Investment
Compound annual growth rate
Take the total growth factor, raise it to 1/n to spread it evenly across every year, and subtract 1 to convert the factor back into a rate.
The Formula
CAGR = (EV / BV)^(1/n) - 1
Take the total growth factor, raise it to 1/n to spread it evenly across every year, and subtract 1 to convert the factor back into a rate.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| BV | Beginning value | currency | Value at the very start of the measurement window. |
| EV | Ending value | currency | Value at the end of the window. Include reinvested income so both endpoints are measured the same way. |
| n | Elapsed time in years | years | Fractions are allowed: 18 months is 1.5. Count elapsed time, not the number of calendar years touched. |
What Each Symbol Means
BVcurrency
Beginning value
Value at the very start of the measurement window.
EVcurrency
Ending value
Value at the end of the window. Include reinvested income so both endpoints are measured the same way.
nyears
Elapsed time in years
Fractions are allowed: 18 months is 1.5. Count elapsed time, not the number of calendar years touched.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate cagr page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate CAGR, filed under Finance. Every number the guide produces comes from substituting into this one line.