survey map projections

Penn State Surveying Program 1 Ellipsoid Defining Parameters

DEFINING PARAMETERS FOR SELECTED ELLIPSOIDS

Name GRS 80 WGS 84 CLARKE 1866

a = 6,378,137.0 6,378,137.0 6,378,206.4

1/f = ############# 298.257223563 294.97870

Enter in the name exactly as it appears on the following computation sheets. The software will lookup and insert the ellipsoidal values. Important to note that the U.S. State Plane Coordinate System of 1983 using the GRS 80 ellipsoid, and that the UTM projection is usually uses WGS 84.

International user can add ellipsoid definitions in columns E, F, ..., Z. Remember to unprotect the sheet under the tools menu before attempting to add an ellipsoid.

U.S. State Plane Coordinate Systems Projection Parameters (taken from Stem, J. 1989. "State Plane Coordinate Systems of 1983." NOAA Manual NOS NGS 5.

Lambert Conformal Conic Projection states U.S. Government Printing Office. Washington, D.C,)

State AR AR CA CA CA CA CA CA

Zone North South 401 402 403 404 405 406

fs 34°56' 33°18' 40°00' 38°20' 37°04' 36°00' 34°02' 32°47'

fn 36°14' 34°46' 41°40' 39°50' 38°26' 37°15' 35°28' 33°53'

fb 34°20' 32°40' 39°20' 37°40' 36°30' 35°20' 33°30' 32°10'

l0 92°00'W 92°00'W 122°00'W 122°00'W 120°30'W 119°00'W 118°00'W 116°15'W

Nb 0.000 400,000.000 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0

E0 400,000.000 400,000.000 2,000,000.0 2,000,000.0 2,000,000.0 2,000,000.0 2,000,000.0 2,000,000.0

TRANSVERSE MERCATOR PROJECTION STATES

State AL AL AK AK AK AK AK AK

Zone East West 5001/O.M. 5002 5003 5004 5005 5006

CM 85°50'W 87°30'W ATAN(-3/4) 142°00'W 146°00'W 150°00'W 154°00'W 158°00'W

1:k0 25,000 15,000 10,000 10,000 10,000 10,000 10,000 10,000

f0 30°30' 30°00' 57°00' 54°00' 54°00' 54°00' 54°00' 54°00'

l0 85°50'W 85°50'W 133°40'W 142°00'W 146°00'W 150°00'W 154°00'W 158°00'W

E0 200,000.0 600,000.0 5,000,000.0 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0

N0 0.0 0.0 -5,000,000.0 0.0 0.0 0.0 0.0 0.0

(taken from Stem, J. 1989. "State Plane Coordinate Systems of 1983." NOAA Manual NOS NGS 5.

U.S. Government Printing Office. Washington, D.C,)

CO CO CO CT FL IA IA KS KS

North Central South 600 North North South North South

39°43' 38°27' 37°14' 41°12' 29°35' 42°04' 40°37' 38°43' 37°16'

40°47' 39°45' 38°26' 41°52' 30°45' 43°16' 41°47' 39°47' 38°34'

39°20' 37°50' 36°40' 40°50' 29°00' 41°30' 40°00' 38°20' 36°40'

105°30'W 105°30'W 105°30'W 72°45'W 84°30'W 93°30'W 93°30'W 98°00'W 98°30'W

304,800.6096 304,800.6096 304,800.6096 152,400.3048 0.0 1,000,000.0 0.0 0.0 400,000.0

914,401.8289 914,401.8289 914,401.8289 304,800.6096 600,000.0 1,500,000.0 500,000.0 400,000.0 400,000.0

AK AK AK AZ AZ AZ DE FL FL

5007 5008 5009 East Central West 700 East West

162°00'W 166°00'W 170°00'W 110°10'W 111°55'W 113°45'W 75°25'W 81°00'W 82°00'W

10,000 10,000 10,000 10,000 10,000 15,000 200,000 17,000 17,000

54°00' 54°00' 54°00' 31°00' 31°00' 31°00' 38°00' 24°20' 24°20'

