of 72 is off by less than half a year. That makes it reliable enough for quick mental estimates when you want a rough sense of doubling time without pulling out a calculator. For precise planning over specific time horizons, use the exact logarithmic formula that this tool runs automatically alongside the shortcut.

The Rule of 72 assumes a fixed, constant rate compounded annually. In practice, returns fluctuate and compounding frequency varies.