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I have a data file that contains locations of different places of Wilmington, North Carolina. The data file contains the X Coordinates, Y Coordinates, and Latitude. I want to calculate the Longitude value of those places? How can I do this? I have used the arctan2(y,x) formula but it is not giving the correct location.

Sample Data:

X Coord: 2579880
Y Coord: 12401479
Latitude: 34.1213976435541
Longitude: ?

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    What is the coordinate reference system of the XY data? What software do you want to use?
    – Mike T
    Apr 29, 2021 at 22:14
  • Where did you get your data, did it come with any explanatory info? Do you why the data would have both a Latitude and a Y coordinate?
    – Don
    Apr 30, 2021 at 0:59
  • @MikeT I actually don't have the coordinate reference system. I am using excel. Apr 30, 2021 at 6:36
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    – Ian Turton
    Apr 30, 2021 at 9:21
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    The arctan2(y,x) function would output the longitude of the point if they were expressed in a polar orthographic or geocentric coordinate system, but I doubt this is the case here. My crs guess for the point would be UTM Zone 17N, but feet instead of meters. This would translate to 34.12139764, -77.89539463, near 6001 Appomattox Dr, Wilmington, NC. If that location rings a bell, then your points are likely in UTM Zone 17N - feet. Looks promising to me, because the latitude matches.
    – FSimardGIS
    May 1, 2021 at 3:31

2 Answers 2

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The arctan2(y,x) function would output the longitude of the point if they were expressed in some specific coordinate systems like polar azimuthal or geocentric, but I doubt this is the case here. My coordinate system guess for your points would be WGS84 UTM Zone 17N, but feet instead of meters. This would translate to 34.12139764, -77.89539463, near 6001 Appomattox Dr, Wilmington, NC. If that location rings a bell, then your points are likely in UTM Zone 17N - feet. Looks promising to me, because the latitude matches exactly.

In order to find the latitude and longitude of your points from X, Y, there are different options. The math being much more complex for transverse Mercator projections, I suggest using a GIS software, like QGIS, ArcGIS, to import your points as WGS84 UTM Zone 17N, transform them to Geographic WGS84, and calculate the new geometry coordinates. Or you can use a transformation library like Pyproj, GDAL ogr2ogr, etc.

There also exists some websites where you can convert coordinates, like cs2cs, where you can input a list of delimited coordinates, and choose the source and target projection, to get your desired output. In your case, the input proj string to use would be:

+proj=utm +zone=17 +datum=WGS84 +units=ft +no_defs

and the output would be:

+proj=longlat +datum=WGS84 +no_defs

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If you are looking for a way to do it in Excel, in spite of the availability of tools like Proj, you can always refer to Guidance Note Number 7, part 2 from the EPSG. The UTM transformation calculation is great fun and you will enjoy doing it for yourself very much, for hours and hours.

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