# What is the RMSE normalized by the mean observed value called?

I have been using the Root Mean Squared Error (RMSE) to measure the accuracy of values predicted using a model. I understand that the value returned is using the units of my measures (rather than a percentage). However, I would like to quote my values as a percentage. The approach that I have taken is to normalize the RMSE by the mean value of my observations.

Is there a term for RMSE/mean ?

• +1. Isn't also called: relative root mean square error (rRMSE)? , cc/ @celenius. Jan 30, 2014 at 11:28

In my field (analytical chemistry), absolute error / absolute value = relative error, so relative RMSE [at mean x] would be understood easily.

I'd clarify that the value I divide by is the average, as often the relative error at the extreme values is used:

• error specification of measuring instruments often is relative error at maximum value
• in (chemical-analytical) calibration the relative error at the limit of quantitation or the lower limit of the actual calibration is important.
• I'm not sure if there is a standard term in my field, so I will probably use relative error as it sounds a little more self-explanatory. Apr 21, 2012 at 13:37

It is called Normalised Root Mean Square Error (nRMSE) or Relative Root Mean Square Error (rRMSE). You can use either mean or range as the denominator. Read the Wikipedia article