In QGIS, it's very straightforward. First, ensure that you have the correct coordinate system for your original shapefile:
- Add the layer to the map canvas;
- Right-click on the layer and select "Set layer CRS";
- Choose the correct coordinate reference system (CRS) from the list - it is probably in UTM (a metric grid) and you will have to know the zone and datum for the data; it may be already automatically selected!
After this:
- You right-click on the layer and select "Save as ...":
- Click 'Browse' near CRS in the resulting dialog and select WGS84 EPSG:4326 as the CRS for the new file - this will save it with decimal degrees as the coordinate system.
It's a very good idea to make sure you select a good name in the "Save as" dialog - appending the coordinate system to the name can be very helpful, e.g. my_shape_file_DD_WGS84 to remember that it's in degrees, WGS84.
Since you have ArcGIS 10.1 available, it would be easy to import your current data in excel format, plot the XY coordinates in the current coordinate system, reproject your points to your desired coordinate system, and then export the data back to a new spreadsheet.
To do this, follow these steps:
1.) Add your existing spreadsheet to ArcMap
2.) Right click your spreadsheet in the table of contents and select "Display XY Data"
- Choose the appropriate fields for your X and Y coordinates
- Under "Coordinate System of Input Coordinates" select "Edit..." and choose the correct coordinate system.
3.) Once your points are plotted, right click your plotted data in the table of contents and select data -> Export Data. Save the plotted points to a shapefile and add it to your map.
4.) Reproject the shapefile to the desired projection.
5.) In the Data Management -> Features toolbox, run Add XY Coordinates on your newly projected shapefile. You may have to rename your existing XY fields if they are named POINT_X and POINT_Y, as these are the field names the tool uses. This will add the XY coordinates in the new coordinate system to your attribute table.
6.) Open the attribute table of your shapefile, under table options select Export. Choose an appropriate format and location to save your spreadsheet to.
Voila, you have a new spreadsheet with projected XY data. If your ultimate goal is just to get the data into shapefile format in the correct projection, just do steps 1-4.
Best Answer
You can do this in a dodgy way by using a form like this: https://www.engineeringtoolbox.com/utm-latitude-longitude-d_1370.html
This one looks a little more robust: http://franzpc.com/apps/coordinate-converter-utm-to-geographic-latitude-longitude.html
But as the comments suggest, to do it properly, you really need to know what datum you're on, and you've only provided info on your projection. You can get something that should be ok by assuming you're on the WGS84 datum, and your lat/lon will then be on that too. To do it right, you should use the right datum, though!