By John M Quick

The R Tutorial Series provides a collection of user-friendly tutorials to people who want to learn how to use R for statistical analysis.

My Statistical Analysis with R book is available from Packt Publishing and Amazon.

R Tutorial Series: Centering Variables and Generating Z-Scores with the Scale() Function

Centering variables and creating z-scores are two common data analysis activities. While they are relatively simple to calculate by hand, R makes these operations extremely easy thanks to the scale() function.

Tutorial Files

Before we begin, you may want to download the dataset (.csv) used in this tutorial. Be sure to right-click and save the file to your R working directory.

The Scale() Function

The scale() function makes use of the following arguments.
  • x: a numeric object
  • center: if TRUE, the objects' column means are subtracted from the values in those columns (ignoring NAs); if FALSE, centering is not performed
  • scale: if TRUE, the centered column values are divided by the column's standard deviation (when center is also TRUE; otherwise, the root mean square is used); if FALSE, scaling is not performed

Centering Variables

Normally, to center a variable, you would subtract the mean of all data points from each individual data point. With scale(), this can be accomplished in one simple call.
  1. > #center variable A using the scale() function
  2. > scale(A, center = TRUE, scale = FALSE)
You can verify these results by making the calculation by hand, as demonstrated in the following screenshot.

Centering a variable with the scale() function and by hand

Generating Z-Scores

Normally, to create z-scores (standardized scores) from a variable, you would subtract the mean of all data points from each individual data point, then divide those points by the standard deviation of all points. Again, this can be accomplished in one call using scale().
  1. > #generate z-scores for variable A using the scale() function
  2. > scale(A, center = TRUE, scale = TRUE)
Again, the following screenshot demonstrates equivalence between the function results and hand calculation.

Generating z-scores from a variable by hand and using the scale() function

Complete Scale() Example

To see a complete example of how scale() can be used to center variables and generate z-scores in R, please download the scale() example (.txt) file.


The official scale function manual page is available from:


  1. Very good!! Thanks!!!

  2. A huge thank-you for a clear and well explained tutorial.

  3. this is really what I need. Thanks a lot

  4. Good function, but why are there "center" and "scale" attributes attached to the scaled data? This will slow down the computation and take more memory when you copy the matrix.

  5. Is there an easy way to get back from z-scores to original scores? Say you used the scaled values to generate a model, and you predict new values but they are in z-scores. Is there an easy command to get the prediction values in original units?

  6. Why should the scaling be done with RMS? The variance will be 1 only if divided by Standard Deviation in all cases (whether center is True or not).