What is the Origin of WGS84 UTM 18N?

Question

I was given an unprojected coordinate in the form of lat, lon and I am using pyproj to convert to projected coordinate as such:

from pyproj import Proj

# New Jersey
lat = 40.704895
lon = -74.094994

wgs84 = Proj(proj='utm', zone=18, ellps='clrk66')
x, y = wgs84(sample_data['lon'], sample_data['lat'])

# x = 576453.375, y = 4506180.871
# 576453 meters east and 4508180 meters north of the zone's origin

I'd like to know the origin (0, 0) of the UTM zone 18N. I tried using inverse conversion with

wgs84(0, 0, inverse=True)

I got (-79.48869479772156, 0.0) which means it's 79 meters south and right at the Prime Meridian which seems wrong.

Answer 1

Many projected coordinate systems use a false Easting and/or a false Northing to avoid negative coordinates and/or to reduce potential ambiguities with other CRS of the same region.

In the case of UTM 18N, the origin of the projection, in lat long, is (0°, -75°), but the false easting is 500 000 m meaning that the XY coordinate system has been shifted.

Note that when you invert the projection the result is back in Lat/long. So your result mean that you are on the equator with a longitude of -79.5, which comes from -75°(central meridian) - 500/111 (false easting approximately converted in degrees)

Projection: Transverse_Mercator (in your case on the NAD1927 ellipsoid)

False_Easting: 500000,0

False_Northing: 0,0

Central_Meridian: -75,0

Scale_Factor: 0,9996

Latitude_Of_Origin: 0,0

Linear Unit: Meter (1,0)

Answer 2

The units of WGS84 are degrees, so your result says 79 degrees west of the Greenwich prime meridian.

Generally, UTM coordinates have a false easting of 500km, so the origin is really 500km west of the UTM 18N meridian at 75° West cutting the equator.

Answer 3

Zone 1 covers longitude 180° to 174° W, hence it's origin is (177° W,0° N). similarly moving eastward Zone 2 covers longitude 174° to 168° W, with origin (171° W,0° N). so Zone 18 is 78° W to 72° W, with origin (75°W, 0°N)