162°00'W 166°00'W 170°00'W 110°10'W 111°55'W 113°45'W 75°25'W 81°00'W 82°00'W

500,000.0 500,000.0 500,000.0 213,360.0 213,360.0 213,360.0 200,000.0 200,000.0 200,000.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

KY KY LA LA LA MD MA MA MI

North South North South Offshore 1900 Mainland Island North

37°58' 36°44' 31°10' 29°18' 26°10' 38°18' 41°43' 41°17' 45°29'

38°58' 37°56' 32°40' 30°42' 27°50' 39°27' 42°41' 41°29' 47°05'

37°30' 36°20' 30°30' 28°30' 25°30 37°40' 41°00' 41°00' 44°47'

84°15'W 85°45'W 92°30'W 91°20'W 91°20'W 77°00'W 71°30W 70°30'W 87°00'W

0.0 500,000.0 0.0 0.0 0.0 0.0 750,000.0 0.0 0.0

500,000.0 500,000.0 1,000,000.0 1,000,000.0 1,000,000.0 400,000.0 200,000.0 500,000.0 8,000,000.0

GA GA HI HI HI HI HI ID ID

East West 5101 5102 5103 5104 5105 East Central

82°10'W 84°10'W 155°30'W 156°40'W 158°00'W 159°30'W 160°10'W 112°10'W 114°00'W

10,000 10,000 30,000 30,000 100,000 100,000 0 19,000 19,000

30°00' 30°00' 18°50' 20°20' 21°10' 21°50' 21°40' 41°40' 41°40'

82°10'W 82°10'W 155°30'W 156°40'W 158°00'W 155°30'W 155°30'W 112°10'W 114°00'W

200,000.0 700,000.0 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0 200,000.0 500,000.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

MI MI MN MN MN MT NE NY NC

Central South North Central South 2500 2600 Long Island 3200

44°11' 42°06' 47°02' 45°37' 43°47' 45°00' 40°00' 40°40' 34°20'

45°42' 43°40' 48°38' 47°03' 45°13' 49°00' 43°00' 41°02' 36°10'

43°19' 41°30' 46°30' 45°00' 43°00' 44°15' 39°50' 40°10' 33°45'

84°22'W 84°22'W 93°06'W 94°15'W 94°00'W 109°30'W 100°00'W 74°00'W 79°00'W

0.0 0.0 100,000.0 100,000.0 100,000.0 0.0 0.0 0.0 0.0

6,000,000.0 4,000,000.0 800,000.0 800,000.0 800,000.0 600,000.0 500,000.0 300,000.0 609,601.2199

ID IL IL IN IN ME ME MS MS

West East West East West East West East West

115°45'W 88°20'W 90°10'W 85°40'W 87°05'W 68°30'W 70°10'W 88°50'W 90°20'W

15,000 40,000 17,000 30,000 30,000 10,000 10,000 20,000 20,000

41°40' 36°40' 36°40' 37°30' 37°30' 43°40' 42°50' 29°30' 29°30'

115°45'W 88°20'W 90°10'W 85°40'W 87°05'W 68°30'W 70°10'W 88°50'W 90°20'W

800,000.0 300,000.0 700,000.0 100,000.0 900,000.0 300,000.0 900,000.0 700,000.0 700,000.0

0.0 0.0 0.0 250,000.0 250,000.0 0.0 0.0 0.0 0.0

ND ND OH OH OK OK OR OR PA

North South North South North South North South North

47°26' 46°11' 40°26' 38°44' 35°34' 33°56' 44°20' 42°20' 40°53'

48°44' 47°29' 41°42' 40°02' 36°46' 35°14' 46°00 44°00' 41°57'

