Rule of 72 Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The Rule of 72 estimates how many years it takes for a sum to double by dividing 72 by the annual interest rate. At 6% a year, a sum doubles in about 12 years (exact calculation: 11.9 years).
Explanation
The Rule of 72 is a classic personal-finance shortcut for quickly estimating, in your head, how long it takes for a sum to double at a constant annual compound interest rate: just divide 72 by the rate expressed as a percentage. This approximation comes from the exact formula for doubling under compound interest, which involves the natural logarithm of 2 (about 0.693, or 69.3%): 72 is used instead of 69.3 because it divides evenly by many common whole numbers (2, 3, 4, 6, 8, 9, 12), making it easy to calculate mentally for most typical rates, at the cost of a small loss of precision. This calculator always shows both values side by side: the quick Rule-of-72 approximation, and the exact calculation (ln(2) ÷ ln(1 + rate/100)), so the gap between the two stays visible rather than hidden. That gap stays small for typical savings rates (under 10%), but widens noticeably at higher rates: at 24%, the Rule of 72 gives 3 years while the exact calculation gives about 3.22 years — a gap of several months that's no longer negligible. The Rule of 72 assumes compound interest with no additional deposits; for a full calculation including regular deposits, see our compound interest calculator.
Example: a 6% annual rate
Inputs
Annual interest rate: 6%.
Calculation
Approximation (Rule of 72) = 72 ÷ 6 = 12 years. Exact calculation = ln(2) ÷ ln(1.06) ≈ 0.6931 ÷ 0.0583 ≈ 11.9 years.
Result
At 6% a year, a sum doubles in about 12 years under the Rule of 72 (11.9 years exactly).
Frequently asked questions
Why use 72 instead of the exact value 69.3?
Because 72 divides evenly by many common whole numbers (2, 3, 4, 6, 8, 9, 12), making quick mental math possible for most typical rates — a practical advantage that outweighs the small loss of precision, as long as the rate stays in a reasonable range (roughly under 15-20%).
At what rate does the approximation become too imprecise?
The gap between the approximation and the exact calculation stays small (often less than a few weeks) for rates between 4% and 10%, the most common range for savings. Above about 20%, the gap becomes more significant (several months, or even over a year at very high rates): for those cases, it's better to rely only on the exact calculation shown by this calculator.
Does this rule also work for estimating a tripling time?
Not directly with the same constant: the Rule of 72 is specifically calibrated for doubling (ln 2). For tripling, the equivalent constant would be closer to 114 (based on ln 3 ≈ 1.0986, or about 109.9%) — a much less well-known rule that's cited far less often than the doubling one.