CAGR Formula
Learn the compound annual growth rate formula for converting beginning value, ending value and time into an annualized growth rate.
CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1What the formula means.
Find the growth multiple from beginning to end, take the root corresponding to the number of years, then subtract one. Multiply by 100 to express the result as a percentage.
CAGR is a smoothed annual rate, not the actual return in every year.
Beginning value must be positive for the standard real-number formula.
CAGR is useful for comparing growth over different time spans.
Variables.
BThe starting value at the beginning of the period.
EThe value at the end of the period.
nLength of the growth period in years.
Worked example.
- $18,000 ÷ $10,000 = 1.8
- 1.8^(1 ÷ 5) ≈ 1.1247
- 1.1247 − 1 ≈ 0.1247
Common mistakes.
- Dividing total growth by the number of years.
- Treating CAGR as evidence that each year grew at the same rate.
- Using zero or negative starting values in the standard formula.
Quick questions.
Is CAGR the average of yearly returns?
No. It is the constant annual compound rate that links the beginning and ending values.
Does CAGR show volatility?
No. Two series can have the same CAGR but very different paths between the start and end.