47°00' 45°40' 39°40' 38°00' 35°00' 33°20' 43°40' 41°40' 40°10'

100°30'W 100°30'W 82°30'W 82°30'W 98°00'W 98°00'W 120°30'W 120°30'W 77°45'W

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

600,000.0 600,000.0 600,000.0 600,000.0 600,000.0 600,000.0 2,500,000.0 1,500,000.0 600,000.0

MO MO MO NV NV NV NH NJ/NY East NM

East Central West East Central West 2800 2900 East

90°30'W 92°30'W 94°30'W 115°35'W 116°40'W 118°35'W 71°40'W 74°30'W 104°20'W

15,000 15,000 17,000 10,000 10,000 10,000 30,000 10,000 11,000

35°50' 35°50' 36°10' 34°45' 34°45' 34°45' 42°30' 38°50' 31°00'

90°30'W 92°30'W 94°30'W 115°35'W 116°40'W 118°35'W 71°40'W 74°30'W 104°20'W

250,000.0 250,000.0 250,000.0 200,000.0 500,000.0 800,000.0 300,000.0 150,000.0 165,000.0

0.0 0.0 0.0 8,000,000.0 6,000,000.0 4,000,000.0 0.0 0.0 0.0

PA SC SD SD TN TX TX TX TX

South 3900 North South 4100 North North Central Central South Central

39°56' 32°30' 44°25' 42°50' 35°15' 34°39' 32°08' 30°07' 28°23'

40°58' 34°50' 45°41' 44°24' 36°25' 36°11' 33°58' 31°53' 30°17'

39°20' 31°50' 43°50' 42°20' 34°20' 34°00' 31°40' 29°40' 27°50'

77°45'W 81°00'W 100°00W 100°20W 86°00'W 101°30'W 98°30'W 100°20'W 99°00'W

0.0 0.0 0.0 0.0 0.0 1,000,000.0 2,000,000.0 3,000,000.0 4,000,000.0

600,000.0 609,600.0 600,000.0 600,000.0 600,000.0 200,000.0 600,000.0 700,000.0 600,000.0

NM NM NY NY NY RI VT WY WY

Central West East Central West 3800 4400 East East Central

106°15'W 107°50'W 74°30'W 76°35'W 78°35'W 71°30'W 72°30'W 105°10'W 107°20'W

10,000 12,000 10,000 16,000 16,000 160,000 28,000 16,000 16,000

31°00' 31°00' 38°50' 40°00 40°00 41°05' 42°30' 40°30' 40°30'

106°15'W 107°50'W 74°30'W 76°35'W 78°35'W 71°30'W 72°30'W 105°10'W 107°20'W

500,000.0 830,000.0 150,000.0 250,000.0 350,000.0 100,000.0 500,000.0 200,000.0 400,000.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100,000.0

TX UT UT UT VA VA WA WA WV

South North Central South North South North South North

26°10' 40°43' 39°01' 37°13' 38°02' 36°46' 47°30' 45°50' 39°00'

27°50' 41°47' 40°39' 38°21' 39°12' 37°58' 48°44' 47°20' 40°15'

25°40' 40°20' 38°20' 36°40' 37°40' 36°20' 47°00' 45°20' 38°30'

98°30'W 111°30'W 111°30'W 111°30'W 78°30'W 78°30'W 120°50'W 120°30'W 79°30'W

5,000,000.0 1,000,000.0 2,000,000.0 3,000,000.0 2,000,000.0 1,000,000.0 0.0 0.0 0.0

300,000.0 500,000.0 500,000.0 500,000.0 3,500,000.0 3,500,000.0 500,000.0 500,000.0 600,000.0

WY WY

West Central West

108°45'W 110°05'W

16,000 16,000

40°30' 40°30'

108°45'W 110°05'W

600,000.0 800,000.0

0.0 100,000.0

WV WI WI WI PR VI

South North Central South 5200

37°29' 45°34' 44°15' 42°44' 18°02'

