This site:
http://rla.unc.edu/postanal/
provides a free tool for ArcGIS that does something called “Archaeological Post Analysis,” used by archaeologists “to help identify walls and other structural alignments in archaeological maps containing palimpsests of postholes.” But above and beyond all of that, the “Post Tool Bar” (which is created inside of ArcGIS when you install the tool) will also compute centroids of polygon features. The centroid of a polygon is simply the point defined by the mean X- and Y-coordinates, and is often used as a label point. The site provides the software for ArcGIS 9.2 and above, which is the version that Holy Cross GIS users should download. The site also provides documentation for use of the software. When run on a polygon layer, the Post Tool Bar creates a new point layer in which each point is the centroid of the corresponding polygon. If you need the actual centroid coordinates, one approach is to export the centroid layer to a KMZ file (a compressed version of KML), which can also be displayed in Google Earth. Once in Google Earth the KMZ file can be saved as uncompressed KML, which you can then view in any text editor in order to obtain the centroid coordinates. (There is another free ArcGIS tool, Export to KML, which IMHO does a better job of creating KML files from shapefiles than the KML tools provided within ArcToolbox.)