## Introduction to the Geometric Mean Calculator:

A geometric mean calculator is an online tool that is used to **find the average value** from a given set of numbers. It computes the given number in which it takes the product of all numbers and then square roots them to get the central tendency value in a couple of minutes.

You can use our geometric average calculator for mean value problems and get the solution without consuming your time in doing complex calculations manually.

## What is the Geometric Mean?

The geometric mean is the average value that **indicates the central tendency** which comes from a set of numbers that multiply from the nth root to n numbers. It is a statistical method that describes the whole of about given number set.

Geometric mean has real-life applications as well like finding the annual growth and investment, in a stock exchange or financial growth rate. It is a commonly used application in biology to determine the growth of cell division or bacteria and its results after experiments.

## Geometric Mean Formula:

The **geometric mean formula** is mathematically written in square root form or with a square in an exponential form where its power is 1/n. The formula used by the geometric mean calculator with steps to solve such problems is,

$$ \biggr( \prod_{i = 1}^{n} X_i \biggr)^{\frac{1}{n}} \;=\; \sqrt[n]{x_1 x_2 … x_n} $$

Whereas,

n Total number of elements in a set

xn total element in a set

1/n is the exponential power of a number set

## How to Find the Geometric Mean by Using Geomean Calculator?

Geometric mean gives the mean value of a number set with the help of the geometric mean formula and Its solution gives you an idea about the **growth rate of a given set**. To find the geometric mean you should use the geometric mean calculator and follow some simple steps to get the right result for your question.

**Step 1:**

Identify the total number of elements n and total elements value x from the given number set

**Step 2:**

Apply the geometric mean formula and **add all the values** in it

**Step 3:**

Take the product of all these elements values as x1*x2*x3…..xn.

**Step 4:**

Take the square root of the result that gets after multiplication and the square root power is 1/n.

**Step 5:**

After taking the square root you will get the solution of the average value of a given set number.

## Solved Example of Geometric Mean:

The geometric means calculator can solve the geometric mean problems easily but it is important to understand the manual calculation. So, an example is given below,

### Example:

Find the geometric mean of the numbers 4, 9, and 16.

**Solution**:

apply the geometric mean formula on the given set of number

$$ Geometric\; Mean \;=\; \sqrt{x^1 \times x^2 \times … \times x^n} $$

Here n=3 and x=4*9*16

$$ 4 \times 9 \times 16 \;=\; 576 $$

$$ Geometric\; Mean \;=\; \sqrt[3]{576} $$

$$ Geometric\; Mean \;=\; \sqrt[3]{576} \approx 8 $$

The geometric mean of a given set of numbers is approximately 8. To find the geometric mean of 14 and 20 you can use geomean calculator and would follow similar steps.

## How to Calculate Geometric Mean on Geometric Average Calculator?

Geometric mean calculator with steps provides you with the easiest method to **solve mean values** from a particular number set of problems. Follow some of our guidelines so that you can use our geomean calculator correctly for the evaluation. These steps are:

- Enter all the values of elements in the input box
- Enter the value of the total number of elements n in the second input box
- Click on the “Calculate” button to get the solution of the geometric mean problem from our calculator
- The Recalculate button will bring you back to the home page where you can evaluate more examples of geometric mean problem
- If you want to check the accuracy of our geometric means calculator then you use load example solution so that you get an idea about its precise solution

## Outcome from Geometric Mean Calculator with Steps:

The geometric average calculator gives a **solution of the average value** that describes the number set immediately when you click on the calculate button. It may include as:

**Result Section**:

When you click on the result button it provides you with solutions of mean value problems

**Possible Steps Section**:

It provides you with solutions of geometric mean problems in step by step process.

## Useful Features for Using Geometric Means Calculator:

The geometric mean calculator provides you with multiple benefits whenever you use it to calculate mean value problems and give a solution. These benefits are:

- The geometric average calculator is a
**free tool**so you can use it to find the geometric mean value problems in real time. - It is a versatile tool that allows you to get the solution of various types of geometric mean problems
- You can try out our geomean calculator for practice with more examples so that you get a strong hold on the geometric average mean problem concept
- Our tool saves you time and effort from doing average value calculations without taking much time.
- It is a trustworthy tool that provides you with accurate solutions every time whenever you use it to calculate the geometric mean examples.
- It provides the solution with a complete process in a step-by-step method so that you get a better understanding on the geometric mean concept.