EPSG:1130

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

The forward conversion from 2D geographic coordinates latitude and longitude (Lat, Lon) begins by:
Xp = nu cos(Lat) sin(Lon – LonC)
Yp =  –sin(LatC) [nu cos(Lat) cos(Lon – LonC) – nuC cos(LatC)] + cos(LatC) [nu (1.0 – e^2) sin(Lat) –  nuC (1.0 – e^2) sin(LatC)]
where 
LatC, LonC are the latitude and longitude of the projection origin on the ellipsoid,
e is the eccentricity of the ellipsoid and e^2 = (a^2 – b^2)/a^2 = 2f – f^2,
nu is the radius of curvature in the prime vertical at latitude Lat; nu = a / (1 – e^2 sin^2(Lat))^0.5,
nuC is the radius of curvature in the prime vertical at the latitude of the projection centre LatC; nuC = a / (1 – e^2 sin^2(LatC))^0.5,

Then applying the azimuth α (positive clockwise from true North),  scale factor at the projection centre kc, and false easting and false northing at the projection centre (Ec,Nc): 

E = Ec + kc [cos(α) Xp – sin(α) Yp]
N = Nc + kc [sin(α) Xp + cos(α) Yp]

Reverse
For the reverse formulas for latitude and longitude corresponding to a given Easting (E) and Northing (N), first remove the false easting, false northing, rotation, and scale factor: 

	Xp = cos(α) (E – Ec) / kc + sin(α) (N – Nc) / kc
	Yp = –sin(α) (E – Ec) / kc + cos(α) (N – Nc) / kc

To simplify the calculation of the latitude and longitude values, some interim quantities are calculated:
	B = 1 – e^2 cos^2(LatC)
	C = Yp – nuO sin(LatC) cos(LatC) + nuC (1 – e^2) cos(LatC) sin(LatC)
	D = { (1 – e^2) [(a^2 – Xp^2) (1 – e^2 cos^2(latC)) – C^2] }^0.5
	Xg =  (–C sin(LatC)  + D cos(LatC)) / B
	Yg = Xp
	Zg = (C cos(LatC) (1 – e^2) + D sin(LatC) ) / B
Then:
	Lat = atan2(Zg, (1 – e^2) [Xg^2 + Yg^2]^0.5)
	Lon = LonC + atan2(Yg, Xg)