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I have a point file with elevation values I want to combine with a raster of the same area. I'm assuming I will need to extract points from the raster to store as a .shp file.

Then I need to combine the two sets of z values to create one elevation (in this case i'm adding the one to the other.) Can this be done within ArcMAP 10.3.1?

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If you have the Spatial Analyst extension you can use the Extract Values to Points tool to add the data from the raster to the point data. You could then use the field calculator to add the two values, either in an existing field or in a new one.

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