Geometric Mean Calculator
Calculate geometric mean instantly in your browser.
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What this tool does
Calculate geometric mean instantly in your browser. Use the geometric mean for growth rates and ratios — it is always at or below the arithmetic mean (AM–GM inequality).
How to use the Geometric Mean Calculator
- Enter or select numbers separated by commas or whitespace.
- Read the calculated result; change any measurement to compare alternatives.
Formula
geometric mean = (x₁ × x₂ × … × xₙ)^(1/n), computed as exp(mean of ln x) so very large or small values do not overflow.
- values
- Numbers separated by commas or whitespace
Use the geometric mean for growth rates and ratios — it is always at or below the arithmetic mean (AM–GM inequality).
Worked example
For geometric mean calculator, the following measurements illustrate the exact method: Numbers separated by commas or whitespace: 4, 9, 16.
Inputs
- Numbers separated by commas or whitespace4, 9, 16
Result
- Geometric mean8.32
- Arithmetic mean (for comparison)9.67
- Count3
- Product576
Results explained
- Geometric mean
- Geometric mean from the formula above. Use the geometric mean for growth rates and ratios — it is always at or below the arithmetic mean (AM–GM inequality).
- Arithmetic mean (for comparison)
- Arithmetic mean (for comparison) from the formula above. Use the geometric mean for growth rates and ratios — it is always at or below the arithmetic mean (AM–GM inequality).
- Count
- Count from the formula above. Use the geometric mean for growth rates and ratios — it is always at or below the arithmetic mean (AM–GM inequality).
- Product
- Product from the formula above. Use the geometric mean for growth rates and ratios — it is always at or below the arithmetic mean (AM–GM inequality).
Frequently asked questions
geometric mean = (x₁ × x₂ × … × xₙ)^(1/n), computed as exp(mean of ln x) so very large or small values do not overflow.
Use the geometric mean for growth rates and ratios — it is always at or below the arithmetic mean (AM–GM inequality).
Where mathematically meaningful, yes. Fields specify permitted ranges and undefined operations display an error.
Exact integer calculations use safe integers; decimal calculations use browser floating point, so small rounding differences can occur.
All values remain in your browser and are never uploaded.