Geometric Mean Calculator
Calculate the geometric mean of a list of positive numbers — commonly used for averaging growth rates, ratios, and investment returns.
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Your result
6
Geometric mean
AI explanation
Formula
Geometric mean = (x₁ × x₂ × ... × xₙ)^(1/n)Worked example
4 and 9
| Field | Value |
|---|---|
| Numbers (all positive) | 4, 9 |
| Geometric mean | 6 |
| Count of numbers | 2 |
Assumptions
- All numbers must be positive — the geometric mean of a set containing zero or a negative number is not a real number in general.
Frequently asked questions
When should I use geometric mean instead of arithmetic mean?
Use geometric mean when averaging rates of change, ratios, or growth rates that compound over time (like annual investment returns) — arithmetic mean overstates the true average growth rate in these cases.
How is geometric mean related to CAGR?
CAGR (Compound Annual Growth Rate) is a specific application of the geometric mean concept, applied to a single starting and ending value over a number of years rather than a general list of numbers.
Why must all numbers be positive?
The geometric mean involves taking a root of the product of the numbers — if any value is zero, the product is zero; if any value is negative, the result may not be a real number depending on how many negatives are in the list. This calculator requires all-positive input to keep the result well-defined.