Rule of 72 Calculator
Divide 72 by an annual growth rate (in percent) to estimate how many years it takes for an amount to double. The approximation is exact at 7.85% and within half a year for rates between 4% and 15%.
Where the rule comes from
The exact relationship is years = ln(2) / ln(1 + r). Taylor-expanding the natural log gives ln(2) / r ≈ 0.693 / r. Multiplying numerator and denominator by 100 gives 69.3 / rate(%). Why 72 then? Because 72 is divisible by 1, 2, 3, 4, 6, 8, 9, and 12 — making mental arithmetic easy — and because for rates between 6% and 10% it is closer to the true value than 69.3 is.
How accurate it is
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2% | 36.0 yrs | 35.0 yrs | +1.0 |
| 5% | 14.4 yrs | 14.2 yrs | +0.2 |
| 8% | 9.0 yrs | 9.0 yrs | 0.0 |
| 12% | 6.0 yrs | 6.1 yrs | −0.1 |
| 20% | 3.6 yrs | 3.8 yrs | −0.2 |
| 30% | 2.4 yrs | 2.6 yrs | −0.2 |
For continuously-compounded rates, the right number is 69.3 instead of 72. For low rates, some practitioners use 70. None of this matters for back-of-the-envelope work; pick 72 and move on.
Practical uses
The Rule of 72 is the fastest way to compare investment returns or growth rates without a calculator. A business growing at 24% per year doubles every three years — eight times in a generation. An economy growing at 2% doubles every 36 years — once in a working life. The same logic applies to inflation eroding purchasing power, debt at compound interest, and engagement metrics compounding from referrals.
Worked example
A retirement account grows at 7.2% per year. 72 / 7.2 = 10 years to double. A $50,000 balance becomes $100,000 in 10 years, $200,000 in 20, $400,000 in 30. This four-fold tripling explains why starting to save in your 20s rather than your 40s is approximately a 4× difference in nominal terminal wealth.