Root Mean Square (RMS) Calculator

About Root Mean Square (RMS) Calculator

RMS is the square root of the mean of squared values. For AC signals, RMS gives the effective (DC equivalent) value.

How to use this calculator

1. Enter the values you want to analyze, separated by commas or spaces.
2. Count how many values there are, this is \(n\).
3. Square each value, then add all of those squares.
4. Divide the sum by \(n\), then take the square root of the result.

The formula explained

The formula \(RMS = \sqrt{\frac{1}{n}\sum x_i^2}\) computes the square root of the average of the squared values. It gives a single number that represents the overall size of the data set.

• \(RMS\) = the root mean square of the values
• \(n\) = the number of values in the data set
• \(x_i\) = the \(i\)th value in the list
• \(\sum x_i^2\) = the sum of the squares of all values

Step by step method

1. Square every value in the list.
2. Add the squared values together.
3. Divide that total by \(n\), then take the square root.

Worked example

Problem. Find the \(RMS\) of the values \(3\), \(4\), and \(12\).

1. Square the values: \(3^2 = 9\), \(4^2 = 16\), and \(12^2 = 144\).
2. Add the squares: \(9 + 16 + 144 = 169\). Divide by \(n = 3\): \(169 \div 3 = 56.333...\).
3. Take the square root: \(\sqrt{56.333...} \approx 7.51\).

Tips and common mistakes

• Do not average the original numbers first, because \(RMS\) uses squared values.
• Be careful with negative numbers, since squaring them makes them positive before averaging.

Frequently asked questions