Formula
CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1doubling time = ln 2 ÷ ln(1 + CAGR)
- years can be fractional, such as 2.5
The single yearly rate that would grow the start value into the end value.
Worked example
10,000 → 25,000 in 5 years
- Starting value
- 10,000
- Ending value
- 25,000
- Number of years
- 5 years
CAGR
20.1124%
Total return: 150%
Absolute gain or loss: 15,000
Years to double at this rate: 3.78 years
How it works
An investment that grows from 10,000 to 25,000 over 5 years has a CAGR of (25,000 ÷ 10,000)^(1/5) − 1 = 20.11% a year. A value that doubles in 10 years has a CAGR of 7.18%, and at that rate would double again every 10 years.
CAGR smooths a bumpy path into a single number, so it hides volatility and says nothing about money added or withdrawn along the way — for regular investing use the SIP Calculator. To project forward from a known rate use the Compound Interest Calculator, and for a one-off change between two values without the time element use Percentage Change Calculator.
Assumptions and limits
- A starting value of zero or less is invalid; an ending value of zero gives −100%.