The short answer
The compound annual growth rate (CAGR) is the single yearly rate that, applied every year and compounded, turns the starting value into the ending value over the given number of years. It summarises the start and the end; it says nothing about what happened in between.
The formula
CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1
Input rules used by this site’s calculator:
- Starting value must be greater than 0.
- Ending value must be 0 or more. An ending value of 0 means everything was lost, and CAGR is −100%.
- Years must be greater than 0 and may be fractional, such as 0.5 or 2.25.
A worked example
A value grows from 100 to 121 over 2 years. This is example data, not any real security.
- Ending value ÷ starting value = 121 ÷ 100 = 1.21
- Exponent = 1 ÷ 2 = 0.5
- 1.21^0.5 = 1.1
- 1.1 − 1 = 0.10, so CAGR = 10.00%
Check it forwards: 100 × 1.10 = 110 after one year, and 110 × 1.10 = 121 after two. The calculator shows the same four steps.
Compare this with the total return: (121 − 100) ÷ 100 = 21% over the whole period. CAGR instead expresses it as one rate compounded every year: 10% a year, not 21% ÷ 2.
Limits and common misreadings
- Money added or withdrawn changes the question. If cash went in or out during the period, the first and last values no longer describe one investment’s growth. A CAGR from those two values cannot answer how that investment performed.
- The path is invisible. Two histories with the same starting value, ending value and number of years have the same CAGR, even if one of them fell by half on the way. The number of years matters: 100 to 121 is 21% a year over 1 year but 10% a year over 2 years. For falls along the way, use the maximum drawdown instead.
- Short periods are extrapolated. With fewer than 1 year, CAGR stretches a short-term change into a yearly rate. That is arithmetic, not a forecast.
- A total loss is −100%. With an ending value of 0 the result is exactly −100%. A result that rounds to −100.00% while the ending value is still above 0 is not a total loss.
- It is not a promise. A past CAGR does not mean future years will grow at that rate.