Geometric Mean Calculator
Find the geometric mean of positive numbers, the right average for growth rates, ratios and returns.
About the Geometric Mean Calculator
The geometric mean multiplies n numbers and takes the n-th root. It's the correct way to average rates of growth: if an investment gains 10%, 25%, then loses 5% and gains 8%, its average yearly growth is the geometric mean of 1.10, 1.25, 0.95 and 1.08, minus 1.
The formula
G = (x₁ × x₂ × … × xₙ)^(1/n)
- Computed as
- exp(average of ln xᵢ), which avoids overflow
Worked example
Example: Geometric mean = 4
- Input: Positive numbers (e.g. growth factors): 2, 8, 4.
- Formula: G = (x₁ × x₂ × … × xₙ)^(1/n)
- Result: Geometric mean = 4
- Arithmetic mean: 4.6666666667
- Harmonic mean: 3.4285714286
- As average growth rate: 300% per period
Questions people ask
Why is it always at most the arithmetic mean?
That's the AM–GM inequality; they're equal only when all values are the same.
How do I average percentage returns?
Convert each to a factor (1 + r), take the geometric mean, then subtract 1.