38°53' 46°46' 45°30' 44°04' 18°26'

37°00' 45°10' 43°50' 42°00' 17°50'

81°00'W 90°00'W 90°00'W 90°00'W 66°26'W

0.0 0.0 0.0 0.0 200,000.0

600,000.0 600,000.0 600,000.0 600,000.0 200,000.0

Penn State Surveying Program 10 State Plane Coordinate System

Defining Zone ParametersU.S. State Plane Coordinate Systems Projection Parameters (taken from Stem, J. 1989. "State Plane Coordinate Systems of 1983." NOAA Manual NOS NGS 5.

Lambert Conformal Conic Projection states U.S. Government Printing Office. Washington, D.C,)

State AR AR CA CA CA CA CA CA CO CO CO

Zone North South 401 402 403 404 405 406 North Central South

fs 34°56' 33°18' 40°00' 38°20' 37°04' 36°00' 34°02' 32°47' 39°43' 38°27' 37°14'

fn 36°14' 34°46' 41°40' 39°50' 38°26' 37°15' 35°28' 33°53' 40°47' 39°45' 38°26'

fb 34°20' 32°40' 39°20' 37°40' 36°30' 35°20' 33°30' 32°10' 39°20' 37°50' 36°40'

l0 92°00'W 92°00'W 122°00'W 122°00'W 120°30'W 119°00'W 118°00'W 116°15'W 105°30'W 105°30'W 105°30'W

Nb 0.000 400,000.000 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0 304,800.6096 304,800.6096 304,800.6096

E0 400,000.000 400,000.000 2,000,000.0 2,000,000.0 2,000,000.0 2,000,000.0 2,000,000.0 2,000,000.0 914,401.8289 914,401.8289 914,401.8289

State FL IA IA KS KS KY KY LA LA LA MD

Zone North North South North South North South North South Offshore 1900

fs 29°35' 42°04' 40°37' 38°43' 37°16' 37°58' 36°44' 31°10' 29°18' 26°10' 38°18'

fn 30°45' 43°16' 41°47' 39°47' 38°34' 38°58' 37°56' 32°40' 30°42' 27°50' 39°27'

fb 29°00' 41°30' 40°00' 38°20' 36°40' 37°30' 36°20' 30°30' 28°30' 25°30 37°40'

l0 84°30'W 93°30'W 93°30'W 98°00'W 98°30'W 84°15'W 85°45'W 92°30'W 91°20'W 91°20'W 77°00'W

Nb 0.0 1,000,000.0 0.0 0.0 400,000.0 0.0 500,000.0 0.0 0.0 0.0 0.0

E0 600,000.0 1,500,000.0 500,000.0 400,000.0 400,000.0 500,000.0 500,000.0 1,000,000.0 1,000,000.0 1,000,000.0 400,000.0

State MA MI MI MI MN MN MN MT NE NY NC

Zone Island North Central South North Central South 2500 2600 Long Island 3200

fs 41°17' 45°29' 44°11' 42°06' 47°02' 45°37' 43°47' 45°00' 40°00' 40°40' 34°20'

fn 41°29' 47°05' 45°42' 43°40' 48°38' 47°03' 45°13' 49°00' 43°00' 41°02' 36°10'

fb 41°00' 44°47' 43°19' 41°30' 46°30' 45°00' 43°00' 44°15' 39°50' 40°10' 33°45'

l0 70°30'W 87°00'W 84°22'W 84°22'W 93°06'W 94°15'W 94°00'W 109°30'W 100°00'W 74°00'W 79°00'W

Nb 0.0 0.0 0.0 0.0 100,000.0 100,000.0 100,000.0 0.0 0.0 0.0 0.0

E0 500,000.0 8,000,000.0 6,000,000.0 4,000,000.0 800,000.0 800,000.0 800,000.0 600,000.0 500,000.0 300,000.0 609,601.2199

