1. Home
  2. Statistics Calculators
  3. Root Mean Square Calculator

Root Mean Square Calculator

The root mean square calculator is designed to compute the quadratic mean (RMS) of a given set of numbers.

Root Mean Square:

Other Statistics Results:

Mean (Average):
Median:
Mode:
Range:
Geometric Mean:
Largest:
Smallest
Total Numbers:
Sum:

How to Use the Root Mean Square Calculator?

  1. Enter the set of numbers with a comma or space separator. Example: 10 12 15 or 10,12,15.
  2. Press the 'Calculate' button.
  3. As a result, the tool shows the root mean square (RMS) result.
  4. In addition, it also shows other statistics results such as mean, median, mode, range, etc.

How to Calculate Root Mean Square?

The quadratic mean (RMS) is calculated using the following formula:

RMS = √

Σ (x2i)

n

Where,
x1, x2, ..., xi = Values in the data set,
n = Number of values in the data set.

Let's take an example:

Example:

Compute the RMS for the data set: [5, 14, 23, 6].

Solution:

Step 1: Square each data point.

52 = 25

142 = 196

232 = 529

62 = 36

Step 2: Find the average (mean) of the squared values.

Mean =
25 + 196 + 529 + 36
4
Mean =
786
4

Mean = 196.5

Step 3: Find the square root of the mean.

RMS = √196.5

RMS = 14.0178.

Related Calculators