Geometric Mean Calculator
Calculate the nth root of the product of positive values.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter positive numbers separated by commas or spaces. The calculator computes the geometric mean using the log-transform method to avoid overflow with large numbers. If any value is zero or negative, a warning is shown because the geometric mean is undefined for non-positive data.
About Geometric Mean
The geometric mean is the nth root of the product of n values. It is always less than or equal to the arithmetic mean (AM-GM inequality). It is the correct average for multiplicative quantities like growth rates, investment returns, and ratios. For example, if an investment grows 10% one year and loses 10% the next, the arithmetic mean return is 0% but the geometric mean reveals the actual slight loss.
Frequently Asked Questions
When should I use geometric mean instead of arithmetic mean?
Use geometric mean for multiplicative data: growth rates, investment returns, ratios, or any values that compound. Arithmetic mean is appropriate for additive data like heights or test scores.
Why does geometric mean not work with negative numbers?
The geometric mean involves taking roots of products. Negative numbers can make the product negative, and even roots of negative numbers are not real. Zero values make the product zero, collapsing the mean to zero regardless of other values.
How does geometric mean compare to harmonic mean?
For positive numbers, harmonic mean is always less than or equal to geometric mean, which is less than or equal to arithmetic mean. Harmonic mean is used for rates (like speed), geometric for growth, and arithmetic for general averages.