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This question already has an answer here:

I have a shapefile. The coordinates (Lat/Long) are projected as decimal degrees. But, I want to re-project it to meters.

How can I do it with ArcMap?

marked as duplicate by whuber Aug 22 '13 at 12:24

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Use the Project tool to project the data to a suitable projection, then if you want to see the coordinates in the table, add two fields (decimal) and use the Calculate Geometry option from the table to get the coordinates

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    (+1) Check first if your shapefile has a coordinate system defined. If no coordinate system is defined use Define Projection to assign the right system to your shapfile (I suspect WGS84 ?) before using Project tool. – Jens Aug 22 '13 at 8:42

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