EPSG:9801

Lambert Conic Conformal (1SP)

Attributes

Data source: EPSG

Information source: EPSG guidance note #7-2, https://epsg.org

Revision date: 2021-01-13

Formula

```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 Easting and Northing coordinates of a point with geographical coordinates (lat,lon):

E = FE + r sin(theta)
N = FN + r0 - r cos(theta)
where
mO = cos(latO)/(1 – e^2 sin^2(latO))^0.5 where latO is the latitude of natural origin
tO = tan(pi/4 – latO/2)/[(1 – e sin(latO))/(1 + e sin(latO))]^e/2
t = tan(pi/4 – lat/2)/[(1 – e sin(lat))/(1 + e sin(lat))]^e/2
n = sin(latO)
F = mO/(n tO^n)
rO = a F tO^n kO
r =  a F t^n kO
theta = n(lon – lonO)
As with other conics, a negative n and r result for projections centered in the Southern Hemisphere.

The reverse formulas to derive the latitude and longitude of a point from its Easting and Northing values are:

lat = pi/2 - 2arctan{t'[(1 - e sin(lat))/(1 + e sin(lat))]^(e/2)}
lon = theta'/n +lon0
where
n, F, and rO are derived as for the forward calculation
r' = +/-[(E - FE)^2 + {r0 - (N - FN)}^2]^0.5  taking the sign of n
t' = (r'/(a k0 F))^(1/n)
If n is positive, theta' = atan2{(E –  FE) , [rO – (N –  FN)]}
but if n is negative the signs of both arguments of the atan2 function  must be reversed and theta' = atan2{– (E –  FE) , – [rO – (N –  FN)]}

Note that the formula for lat requires iteration. First calculate t' and then a trial value for lat using
lat = π/2-2atan(t'). Then use the full equation for lat substituting the trial value into the right hand side of the equation. Thus derive a new value for lat. Iterate the process until lat does not change significantly. The solution should quickly converge, in 3 or 4 iterations.```

Example

```For Projected Coordinate System JAD69 / Jamaica National Grid

Parameters:
Ellipsoid:  Clarke 1866, a = 6378206.400 m., 1/f = 294.97870
then  e = 0.08227185 and e^2 = 0.00676866

Latitude Natural Origin         18°00'00"N  =  0.31415927 rad
Longitude Natural Origin     77°00'00"W = -1.34390352 rad
Scale factor at origin            1.000000
False Eastings  FE               250000.00 m
False Northings FN              150000.00 m

Forward calculation for:
first gives
m0    =  0.95136402        t0 =  0.72806411
F       =  3.39591092        n  =  0.30901699
r        =  19643955.26     r0  =  19636447.86
theta =  0.00030374        t   =  0.728965259

Then Easting E   =     255966.58 m
Northing N =      142493.51 m

Reverse calculation for the same easting and northing first gives

theta' =  0.000303736
t'        =  0.728965259
m0     =  0.95136402
r'        =  19643955.26

Then Latitude     = 17°55'55.800"N
Longitude  = 76°56'37.260"W```