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.¶¶To derive the projected coordinates of a point, geodetic latitude (lat) is converted to authalic latitude (ß). The formulas to convert geodetic latitude and longitude (lat, lon) to Easting (E) and Northing (N) are: ¶Easting (E)     =  EF + (rho . sin(theta)) ¶Northing (N)  =  NF + rhoO – (rho . cos(theta))¶¶where¶theta  = n . (lon - lonO)¶rho  = [a . (C – n.alpha)^0.5] / n¶rhoO = [a . (C – n.alphaO)^0.5] / n¶and¶C  = m1^2 +  (n . alpha1)¶n   = (m1^2 – m2^2) / (alpha2 - alpha1)¶m1 = cos lat1 / (1 – e^2 sin^2(lat1))^0.5¶m2 = cos lat2 / (1 – e^2 sin^2(lat2))^0.5¶alpha  = (1 – e^2) . {[sin(lat) / (1 – e^2 sin^2(lat))] – [1/(2e)] . ln [(1 – e sin(lat)) / (1 + e sin(lat))]}¶alphaO  = (1 – e^2) . {[sin(latO) / (1 – e^2 sin^2(latO))] – [1/(2e)] . ln [(1 – e sin(latO)) / (1 + e sin(latO))]}¶alpha1  = (1 – e^2) . {[sin(lat1) / (1 – e^2 sin^2(lat1))] – [1/(2e)] . ln [(1 – e sin(lat1)) / (1 + e sin(lat1))]}¶alpha2  = (1 – e^2) . {[sin(lat2) / (1 – e^2 sin^2(lat2))] – [1/(2e)] . ln [(1 – e sin(lat2)) / (1 + e sin(lat2))]}¶¶The reverse formulas to derive the geodetic latitude and longitude of a point from its Easting and Northing values are:¶lat = ß' + (e^2/3 + 31e^4/180 + 517e^6/5040) . sin 2ß'] + [(23e^4/360 + 251e^6/3780) . sin 4ß'] + [(761e^6/45360) . sin 6ß']¶¶lon =   lonO + (theta / n)¶where¶ß' =  asin(alpha' / {1 – [(1 – e^2) / (2 . e)] . ln [(1 – e) / (1 + e)]¶alpha' =  [C – (rho^2 . N^2 / a^2)] / n¶rho =  {(E – EF)^2 + [rhoO – (N – NF)]^2 }^0.5¶theta =  atan [(E – EF) / [rhoO – (N – NF)]¶and C, n and rhoO are as in the forward equations.