How does the Geometric Mean work?

GM = (x₁ × x₂ × ... × xₙ)^(1/n) Then: Always ≤ arithmetic mean Then: For investment returns: GM = (final/initial)^(1/n) − 1.

Can you give an example of how to use the Geometric Mean?

Example: Input Annual returns: +50%, −50%, +50% gives a result of GM = (1.5×0.5×1.5)^(1/3)−1 = −6.1%/yr (AM would give +16.7% — completely misleading).

Is the Geometric Mean free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Geometric Mean?

Our Geometric Mean uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Geometric Mean

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Values (comma separated, all positive)

The geometric mean is the nth root of the product of n numbers. It is the correct average for quantities that multiply (growth rates, investment returns) rather than add.

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Did You Know?

A 50% gain followed by a 50% loss leaves you at 75% of your starting value — the geometric mean captures this reality while arithmetic mean doesn't.

References

›Geometric mean — Wikipedia

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