EPSG:1119

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 equidistant conic projection is neither conformal nor equal area, but a compromise between the two. It is most frequently used for very small scale maps in atlases based on a sphere. EPSG carries only the ellipsoidal development in which the meridional arc distance between the parallels of latitude reflects that on the ellipsoid.

The formulas to convert geodetic latitude and longitude (φ, λ) to easting (E) and northing (N) are:

Easting, E = EF + r sin θ
Northing, N = NF + rF – r cos θ

where
M = 	a [(1 – e^2/4 – 3e^4/64 – 5e^6/256 - …)φ – (3e^2/8 + 3e^4/32 + 45e^6/1024 + …)sin 2φ + (15e^4/256 + 45e^6/1024 + …)sin 4φ – (35e^6/3072 + …)sin 6φ + …]
with φ in radians, and with MF, M1 and M2 for φF (latitude of false origin), φ1 (latitude of 1st standard parallel) and φ2 (latitude of 2nd standard parallel) derived in the same way;

m = cos φ / (1 – e^2 sin2 φ)^0.5 with φ in radians, and m1 and m2 for φ1 and φ2 derived in the same way;
n = a (m1 – m2) / (M2 – M1)
G = (m1 / n) + (M1 / a)
rF = a G – MF

r = a G – M
θ = n (λ – λF)

For the reverse calculation:

G and rF are constants for the projection calculated as for the forward calculation above. Then:

r' = ± {(E – EF)^2 + [rF – (N – NF)]^2 }^0.5, taking the sign of n

If n is positive (northern hemisphere case of the projection), 
θ' =  atan2 {(E – EF) , [rF – (N – NF)]}
but if n is negative (southern hemisphere case of the projection), the signs of both arguments of the atan2 function must be reversed: 
θ' =  atan2 {– (E – EF), – [rF – (N – NF)]}

M = a G – r'
μ = M / [a (1 – e^2/4 – 3e^4/64 – 5e^6/256 - …)]

Latitude, φ = μ	+ (3e1/2 – 27e1^3/32 + …)sin 2μ + (21e1^2/16 – 55e1^4/32 + …)sin 4μ + (151e1^3/96 - …)sin 6μ + (1097e1^4/512 - …)sin 8μ
with μ in radians

where e1 = [1 – (1 – e^2)^0.5] / [1 + (1 – e^2)^0.5]

Longitude, λ = λF + (θ' / n)