How it's calculated
Rule of 72: years to double ≈ 72 / r (r in percent, e.g. 8)
Exact: years to double = ln 2 / ln(1 + r/100) (compounded once a year)
Inverse: rate ≈ 72 / years; exact rate = 2^(1/years) − 1
Rule of 70 / 69.3: same idea with 70 or 69.3; 69.3 ≈ 100·ln 2 is exact for continuous compounding
- The rule of 72 is most accurate around 8% (it is almost exact near 7.85%). At low rates it overstates the time slightly; at high rates it understates it.
- "Exact" assumes the rate compounds once a year and stays constant. It works for anything growing at a steady percentage, including inflation (prices double in 72 ÷ inflation years).
Worked examples
1. 8% a year
Rule of 72: 72 ÷ 8 = 9.00 years. Exact: ln 2 ÷ ln 1.08 = 0.693147 ÷ 0.076961 = 9.006 years. The rule is off by only 2 days. Load this example
2. 2% a year
Rule of 72: 36.00 years. Exact: 35.003 years. At low rates the rule of 70 (35.00 years) is closer. Load this example
3. Doubling in 6 years
Rule of 72: 72 ÷ 6 = 12.00% a year. Exact: 21/6 − 1 = 12.246%. Load this example
Frequently asked questions
What is the rule of 72?
A shortcut for compound growth: divide 72 by the annual percentage rate to estimate how many years it takes to double. At 6% that's about 12 years; at 9%, about 8 years.
How accurate is the rule of 72?
Very close for typical rates. Between about 5% and 12% it is within a few months of the exact answer for annual compounding. The table on this page shows the exact error at each rate.
Does the rule of 72 work with monthly contributions?
No. It describes a single lump sum growing at a steady rate. For regular contributions, use the compound interest or millionaire calculators.
Why 72 and not 70 or 69.3?
69.3 (100 × ln 2) is exact for continuous compounding, and 70 is close for low rates. 72 is popular because it is accurate near common investment returns and divides evenly by 2, 3, 4, 6, 8, 9 and 12.
Can I use the rule of 72 for inflation?
Yes. At 3% inflation, prices double in about 72 ÷ 3 = 24 years, which means money loses half its buying power in that time.