How do I combine the values of cells for 3 rasters for cells where they overlap. I want the output raster to cover only the area of the overlap for the 3 rasters and the output cell values to be a sum of the values of the 3 original rasters.
I am using arcmap 10.2. If this is possible through raster calculator it will be preferable. Or any of the spatial analyst tools
Raster Calculator can do this -- indeed, the example illustration on the help page shows exactly what you want to do. The resulting raster will only cover the overlap area, which I often find problematic for my analyses but sounds like what you need.
Other options would work but are more complex than you need. The Plus tool only adds two rasters at a time and would involve running the tool twice. The Weighted Sum tool could work if you assign a weight of 1 to all the rasters. I'd just stick with Raster Calculator.
The tool to do this is called cell statistics
Select the option SUM
In the environments setting (Output Extent) set the output extent to intersect
