Rule of 72 Calculator

Doubling time comes from compound growth: a sum doubles when (1 + r) raised to the number of years equals 2. Solving that exactly requires logarithms, which is awkward to do in your head. The rule of 72 sidesteps the math entirely — divide 72 by the rate expressed as a whole number and you get a close approximation of the years needed.

The number 72 is chosen because it is convenient (it divides cleanly by 2, 3, 4, 6, 8, 9, and 12) and because it happens to track the true logarithmic answer closely across the rates investors care about. The approximation is most accurate around 8%; it drifts slightly at very low or very high rates, generally overstating the time a touch as rates climb.

This tool computes both numbers so the shortcut is never a black box. You see the rule-of-72 estimate, the exact doubling time from the logarithmic formula, and the difference between them — usually a fraction of a year. Use it to sanity-check the mental estimate and to appreciate just how powerful a few extra percentage points of return are over a lifetime.

At an 8% annual return, the rule of 72 estimates doubling in 72 ÷ 8 = 9.0 years. The exact doubling time is ln(2) ÷ ln(1.08) ≈ 9.01 years. The shortcut is off by only about 0.01 years — essentially perfect at this rate, which is exactly why 8% is the sweet spot for the rule of 72.

The rule assumes a fixed annual rate and compounding once per year; with more frequent compounding the exact doubling time shrinks slightly, while the 72 shortcut stays the same. Accuracy degrades away from 8%: at very high rates some people switch to the "rule of 70" or "rule of 69.3" (the latter being the true continuous-compounding constant) for a closer fit. At a 0% or negative rate, money never doubles, so the calculator requires a positive rate. The shortcut is for intuition and back-of-envelope checks — for precise planning, rely on the exact doubling time shown here.