Rule of 72 calculator

The mental-math shortcut

The Rule of 72 says that dividing 72 by an annual growth rate gives the approximate number of years for money to double. At 6% it says 12 years; at 9% it says 8. The same trick works backward: to double in 9 years you need roughly 8% a year. It is handy for quickly sizing up how compounding, inflation or fees work over time.

Where the number comes from

With growth at rate r per year, money doubles when (1 + r)^t = 2, so t = ln 2 / ln(1 + r). For small rates ln(1 + r) is close to r, and ln 2 is about 0.693, which points to a rule of 69.3. People use 72 because it divides evenly by 2, 3, 4, 6, 8, 9 and 12 and is more accurate around 8% to 10% once compounding is accounted for.

Methodology

The calculator computes the shortcut 72 ÷ rate and the exact value ln 2 / ln(1 + rate), then reports the error as (approximation − exact) ÷ exact. In reverse, the exact required rate is 2^(1/years) − 1, compared with 72 ÷ years. The rate is treated as an effective annual rate compounded yearly. The rule holds best for rates from about 6% to 10%, and drifts at very low or very high rates.

Good uses

• See what doubling time a savings or investment rate implies, then compare with the compound interest calculator or the compound interest guide.
• Apply it to inflation: at 3% prices roughly double in 24 years. See the inflation calculator.
• Remember it works for debt too. A balance at a high APR can double surprisingly fast.

Frequently asked questions

This calculator is for education and illustration. It does not account for taxes, fees or your personal situation unless stated, and is not financial advice.