// RULE OF 72 CALCULATOR

Rule of 72 Calculator

Estimate doubling time or required rate using the classic Rule of 72 shortcut, with the exact answer beside it.

// INPUTS

ANNUAL RETURN (%)

// OUTPUT

DOUBLING TIME (RULE OF 72)

8.00 yrs

EXACT8.04 yrs

// FORMULA

DoublingYears ≈ 72 / Rate%
RequiredRate% ≈ 72 / Years

The shortcut is accurate within roughly 1% for rates between 5% and 12%.

// EXAMPLE

// WORKED OUT

At 9% per year:
  Years to double ≈ 72 / 9 = 8 years
  Exact: ln(2) / ln(1.09) = 8.04 years

// WHAT THIS MEANS

The Rule of 72 is a mental-math shortcut that hides the logarithm. You divide 72 by the rate to get the years, or by the years to get the rate. It only works for rates and periods in the same units (annual return, years) and it loses accuracy at extremes — but for a back-of-envelope sanity check it is invaluable.

// FAQ

Why 72 and not 70 or 69.3?+

Mathematically the exact constant for very low rates is ln(2) ≈ 69.3. 72 is preferred because it has many small divisors (2, 3, 4, 6, 8, 9, 12) so it is easier to do in your head.

When does the rule break down?+

Above ~15% or below ~3%, the approximation error grows. Use the exact formula in those cases.