Geometric Mean Calculator

How it is calculated

The geometric mean of n positive numbers is the nth root of their product: GM = (x₁ × x₂ × … × xₙ)^(1/n). The tool computes it through logarithms, GM = exp(average of ln xᵢ), which gives the same value and avoids overflow with long lists. Numbers can be separated by commas, semicolons or spaces. Items that are not numbers are ignored, and an empty list gives no result. Every value must be greater than zero; a zero or negative value makes the geometric mean undefined and the tool returns nothing. Use it for growth factors and ratios, where the arithmetic mean overstates the typical value.

Common mistakes

• Including a zero or a negative number: the geometric mean is undefined, so the tool returns nothing.
• Averaging percentage returns directly; convert them to growth factors (+10% becomes 1.10) first and subtract 1 at the end.
• Using the arithmetic mean for growth rates, which overstates the average yearly growth.
• Mixing a decimal comma with the list separator: write decimals with a point and separate items with spaces or semicolons.
• Typing a stray word or symbol and assuming it counted: non-numeric items are silently skipped.