I want to convert NEW ZEALAND MAP GRID coordinates i.e. Northing and Easting into WGS84 coordinates i.e. Latitude and Longitude.
I have searched on internet but there is no proper explanation of how to do this, or an online calculator to do this.
My final goal is to write a program in C# or JAVA , which will convert NZMG coordinates into WGS84 coordinates.
Best Answer
I wrote a C program to do this many years ago. They are hard, being complex arithmetic series approximations that have to be solved iteratively. I had to define my own structure to handle imaginary numbers and create the complex arithmetic operations. The equations are on the LINZ website to do this. http://www.linz.govt.nz/geodetic/conversion-coordinates/projection-conversions/projection-to-geographic-nzmg-to-nzgd1949
They also have an online calculator that is excellent.
Note that since NZMG used the geodetic datum 1949, which is a copy of the International Datum 1909 you will also have to do a datum shift to get to WGS84. That is also difficult unless you approximate it with a 3 or 7 parameter equation that gets you only within 15 metres or so. Otherwise you need to use a grid adjustment that gets you down to survey accuracy.
NZMG is obsolete and has not been used since 2000. You really only need a one-off conversion to upgrade to NZTM (a standard transverse mercator using the UTM equations) so I cannot see the need to write another conversion program. I have found my code! March 1993, you are welcome to have it.
Note that recent earthquakes in New Zealand have moved large parts by up to 2 metres, so there is a revision of the reference marks underway at the moment.