What CAGR measures
The compound annual growth rate is the single steady yearly rate that would have taken an investment from its starting value to its ending value over the period in question. Real returns are never steady, so CAGR is a smoothed figure — its job is to make investments held for different lengths of time directly comparable.
The formula
CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1$10,000 growing to $26,000 over 7 years: (26,000 ÷ 10,000) = 2.6, and 2.6 raised to the power of 1/7 is 1.1462, so the CAGR is 14.62%. Total growth was 160%, but quoting 160% without the seven years attached tells you nothing useful.
Why the average of yearly returns is the wrong number
| Year | Return | Value of $1,000 |
|---|---|---|
| 1 | +50% | $1,500 |
| 2 | −50% | $750 |
| Simple average | 0% | — |
| Actual CAGR | −13.4% | $750 |
The arithmetic average says you broke even; you actually lost a quarter of your money. Compounding is multiplicative, so gains and losses do not cancel. CAGR is the geometric mean and always tells the truth about what happened to the balance.
What CAGR hides
- Volatility. Two investments can share a 10% CAGR while one moved smoothly and the other halved twice on the way.
- Cash flows. CAGR assumes one sum in at the start and nothing added or withdrawn. If you paid in over time, use an IRR or money-weighted return instead.
- The endpoints you picked. Starting from a market bottom flatters every CAGR. Changing the start date by a few months can change the answer enormously.
- Inflation. A 7% nominal CAGR with 3% inflation is about 3.9% real, not 4% — divide, do not subtract.
Reference points
| CAGR | Doubles in | $10,000 after 20 years |
|---|---|---|
| 4% | 17.7 years | $21,911 |
| 7% | 10.2 years | $38,697 |
| 10% | 7.3 years | $67,275 |
| 15% | 5.0 years | $163,665 |
| 20% | 3.8 years | $383,376 |
Frequently asked questions
Can I use a period that is not a whole number of years?
What if the ending value is lower than the start?
Why is the doubling time missing sometimes?
Is CAGR the same as annualised return?
Should I use price only, or include dividends?
Does anything leave my browser?
Note
A calculation tool, not investment advice. A historical CAGR describes the past and carries no guarantee about the future.