# Root Mean Square Calculator

The Root Mean Square value of a set of values is the square root of the arithmetic mean of the squares of the values.

## What is Root Mean Square Calculator?

'Root Mean Square Calculator' is an online tool that helps to find the root mean square value for the given numbers. This online Root Mean Square Calculator helps you to calculate the root mean square value for the given numbers in a few seconds.

### Root Mean Square Calculator

## How to Use Root Mean Square Calculator?

Please follow the steps below to find the root mean square value for the given numbers:

**Step 1:**Enter the numbers separated by a comma in the given input box.**Step 2:**Click on the**"Calculate"**button to find the root mean square value for the given numbers.**Step 3:**Click on the**"Reset"**button to clear the fields and find the root mean square value for the different numbers.

## How to Find Root Mean Square?

**Root mean square(RMS) **is defined as the square root of the arithmetic mean of given data set or given numbers. Root mean square(RMS) is given by formula:

**Root mean square(RMS) = √{(x _{1}^{2} + x_{2}^{2} + x_{3}^{2} + .... + x_{n}^{2}) / n}**

Where x_{1}, x_{2}, ... are numbers from data set, and n is the number of terms in the data set.

**Solved Examples on Root Mean Square Calculator**

**Example 1:**

Find the root mean square for the following set of data: {1,3,7,4,5} and verify it using the online root mean square calculator.

**Solution:**

Given n = 5

Root mean square(RMS) = √{(x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + .... + x_{n}^{2}) / n}

= √{(1^{2} + 3^{2} + 7^{2} + 4^{2} + 5^{2}) / 5}

= √20

= 4.472

Therefore, the root mean square is 4.472

**Example 2:**

Find the root mean square for the following set of data: {2,4,8,5,6} and verify it using the online root mean square calculator.

**Solution:**

Given n = 5

Root mean square(RMS) = √{(x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + .... + x_{n}^{2}) / n}

= √{(2^{2} + 4^{2} + 8^{2} + 5^{2} + 6^{2}) / 5}

= √29

= 5.38

Therefore, the root mean square is 5.38

**Example 3:**

Find the root mean square for the following set of data: {1,5,7,2,4} and verify it using the online root mean square calculator.

**Solution:**

Given n = 5

Root mean square(RMS) = √{(x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + .... + x_{n}^{2}) / n}

= √{(1^{2} + 5^{2} + 7^{2} + 2^{2} + 4^{2}) / 5}

= √19

= 4.358

Therefore, the root mean square is 4.358

Similarly, you can try the online root mean square calculator to find the root mean square for the following:

- 2, 4, 1, 18, 12, 4, 5, 8
- 5, 11, 17, 5, 6, 1, 4, 2, 7

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