Geometric mean calculator
Calculate the geometric mean of a list of numbers — ideal for growth rates and returns.
The geometric mean applies only to positive numbers. It is always less than or equal to the arithmetic mean.
How the calculation works
The geometric mean is the nth root of the product: GM = (x₁ · x₂ · … · xₙ)1/n. It's the right average for quantities that multiply, like growth rates and interest — so for multi-year returns, use the geometric, not the arithmetic mean.
Examples
- Geometric mean of 4 and 9: √(4×9) = √36 = 6.
- Up 50% then down 50%: GM of 1.5 and 0.5 = √0.75 ≈ 0.866 → −13.4%/yr (a loss).
Frequently asked questions
When should I use the geometric mean?
When values multiply over time — investment returns, population growth, compound interest.
Why not the simple average for returns?
Because the arithmetic mean overstates. +50% and −50% average to 0%, but you actually lost — only the geometric mean shows it.
Is the geometric mean always ≤ the arithmetic one?
Yes, for positive numbers — equal only when all values are identical.
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Updated on June 30, 2026 · by Rafael Rossi · Methodology & sources