EPSG:1108

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 formulas to derive projected Easting and Northing coordinates are:

ko = cos(latSP1)/(1 - e^2*sin^2(latSP1))^0.5 
 
where latSP1 is the absolute value of the first standard parallel (i.e. positive).  

E = FE + a*ko(lon - lonF)             
M = a ko ln{tan(pi/4 + latF/2)[(1 – e sin(latF))/(1 + e sin(latF))]^(e/2)}
N = (NF – M) + a ko ln{tan(pi/4 + lat/2)[(1 – e sin(lat))/(1 + e sin(lat))]^(e/2)}
where logarithms are natural.

The reverse formulas to derive latitude and longitude from E and N values are:

lat = chi + (esq/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2chi) 
+ (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4chi)
+ (7e^6/120 +  81e^8/1120) sin(6chi)  + (4279e^8/161280) sin(8chi)

where chi = pi/2 - 2 atan(t)
t = B^((NF-M-N)/(a*ko)) 
B = base of the natural logarithm, 2.7182818...
and ko is calculated as for the forward transformation above.
lon  =  ((E - EF)/(a*ko)) + lonF