This online Geometric Mean Calculator calculates the geometric mean of a set of numbers. Enter the set of numbers in the input field of the calculator and click the “Calculate” button. You can paste the input data copied from a spreadsheet or csv-file or enter manually using comma, space or enter as separators. The input numbers can be positive or negative because our calculator calculates the geometric mean of the absolute values of the numbers.
Geometric mean formula
In mathematics, the geometric mean, often referred to as the geometric average, is defined as the \(n\)-th root of the product of \(n\) numbers, i.e., for a set of numbers \({ x }_{ 1 },{ x }_{ 2 },…,{ x }_{ n }\), the geometric mean is defined as:
$${\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}} = {\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}}$$
The geometric mean applies only to positive numbers, so in our calculator we calculate it taking the absolute values of the numbers.
The geometric mean is used in a number of problems where a growth rate is of interest, for example in calculating compound interest rates, financial returns or risk and loses, area and volume averages, in computing indexes, and others. It is useful also in surveys and socials studies. The geometric mean is often used in geometry.
Related calculators
Check out our other math calculators such as Arithmetic Mean Calculator or Harmonic Mean Calculator.