State ND OH OH OK OK OR OR PA PA SC SD

Zone South North South North South North South North South 3900 North

fs 46°11' 40°26' 38°44' 35°34' 33°56' 44°20' 42°20' 40°53' 39°56' 32°30' 44°25'

fn 47°29' 41°42' 40°02' 36°46' 35°14' 46°00 44°00' 41°57' 40°58' 34°50' 45°41'

fb 45°40' 39°40' 38°00' 35°00' 33°20' 43°40' 41°40' 40°10' 39°20' 31°50' 43°50'

l0 100°30'W 82°30'W 82°30'W 98°00'W 98°00'W 120°30'W 120°30'W 77°45'W 77°45'W 81°00'W 100°00W

Nb 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

E0 600,000.0 600,000.0 600,000.0 600,000.0 600,000.0 2,500,000.0 1,500,000.0 600,000.0 600,000.0 609,600.0 600,000.0


Defining Zone Parameters

State TN TX TX TX TX TX UT UT UT VA VA

Zone 4100 North North Central Central South Central South North Central South North South

fs 35°15' 34°39' 32°08' 30°07' 28°23' 26°10' 40°43' 39°01' 37°13' 38°02' 36°46'

fn 36°25' 36°11' 33°58' 31°53' 30°17' 27°50' 41°47' 40°39' 38°21' 39°12' 37°58'

fb 34°20' 34°00' 31°40' 29°40' 27°50' 25°40' 40°20' 38°20' 36°40' 37°40' 36°20'

l0 86°00'W 101°30'W 98°30'W 100°20'W 99°00'W 98°30'W 111°30'W 111°30'W 111°30'W 78°30'W 78°30'W

Nb 0.0 1,000,000.0 2,000,000.0 3,000,000.0 4,000,000.0 5,000,000.0 1,000,000.0 2,000,000.0 3,000,000.0 2,000,000.0 1,000,000.0

E0 600,000.0 200,000.0 600,000.0 700,000.0 600,000.0 300,000.0 500,000.0 500,000.0 500,000.0 3,500,000.0 3,500,000.0

State WA WV WV WI WI WI PR VI

Zone South North South North Central South 5200

fs 45°50' 39°00' 37°29' 45°34' 44°15' 42°44' 18°02'

fn 47°20' 40°15' 38°53' 46°46' 45°30' 44°04' 18°26'

fb 45°20' 38°30' 37°00' 45°10' 43°50' 42°00' 17°50'

l0 120°30'W 79°30'W 81°00'W 90°00'W 90°00'W 90°00'W 66°26'W

Nb 0.0 0.0 0.0 0.0 0.0 0.0 200,000.0

E0 500,000.0 600,000.0 600,000.0 600,000.0 600,000.0 600,000.0 200,000.0

TRANSVERSE MERCATOR PROJECTION STATES

State AL AL AK AK AK AK AK AK AK AK AK

Zone East West 5001/O.M. 5002 5003 5004 5005 5006 5007 5008 5009

CM 85°50'W 87°30'W ATAN(-3/4) 142°00'W 146°00'W 150°00'W 154°00'W 158°00'W 162°00'W 166°00'W 170°00'W

1:k0 25,000 15,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000

f0 30°30' 30°00' 57°00' 54°00' 54°00' 54°00' 54°00' 54°00' 54°00' 54°00' 54°00'

l0 85°50'W 85°50'W 133°40'W 142°00'W 146°00'W 150°00'W 154°00'W 158°00'W 162°00'W 166°00'W 170°00'W

E0 200,000.0 600,000.0 5,000,000.0 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0 500,000.0

