Root Mean Square (RMS) Calculator

What is Root Mean Square?

The Root Mean Square (RMS) is a statistical measure of the magnitude of a varying quantity. It's particularly useful in various fields, including electrical engineering, physics, and statistics. The RMS is defined as the square root of the arithmetic mean of the squares of a set of numbers.

Formula and Its Meaning

The formula for RMS is:

\[RMS = \sqrt{\frac{1}{n}\sum_{i=1}^{n} x_i^2}\]

Where:

• \(x_i\) are the individual values in a dataset
• \(n\) is the number of values
• \(\sum\) represents the sum of the squared values

Calculation Steps

1. Square each number in the dataset.
2. Calculate the average (mean) of these squared values.
3. Take the square root of this average.

Example Calculation

Let's calculate the RMS for the dataset: 3, 4, 5

1. Square each number: \(3^2 = 9, 4^2 = 16, 5^2 = 25\)
2. Calculate the mean of squared values: \(\frac{9 + 16 + 25}{3} = \frac{50}{3}\)
3. Take the square root: \(\sqrt{\frac{50}{3}} \approx 4.08\)

Visual Representation

This scatter plot represents the example dataset. The red dashed line indicates the RMS value (approximately 4.08), showing how it relates to the individual data points.