Geometric Mean Calculator
Calculate the geometric mean, the correct average for growth rates and ratios.
What the Geometric Mean Calculator does
The geometric mean multiplies the values and takes the nth root, which makes it the correct average for anything that compounds. Averaging annual returns arithmetically overstates real performance because it ignores the asymmetry of gains and losses.
Formula
Geometric mean = (x₁ × x₂ × … × xₙ)^(1/n)Equivalently: exp((Σ ln xᵢ) ÷ n)For percentage rates, convert to growth factors first: 1 + rate ÷ 100
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Values | text | Yes | Separate values with commas, spaces or new lines. |
| Values are | one of 2 options | Yes | — |
How to use it
- Choose Values are.
- Enter Values.
- Select Calculate.
Worked example
Annual returns of +8%, +12%, −5% and +15%.
- Values
- 8, 12, -5, 15
- Type
- Percentage growth rates
Geometric mean growth factor 1.0722, an average return of 7.22% — below the 7.5% arithmetic average.
Frequently asked questions
Why not just average the percentages?
Because a 50% loss followed by a 50% gain leaves you down 25%, not level. The arithmetic mean says 0%; the geometric mean correctly says −13.4%.
Can it handle negative values?
Not directly. For growth rates, convert to factors — a −5% return becomes 0.95, which is positive and works fine.