Statistics
Average growth rate from growth factors
Convert each return to a factor, average multiplicatively, then subtract one.
The Formula
g = ((1 + r1) x (1 + r2) x ... x (1 + rn))^(1/n) - 1
Convert each return to a factor, average multiplicatively, then subtract one.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| g | Average growth rate | decimal | The constant rate giving the same final value, as a decimal. |
| ri | Period returns | decimal | Each period return as a decimal, so 8 percent is 0.08. |
| n | Periods | unitless | How many periods are averaged. |
What Each Symbol Means
gdecimal
Average growth rate
The constant rate giving the same final value, as a decimal.
ridecimal
Period returns
Each period return as a decimal, so 8 percent is 0.08.
nunitless
Periods
How many periods are averaged.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a geometric mean 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 A Geometric Mean, filed under Math. Every number the guide produces comes from substituting into this one line.