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I am brand new to ArcGIS and having some trouble. I would like to calculate the distances between the border of one polygon to another polygon. However, these polygons overlap. Thus when I use the Near function, it results in zero because the polygons overlap at some points or one is within a larger one. I cannot use the Point Distance because I have shapefiles and so I have nothing to choose from in the drop down menu.

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    Please tell us precisely what you mean by the "distances between the borders" of two overlapping polygons. – whuber Apr 2 '14 at 21:30
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You can create borders by using Polygon to Line tool for each polygon. Then use Near tool on these two borders.

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