Rule of 72 Calculator

Divide 72 by the rate

At 6 percent, money doubles in about 12 years. At 8 percent, about 9. At 9 percent, exactly 8. The rule works in reverse too: to double in 10 years you need about 7.2 percent. Its value is that it runs in your head during a conversation, which the exact logarithmic formula does not.

Why 72 and not 69

The mathematically exact constant for continuous compounding is 69.3, from the natural logarithm of 2. But 72 is close, and it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which is what makes the mental arithmetic possible. The approximation is most accurate between about 6 and 10 percent, and drifts at the extremes — at 2 percent the rule says 36 years against an actual 35, and at 20 percent it says 3.6 against an actual 3.8.

Doubling time is the intuition people lack

The rule's real use is making compounding legible. At 7 percent, money doubles roughly every decade, so 10,000 invested at 25 becomes about 160,000 by 65 with nothing added — four doublings. The same rule applied to a 20 percent credit card shows the debt doubling in under four years, which is the same arithmetic working against you.

It applies to any compounding quantity

Inflation at 3 percent halves purchasing power in about 24 years. Users growing 10 percent a month double in about 7 months. A fee of 1 percent a year sounds small until the rule shows what it removes over four decades of compounding.

Variants for other multiples

The rule of 114 estimates tripling time and the rule of 144 estimates quadrupling. All are the same logarithmic relationship with a constant chosen for convenient division, and all lose accuracy at high rates for the same reason.