Geometric Mean Calculator
The geometric mean summarizes positive values multiplicatively and can be useful for ratios or scale factors.
How to use this calculator
- Type positive numbers separated by commas, semicolons or spaces. The arithmetic mean is also shown for context.
- Check the labels and units before using a result outside this page.
- Change one input at a time if you want to compare scenarios.
Formula and method
GM = (x₁ × x₂ × … × xₙ)¹⁄ⁿ
- GM = (x₁ × x₂ × … × xₙ)¹⁄ⁿ
- The implemented real-valued method requires every input to be strictly positive.
Worked examples
Worked example
Find the geometric mean of 2, 8 and 32.
(2 × 8 × 32)¹⁄³ = 512¹⁄³ = 8.
(2 × 8 × 32)¹⁄³ = 512¹⁄³ = 8.
Understanding the result
The geometric mean summarizes positive values multiplicatively and can be useful for ratios or scale factors.
The implemented real-valued method requires every input to be strictly positive.
Important notes
The implemented real-valued method requires every input to be strictly positive.
Displayed outputs are rounded for readability; preserve full precision when continuing a calculation.
Frequently asked questions
What does this geometric mean calculator show?
The geometric mean summarizes positive values multiplicatively and can be useful for ratios or scale factors.
Which inputs should I check first?
Type positive numbers separated by commas, semicolons or spaces. The arithmetic mean is also shown for context.
Can the result be used as a final professional specification?
The implemented real-valued method requires every input to be strictly positive.
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- Geometric Sequence Calculator — Calculate a term and finite sum in a mathematical geometric sequence with a constant ratio.
- Harmonic Mean Calculator — Calculate the harmonic mean of positive numerical values for suitable rate and ratio problems.
- Trimmed Mean Calculator — Calculate a trimmed mean by removing a chosen percentage of observations from both tails.
- Confidence Interval for Mean Calculator — Estimate a normal-approximation confidence interval around a sample mean from its spread and sample size.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
- Percentage — Understand what a percentage means, how percentages are calculated, and when to use a percentage calculator.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.