N0 0.0 0.0 -5,000,000.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

State AZ AZ DE FL FL GA GA HI HI HI HI

Zone Central West 700 East West East West 5101 5102 5103 5104

CM 111°55'W 113°45'W 75°25'W 81°00'W 82°00'W 82°10'W 84°10'W 155°30'W 156°40'W 158°00'W 159°30'W

1:k0 10,000 15,000 200,000 17,000 17,000 10,000 10,000 30,000 30,000 100,000 100,000

f0 31°00' 31°00' 38°00' 24°20' 24°20' 30°00' 30°00' 18°50' 20°20' 21°10' 21°50'

l0 111°55'W 113°45'W 75°25'W 81°00'W 82°00'W 82°10'W 82°10'W 155°30'W 156°40'W 158°00'W 155°30'W

E0 213,360.0 213,360.0 200,000.0 200,000.0 200,000.0 200,000.0 700,000.0 500,000.0 500,000.0 500,000.0 500,000.0

N0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0



State ID ID ID IL IL IN IN ME ME MS MS

Zone East Central West East West East West East West East West

CM 112°10'W 114°00'W 115°45'W 88°20'W 90°10'W 85°40'W 87°05'W 68°30'W 70°10'W 88°50'W 90°20'W

1:k0 19,000 19,000 15,000 40,000 17,000 30,000 30,000 10,000 10,000 20,000 20,000

f0 41°40' 41°40' 41°40' 36°40' 36°40' 37°30' 37°30' 43°40' 42°50' 29°30' 29°30'

l0 112°10'W 114°00'W 115°45'W 88°20'W 90°10'W 85°40'W 87°05'W 68°30'W 70°10'W 88°50'W 90°20'W

E0 200,000.0 500,000.0 800,000.0 300,000.0 700,000.0 100,000.0 900,000.0 300,000.0 900,000.0 700,000.0 700,000.0

N0 0.0 0.0 0.0 0.0 0.0 250,000.0 250,000.0 0.0 0.0 0.0 0.0

State MO MO NV NV NV NH NJ/NY East NM NM NM NY

Zone Central West East Central West 2800 2900 East Central West East

CM 92°30'W 94°30'W 115°35'W 116°40'W 118°35'W 71°40'W 74°30'W 104°20'W 106°15'W 107°50'W 74°30'W

1:k0 15,000 17,000 10,000 10,000 10,000 30,000 10,000 11,000 10,000 12,000 10,000

f0 35°50' 36°10' 34°45' 34°45' 34°45' 42°30' 38°50' 31°00' 31°00' 31°00' 38°50'

l0 92°30'W 94°30'W 115°35'W 116°40'W 118°35'W 71°40'W 74°30'W 104°20'W 106°15'W 107°50'W 74°30'W

E0 250,000.0 250,000.0 200,000.0 500,000.0 800,000.0 300,000.0 150,000.0 165,000.0 500,000.0 830,000.0 150,000.0

N0 0.0 0.0 8,000,000.0 6,000,000.0 4,000,000.0 0.0 0.0 0.0 0.0 0.0 0.0

State NY RI VT WY WY WY WY

Zone West 3800 4400 East East Central West Central West

CM 78°35'W 71°30'W 72°30'W 105°10'W 107°20'W 108°45'W 110°05'W

1:k0 16,000 160,000 28,000 16,000 16,000 16,000 16,000

f0 40°00 41°05' 42°30' 40°30' 40°30' 40°30' 40°30'

l0 78°35'W 71°30'W 72°30'W 105°10'W 107°20'W 108°45'W 110°05'W

E0 350,000.0 100,000.0 500,000.0 200,000.0 400,000.0 600,000.0 800,000.0

N0 0.0 0.0 0.0 0.0 100,000.0 0.0 100,000.0


Defining Zone Parameters(taken from Stem, J. 1989. "State Plane Coordinate Systems of 1983." NOAA Manual NOS NGS 5.

