Geometric Mean Calculator: Simple and Powerful

Enter numbers separated by commas or spaces:

Formula:
Geometric Mean = ⁿ√(x₁ × x₂ × ... × xₙ)
Where n is the count of numbers

What Is This Tool?

This tool calculates the geometric mean from a list of positive numbers. It also shows the arithmetic mean for quick comparison.

How to Use This Tool

  1. Type your numbers into the input field. Use commas or spaces to separate them.
  2. Press the Calculate button or press Enter.
  3. The tool shows each step of the math.

Input Field Explanation

Enter numbers in the input field. Do not use negative numbers or zeros. The tool checks your entry and warns you if there is a mistake.

Output Explanation

You will see the list of numbers you entered. The tool displays the count of numbers and their full product. It then calculates and shows the geometric mean.

The formula used is the nth root of the product of all numbers. Here, n is the count.

The arithmetic mean is also shown. It is the sum of your numbers divided by the count. Often, the geometric mean is lower than or equal to the arithmetic mean. This can help when working with rates or percentages.

Geometric Mean Formula

Formula: Geometric Mean = nth root of (x₁ × x₂ × ... × xₙ), where n is the number of values entered.

Limitations and Special Notes

This tool only works with positive numbers. Negative values are not allowed. Zeros make the geometric mean zero.

If you enter any invalid numbers, the tool will show an error message.

Examples of Common Use Cases

Students can use this for math homework or tests. Analysts might use it for financial ratios. It is useful for any calculation that deals with positive numbers.

Final Thoughts

This geometric mean calculator is simple to use and gives clear results. It shows every step, which helps with understanding the math. Use it when you need a math check or quick calculation.