How to use
- Choose what to calculate — usually Annual growth rate (CAGR).
- Enter the other three values, such as the starting value, ending value and years.
- Read the result, the total change and the year-by-year table.
Options explained
- CAGR formula
- (ending ÷ starting)^(1 ÷ years) − 1. Doubling in 5 years is about 14.87% a year, not 20%.
- Number of years
- Can be a fraction, e.g. 2.5 years. Solving for years tells you how long it takes to reach a target at a given rate.
Worked example and doubling times
An investment that grows from 10,000 to 30,000 in 4 years has a CAGR of (30,000 ÷ 10,000)^(1 ÷ 4) − 1 = 31.61% a year. The same formula rearranged gives the number of years at a given rate:
years = ln(ending ÷ starting) ÷ ln(1 + rate)Doubling time at some common rates:
| Annual growth | Years to double |
|---|---|
| 3% | 23.4 |
| 5% | 14.2 |
| 7% | 10.2 |
| 10% | 7.3 |
| 12% | 6.1 |
CAGR smooths the growth into one rate. It says nothing about the ups and downs in between, so two investments with the same CAGR can have had very different paths.
Frequently asked questions
Why isn’t CAGR the same as the average yearly return?
The simple average adds up yearly percentages, but gains compound. +50% then −50% averages 0%, yet 100 becomes 75 — a CAGR of about −13.4%.
What if I added money along the way?
CAGR only uses the start and end values. With deposits or withdrawals on different dates, use the XIRR Calculator.
How long does it take to double my money?
Choose Number of years, enter 1 and 2 as the starting and ending values and your rate. At 7% it takes about 10.2 years — close to the rule of 72 (72 ÷ 7 ≈ 10.3).
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