Doubling Time Calculator
Find how many years an investment takes to double at a given annual rate using the exact logarithm formula, the rule of 72 or the rule of 70.
Results · USD
Years to double
- Exact ln comparison
- 10.245
- Rule of 72
- 10.286
You might also need
Educational estimates · not financial advice · free, no signup
How this was calculated
Exact: t = ln(2)/ln(1+r). Rule of 72 ≈ 72/r%; rule of 70 ≈ 70/r%.
Want more detail? Full formula notes & FAQs ↓
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
How long does it take for money to double? At 7% a year, an amount grows 1.07 times each year, and after about 10.2 years it has doubled. The exact answer uses logarithms, but the rule of 72 is a famous shortcut: divide 72 by the percentage rate. It gives 10.29 years at 7%, close to the exact 10.24. The same arithmetic works for anything that grows at a constant percentage rate, including inflation, population and debt. This calculator reports the exact figure and the approximations. The rules are accurate for rates of roughly 6% to 10% and less so at very high or low rates.
When to use / who it helps
- You want a quick sense of how long an investment takes to double.
- You want to see how fast prices double under a given inflation rate.
- You are teaching or learning the rule of 72.
- You are comparing the effect of different rates.
- You are checking a mental calculation.
How to use
Steps
- Enter the annual growth rate as a percentage.
- Choose the method, exact, rule of 72 or rule of 70.
- Read the years to double.
- Compare with the exact value and the rule of 72.
- Try several rates to build intuition.
- Remember that it assumes steady compounding.
How to interpret results
- Higher rates cut the doubling time sharply.
- At rates below roughly 10%, the rule of 72 slightly overstates the exact time, and it is easy to divide in your head.
- The rule of 70 is closer for continuous compounding and low rates.
- Double again to get quadrupling time.
- The same result applies to inflation, so prices double in about 72 ÷ inflation rate years.
Common mistakes & gotchas
- Entering the rate as a decimal, such as 0.07.
- Applying the rule to rates far outside its range.
- Forgetting that returns are not steady in practice.
- Ignoring fees, taxes and inflation.
- Confusing doubling time with the time to earn a fixed amount.
Worked example
Worked example — 7% a year
- Exact: ln 2 ÷ ln 1.07 = 0.6931 ÷ 0.06766 ≈ 10.245 years.
- Rule of 72: 72 ÷ 7 = 10.29 years.
- Rule of 70: 70 ÷ 7 = 10 years.
- At 3% the exact time is 23.45 years, and the rule of 72 gives 24 years.
Result: At 7% an amount doubles in about 10.2 years.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Exact: t = ln(2)/ln(1+r). Rule of 72 ≈ 72/r%; rule of 70 ≈ 70/r%.
Frequently asked questions
What is the rule of 72?
Divide 72 by the annual percentage rate to estimate years to double.
Why 72?
It has many divisors and approximates 100 × ln 2 adjusted for compounding at typical rates.
Is the rule exact?
No, but it is accurate to within a few percent for typical rates.
Does it apply to inflation?
Yes, to estimate when prices double.
How do I find time to triple?
Use ln 3 ÷ ln(1 + r), or roughly 110 ÷ rate.
Does it include contributions?
No. It applies to a single lump sum.