How to use it
- Choose Years to double, from a rate to find how long a sum takes at a rate, or Rate that doubles in some years to find the rate.
- Type the Yearly rate in percent, or the Years to double, depending on your choice.
- Read the exact figure, then the rule of 72 and the rule of 70 estimates beside it.
- Open the table to compare the exact years and the two rules at common rates.
The exact formula and the rules
A sum that grows at a steady rate each period doubles when its growth reaches the same amount again. The exact time to double is the natural logarithm of 2 divided by the logarithm of one plus the rate. The rule of 72 gives the same answer quickly in the head: divide 72 by the rate in percent.
The rule of 70 divides 70 instead of 72. Both are approximations. Wikipedia notes that 72 is most accurate for rates around 8%, that 70 is most accurate around 2%, and that the accuracy falls at higher rates.
Years to double = ln 2 ÷ ln(1 + r ÷ 100)
Rule of 72: years ≈ 72 ÷ r
Rule of 70: years ≈ 70 ÷ r
Rate to double in t years: r = 2^(1 ÷ t) − 1
Rule of 72 for a rate: r ≈ 72 ÷ t- At 8%, the exact time is 9.01 years, the rule of 72 gives 9 and the rule of 70 gives 8.75.
- At 2%, the exact time is 35.00 years, the rule of 70 gives 35 and the rule of 72 gives 36.
Where the rule can mislead
The rules describe growth that is compounded once per period, with the period the same as the rate's. Monthly or daily compounding of a yearly rate changes the answer slightly, and very high rates make the rules less accurate. For a sum that is paid in or out during the period, the rules do not apply.
What this calculator does not include
- Taxes, fees and inflation, which slow the growth of the money you actually keep.
- Changes in the rate during the period.
- Money added or withdrawn while it grows. Use the compound interest calculator for regular payments.
Worked example: a sum at 8% a year
The exact doubling time is ln 2 ÷ ln 1.08 = 0.6931 ÷ 0.0770 = 9.01 years.
The rule of 72 gives 72 ÷ 8 = 9 years, which is close. The rule of 70 gives 70 ÷ 8 = 8.75 years, a little short.
| Years | |
|---|---|
| Exact | 9.01 |
| Rule of 72 | 9.00 |
| Rule of 70 | 8.75 |
Frequently asked questions
Why is the rule 72 and not 100?
72 has many divisors, and at common rates it gives a time close to the exact figure. Dividing 100 by the rate gives a time that is much further off, because the growth per year is not linear.
Is the rule of 72 exact?
No. It is an approximation, most accurate for rates around 8% and less accurate as the rate rises. The exact time is ln 2 divided by ln of one plus the rate, which this calculator also shows.
What rate doubles my money in 10 years?
About 7.18% a year: 2^(1/10) − 1 = 0.0718. The rule of 72 gives 72 ÷ 10 = 7.2%, which is close.
Can I use it for debt?
Yes. The same rule shows how fast a debt doubles at its interest rate if nothing is paid. It assumes the interest is added once per period and nothing is repaid.
Is my data sent to a server?
No. The calculation runs in your browser, and nothing you enter is sent to us.
Sources
Figures and text last checked on Tuesday, November 10, 2026.