In the previous recipe, you saw the same NUTS_RG_03M_2010 feature class that has the ETRS89-GRS80 geographic coordinate system in nine data frames that have different projected coordinate systems. The projection of the feature class was made on the fly by ArcMap based on every data frame's projected coordinate system. To permanently transform the coordinate reference system of a feature class, use the Project tool from ArcToolbox. This will create a new feature class with the new coordinates for the features. ArcGIS offers multiple versions of a transformation between different datums. It's important to choose the optimal transformation because it will affect the coordinates' accuracy. At <,ARCGISHOME>,:Desktop10.2Documentation, you will find a PDF file called geographic_transformations.pdf that lists all supported datum transformations and the areas for which they are suited. For theory and worked examples about coordinate system transformations, please refer to Datums and Map Projections 2nd Edition Jonathan Iliffe and Roger Lott, Whittles Publishing, 2012, chapter Map Projection,... Source.