Root Mean Square Calculator

Root Mean Square Formula: Xrms= x12+X22+…..+xn2n 

Enter Inputs separated by comma=
Number of Inputs =
Root Mean Square =

Root Mean Square Calculator is a free online tool that displays the root mean square value for the given input values. BYJU’S online root mean square calculator tool performs the calculation faster, and it displays the root mean square value in a fraction of seconds.

How to Use the Root Mean Square Calculator? 

The procedure to use the root mean square calculator is as follows:

Step 1: Enter the numbers separated by a comma in the input field

Step 2: Now click the button “Solve” to get the result

Step 3: Finally, the root mean square value will be displayed in the output field

What is Meant by Root Mean Square?

In mathematics, the root mean square is also known as the quadratic mean. It is represented by RMS or rms. The root mean square is defined as the square root of the mean square. We can also say that it is a generalised mean with the exponent value as 2. The root mean square value is given as:

For the set of numbers, x1, x2, x3, …xn, the root mean square (RMS) is

\(\begin{array}{l}x_{RMS}=\sqrt{\frac{1}{n}(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+…+x_{n}^{2})}\end{array} \)

For example, the set of values are 4, 2, 6, 8, then the root mean square is calculated as:

Here, n= 4

Now, substitute the values in the formula, we get

\(\begin{array}{l}x_{RMS}=\sqrt{\frac{1}{4}(4^{2}+2^{2}+6^{2}+8^{2})}\end{array} \)

\(\begin{array}{l}x_{RMS}=\sqrt{\frac{1}{4}(16+4+36+64)}\end{array} \)

\(\begin{array}{l}x_{RMS}=\sqrt{\frac{1}{4}(120)}\end{array} \)

\(\begin{array}{l}x_{RMS}=\sqrt{30}\end{array} \)

\(\begin{array}{l}x_{RMS}=5.477\end{array} \)

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