Geometric Mean Calculator is a free online tool used to calculate the geometric mean of numbers.
What is the geometric mean?
The geometric mean corresponds to the central tendency of a set of numbers using the product of the values, and it contrasts with the arithmetic mean, which uses the sum of values. So, the geometric mean is computed as the Nth root of the product of n numbers. A geometric mean is only calculated for positive integers. The formula for the geometric mean is
For example, the geometric mean of 1, 2, 3 and 4 can be computed as
G4 = 4√ 1 * 2 * 3 * 4 = 4√ 24 = 2.21
The geometric mean is widely used in calculating the average growth rate of something, and it is used in applications where promotional growth needs to be calculated. Various financial, social sciences, and other industries use this geometric mean.
Fun-Facts of Geometric Mean
- The geometric mean for any data set is always less than its arithmetic mean.
- If the geometric mean replaces each value in the data set, then the product of the values in the data set remains unchanged.
- When there are two data series, the product of the corresponding items will be equal to the product of the geometric mean of the two series.
How to use the geometric mean calculator
The procedure to use the geometric mean calculator is as follows:
- Enter numbers in the input boxes. Separate each number with a comma or newline.
- Click Calculate button to calculate the geometric mean of input numbers.
- Click the Reset button to start a new calculation.
Solved examples using the geometric mean calculator
Example 1: What is the geometric mean of 5 and 125?
Enter 5, 125 into the input box and click Calculate button, as shown in the figure, the geometric mean of them is 25.
√5 * 125 = √625 = 25
Example 2: What is the geometric mean of 4 and 16?
Enter 4, 16 into the input box and click Calculate button, as shown in the figure, the geometric mean of them is 8.
√4 * 16 = √64 = 8
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