How to use this calculator
- Type your expected Annual return as a percentage (for example 8).
- Read Years to double (rule of 72), the quick estimate.
- Compare it with Exact years to double to see how accurate the shortcut is at that rate.
- Check Years to triple, and scan the table below for other rates from 1% to 20%.
Where the rule comes from
With compound growth, money doubles when (1 + r)^n = 2. Solving for n needs a logarithm, but ln(2) is about 0.693, and for small rates ln(1 + r) is close to r. That gives n ≈ 69.3 / rate. Seventy-two is used instead of 69.3 because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, and it corrects slightly for typical rates of 6% to 10%.
Years to double ≈ 72 / r; exact: n = ln(2) / ln(1 + r)- r = annual return in percent for the shortcut (8, not 0.08)
- In the exact formula r is a decimal (0.08)
- ln = natural logarithm
Example: three rates side by side
At 6% the rule gives 12 years and the exact answer is 11.9, so the shortcut is nearly perfect. At 10% the rule says 7.2 years against an exact 7.27. At 3% it says 24 years, while the exact figure is 23.45.
The shortcut drifts at the extremes: at 1.5% it gives 48 years but the exact figure is 46.56. For rates between roughly 6% and 10% it is within a few weeks. Past 15%, the rule becomes slightly optimistic, saying 4.8 years at 15% where the exact value is 4.96.
Using it to make decisions
The rule is most useful as a mental yardstick. If a savings account pays 3%, your balance needs about 24 years to double. At 6% it needs 12. Money that doubles twice grows fourfold, so a 30-year-old earning 6% would see four times the original amount by about age 54 and eight times by about age 66, before inflation and tax.
Run it in reverse to find the return you need: to double money in 9 years you need about 8% a year. Use the compound interest calculator to see actual balances with regular deposits.
Applying it to costs and inflation
The same maths works against you. At 3% inflation, prices double in about 24 years, so what costs $1,000 today would cost about $2,000 then. Fees behave similarly: a fund charging 2% a year consumes a large share of long-run growth, because the lost amount compounds too.
To measure this precisely, try the inflation calculator. If you want the growth rate implied by a start and end value, use the CAGR calculator.
Limits of the shortcut
The rule assumes a constant annual return compounding once a year, with no deposits, withdrawals, tax or fees. Real investment returns vary from year to year, and a high average return does not guarantee a smooth path. Treat the answer as a rough guide. It is not a forecast, and past or expected returns carry no guarantee.
Frequently asked questions
What is the Rule of 72?
It is a shortcut: divide 72 by the annual percentage return to estimate how many years it takes an investment to double.
Why 72 and not 69 or 70?
The exact constant is about 69.3, but 72 has many whole-number divisors and fits typical returns of 6% to 10% well.
Does the Rule of 72 work for inflation?
Yes. Divide 72 by the inflation rate to see how many years prices take to double, or your buying power to halve.
How accurate is it at very high or low rates?
It is least accurate far from 8%. At 1% it overstates the time by about 2 years (72 vs 69.66), and at 20% it understates by about 0.2 years. Use the exact figure shown above.
Can I use it for debt?
Yes. A credit card at 24% interest doubles an unpaid balance in about 3 years if no payments are made and interest compounds yearly.