Easting northing to latitude longitude

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Eastings and northings are distances east and north, respectively, of a base point. The base point is usually a latitude and longitude, and eastings and northings are normally expressed in meters or feet. The easting and northing, however, is usually offset a particular value to make them positive and allow them to express places west and south of the base point.

In general, converting from one coordinate system to another is not simple, since both may have different ellipsoids (Earth models) and datums. As I understand, the formulas for converting from one coordinate system to another are rather complex.

SVY21, however, uses the exact same datum and ellipsoid as WGS84, making the task simpler. In SVY21, the base point for eastings and northings is Base 7 at Pierce Reservoir. According to the geodetic version of SVY21, this base point is 1 deg. 22 min. 02.9154 sec. North and 103 deg. 49 min 31.9752 sec. East (that is, a latitude of about 1.3674765 degrees and a longitude of about 103.8255487 degrees; the well known text for the projected version, however, uses a slightly different latitude and longitude). The offset for the easting is 28001.642 meters, and the offset for the northing is 38744.572 meters. The EPSG code is 3414. I will assume your eastings and northings are expressed in meters.

Since SVY21 uses the same system as WGS84, all you have to do is:

  • Subtract the easting and northing by their respective offset values. (The values will be in meters.)
  • Find the longitude of the given point by finding the destination point given the base point, the absolute value of the easting, and the bearing of 90 degrees if the easting is positive, or 270 degrees if it’s negative. This calculation is called solving the “direct geodesic problem”, and this is discussed in C.F.F. Karney’s article “Algorithms for geodesics, 2012.
  • Find the latitude of the given point by finding the destination point given the base point, the absolute value of the northing, and the bearing of 0 degrees if the northing is positive, or 180 degrees if it’s negative.

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