Northings & Eastings
Lesson- Legal Land Descriptions
TYPE 1
Metes and Bounds Description:
“; thence N 67° 35’ E along said right of way
line of State Road No.1 a distance of 120 ft.”
TYPE 2
Rectangular Survey System Description:
“Township 1 South, Range 1 East, 3rd PM
Section 25: S1/2 NW1/4”
Universal Transverse Mercator
Coordinate System (UTM)
• Means of stating any position on the earth
by giving two coordinates: An east
coordinate (easting) and a north coordinate
(northing)
US Zones - UTM
SPCS
State Plane Coordinate System
Based on zones described by political
boundaries – states or areas within
states
More accurate than UTM
Zones SPCS
Coordinate System Origin - SPCS
Established by each state – Generally
2 million feet west of the zone’s
central meridian and some
distance south of the zone’s
southernmost point.
Northing – North Coordinate
Easting – East Coordinate
Important Terms
Departure:
A distance in the east-west direction (xaxis)
Latitude:
A distance in the north-south direction
(y-axis)
Graphically
Pt. 2
Latitude
Departure
Pt. 1
Professional Development ID Code: 8005
Right Triangle Trigonometry 1
Departure
sin β = Distance
Departure = (sin β)(Distance)
β
Right Triangle Trigonometry 2
Latitude
cos β = Distance
Latitude = (cos β)(Distance)
β
Ties to Metes and Bounds
β
N 48º E, 200 feet
Ties to Metes and Bounds
β
Latitude = (cos β)(Length of property line)
Departure = (sin β)(Length of property line)
N 48º E, 200 feet
Latitude = (cos β)(Length of property line)
= (cos 48°)(200 feet)
= 133.826 feet
Departure = (sin β)(Length of property line)
= (sin 48°)(200 feet)
= 148.629 feet
Convert to Northing & Easting
Latitude added (N direction) or subtracted
(South direction) from the previous
Northing
Departure added (E direction) or
subtracted (W direction) from the
previous Easting
An Example
SOUTH
WEST
Latitude and Departure
Latitude = (cos β)(Length of property line)
= (cos 73°)(249.08 ft)
= 72.82 ft
Departure = (sin β)(Length of property line)
= (sin 73°)(249.08 ft)
= 238.20 ft
Northing – End 1st Property Line
Latitude = 72.82 ft.
Known Benchmark Northing = 1000 ft.
Bearing South therefore subtract 72.82 ft.
Northing = 927.18 feet at the end of the 1st
Property Line
Easting – End 1st Property Line
Departure = 238.20 feet
Known Benchmark Easting = 1000 ft.
Bearing West therefore Subtract 238.20 ft.
Easting = 761.80 feet at the end of the 1st
Property Line
End of Second Property Line
Latitude and Departure – line 2
Latitude = (cos β)(Length of property line)
= (cos 0°)(201.42 ft)
= 201.42 feet
Departure = (sin β)(Length of property line)
= (sin 0°)(201.42 ft)
= 0 feet
Northings-Eastings End
Latitude = 201.42 ft
Previous Northing = 927.18 ft
Bearing South therefore subtract 201.42 ft
Northing = 725.76 ft at the end of the
2nd Property Line
Departure = 0 ft
Previous Easting = 761.80 ft
Bearing West therefore Subtract 0 ft.
Easting = 761.80 feet at the end of the
2nd Property Line
nd
2
Line
End of 3rd Property Line
Latitude and Departure – line 3
Latitude = (cos β)(Length of property line)
= (cos 83°)(368 ft)
= 44.85 feet
Departure = (sin β)(Length of property line)
= (sin 83°)(368 ft)
= 365.26 feet
Northings-Eastings End 3rd Line
Latitude = 44.85 ft
Previous Northing = 725.76 ft
Bearing North therefore add
44.85 ft
Northing = 770.61 ft at the
end of the 3rd Property
Line
Departure = 365.26 ft
Previous Easting = 761.80 ft
Bearing East therefore add
365.26 ft.
Easting = 1127.06 feet at
the end of the
3rd Property Line
End of
th
4
Property Line
Convert 28º 58´ 53´´ to Decimal:
28º + 58/60º + 53/3600º = 28.9814º
Latitude and Departure – line 4
Latitude = (cos β)(Length of property line)
= (cos 28.9814°)(262.23 ft)
= 229.39 feet
Departure = (sin β)(Length of property line)
= (sin 28.9814°)(262.23 ft)
= 127.06 feet
Northings-Eastings End
Latitude = 229.39 ft
Previous Northing = 770.61 ft
Bearing North therefore add 229.39 ft
Northing = 1000 ft at the end of the
4th Property Line
Departure = 127.06 ft
Previous Easting = 1127.06 ft
Bearing West therefore subtract
127.06 ft.
Easting = 1000 feet at the end of the 4th
Property Line
th
4
Line
Finished Property Lines
Using Software
Click here to download a Template for Calculating
Northings and Eastings Using Excel