How to use the rule of 72 calculator
- Choose Years to double to start from a rate, or Rate needed to double to start from a time frame.
- Enter the annual rate as a percent, such as a return, an interest rate or inflation, or the number of years you have.
- Optionally enter a starting amount to see what it grows to after one and two doublings.
- Compare the rule of 72, the rule of 70 and the exact answer, and use the table to see how well the rule fits at other rates.
Formula
Rule of 72: years to double = 72 / annual rate (in percent)
Rule of 72: rate to double = 72 / years
Exact years = ln 2 / ln(1 + rate)
Exact rate = 2^(1 / years) - 1
The rule works because ln 2 is about 0.693 and 72 has many small divisors. The rules of 70 and 69.3 are closer for low rates.
Worked example
At 8% a year, the rule of 72 says money doubles in 72 / 8 = 9 years. The exact answer is ln 2 / ln 1.08 = 9.006 years, so the shortcut is off by less than 0.1%.
To double in 10 years you need 2^(1/10) - 1 = 7.1773% a year exactly, and the rule says 7.2%. At 3% inflation, prices double in about 23.45 years.
Why the shortcut works
Doubling means (1 + r)^t = 2, so t = ln 2 / ln(1 + r). For small r, ln(1 + r) is close to r, which makes t about 0.693 / r. Using 72 instead of 69.3 corrects for the way ln(1 + r) falls below r at ordinary rates, which is why 72 fits well around 6% to 10%.
Beyond investing
The same rule applies to anything that grows at a steady percent, such as inflation, debt with unpaid interest or a population. Use it to feel how fast prices rise with the inflation calculator, or see exact growth in the compound interest calculator and the CAGR calculator.
When not to use it
The rule assumes one yearly compounding at a constant rate. Real returns vary, fees and taxes reduce them, and very high or low rates drift from the rule. Use the exact result for anything you plan around. The savings calculator shows growth with regular deposits.
Assumptions and limits
- The rate is constant and compounds once a year.
- The rate is not a prediction of any investment return.
- Fees, taxes and inflation are not applied unless you enter a rate that already includes them.
- Rates up to 1,000% and up to 10,000 years are accepted.
Frequently asked questions
What is the rule of 72?
It is a shortcut that divides 72 by an annual percent rate to estimate how many years it takes to double. At 8% that gives 9 years.
How accurate is the rule of 72?
It is very close for rates around 6% to 10% and gets less accurate at very low or very high rates. The table on the page shows the exact figures.
How do I find the rate to double my money in 10 years?
Divide 72 by 10 for about 7.2%, or compute 2 to the power one tenth minus 1 for the exact 7.1773%.
Does the rule of 72 work for inflation?
Yes. At 3% inflation, prices double in roughly 72 / 3 = 24 years, close to the exact 23.45 years.