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I have an attribute table of points and the coordinates are stated in decimal degrees. I would like to add two fields where the coordinates are also stated in meters or kilometers. I am using ArcGIS 10.2.

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From the ArcView help files

You can use the coordinate system of the data source or of the data frame when performing calculations. In addition, if one or more records are currently selected, only the selected records are calculated.

Source quote Hence, if you have data in decimal degrees, set the dataframe to the desired coordinate system. It is then a simple matter of adding fields to reflect the desired unprojected and projected data, then performing 4 field calculator calculations to obtain said data

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seems like the calculate geometry does the work, or? – dimitris Jul 3 '14 at 8:21
as suggested, it does – Dan Patterson Jul 3 '14 at 8:32
+1 for describing how to choose the coordinate system for the meters. – mr.adam Apr 22 '15 at 15:47

To do this just add new fields for the meters and kilometres values, and then use the Calculate Geometry tool to update them:

The Calculate Geometry tool allows you to access the geometry of the features in a layer. The tool can calculate coordinate values, lengths, and areas, depending on the geometry of the input layer. You can only calculate the area, length, or perimeter of features if the coordinate system being used is projected. Keep in mind that different projections have different spatial properties and distortions. If the coordinate system of the data source and data frame are not the same, you may get a different result if you calculate geometry using the data frame's coordinate system than when you calculate using the data source's coordinate system. It is recommended that an equal-area projection be used when calculating areas.

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