CT

600

41°12'

41°52'

40°50'

72°45'W

152,400.3048

304,800.6096

MA

Mainland

41°43'

42°41'

41°00'

71°30W

750,000.0

200,000.0

ND

North

47°26'

48°44'

47°00'

100°30'W

0.0

600,000.0

SD

South

42°50'

44°24'

42°20'

100°20W

0.0

600,000.0



WA

North

47°30'

48°44'

47°00'

120°50'W

0.0

500,000.0

AZ

East

110°10'W

10,000

31°00'

110°10'W

213,360.0

0.0

HI

5105

160°10'W

0

21°40'

155°30'W

500,000.0

0.0



MO

East

90°30'W

15,000

35°50'

90°30'W

250,000.0

0.0

NY

Central

76°35'W

16,000

40°00

76°35'W

250,000.0

0.0

Penn State Surveying Program 5/12/2014 Lambert Conformal Conic

Ellipsoid parameters Zone parameters PA

Name = GRS 80 North

a = 6,378,137.0 m Origin fb = 40° 10'

1/f = 298.257222101 l0 = -77° 45'

e² = 0.006694380 Standard parallels

e = 0.081819191 fSouth = 40° 53'

fNorth = 41° 57'

E0 = 600,000.0 m

Nb = 0.0 m

Direct solution

Position

f = 42° 30' 00.00000"

l = -80° 30' 00.00000"

Solution:

X = 373,960.0266 m

Y = 262,736.6621 m

k = 1.0001357076

Inverse solution

Position

X = 373,960.027 m

Y = 262,736.662 m

f = 0.741765 rad 42.50° 42° 29' 60.00000" N

l = -1.404990 rad 80.50° 80° 29' 59.99998" W

k = 1.000135708

Steps: Enter the appropriate ellipsoid name

(GRS 80, WGS 84, Clarke 1866) in cell B2 and the parameters from the

Ellipsoid sheet will appear. Note that U.S. State Plane Coordinate System of 1983 uses GRS 80.

Enter the zone parameters including

the grid origin fb and l0, latitudes of

the standard parallels (fSouth and

fNorth), and the false easting E0 and

northing Nb. These values can be obtained from the SPCS Defining

Parameters sheet. Direct solution: Enter the latitude

and longitude of the point were southern latitude and western longitude are considered negative.

Inverse solution: Enter the grid xy coordinates of the point.


Steps: Enter the appropriate ellipsoid name

(GRS 80, WGS 84, Clarke 1866) in cell B2 and the parameters from the

Ellipsoid sheet will appear. Note that U.S. State Plane Coordinate System of 1983 uses GRS 80.



the standard parallels (fSouth and

fNorth), and the false easting E0 and



and longitude of the point were southern latitude and western longitude are considered negative.


Penn State Surveying Program Transverse Mercator

Ellipsoid Parameters Origin

Name = GRS 80 Zone = NJ 2900

a = 6,378,137.0 m f0 = 38° 50' 00"

1/f = 298.257222101 l0 = -74° 30' 00"

e² = 0.006694380 k0 = 0.9999

e = 0.081819191 E0 = 150,000.0

e'² = 0.006739497 N0 = 0.0

DIRECT PROBLEM

Point information

f = 39° 00' 15.37930"

l = -74° 47' 59.39450"

Solution:

x = 124,030.7831 m

y = 19,017.4449 m

k = 0.9999083015

Convergence angle

g = -0.00329 rad -0.1887° 0° -11' -19.4"

INVERSE PROBLEM

Point information

x = 124,030.783 m

y = 19,017.445 m

Solution:

f = 0.680753 rad 39.00° 39° 00' 15.37930"

l = -1.305503 rad -74.80° -74° 47' 59.39450"

k = 0.9999083015

Convergence Angle

g = -0.003294 rad -0.1887° 0° -11' -19.4"

Transverse Mercator You can use this spreadsheet for any Transverse Mercator map projection

including the State Plane Coordinate System and Universal Transverse Mercator.

For the State Plane Coordinate System, o Obtain the appropriate values for the zone parameters from

the Defining SPCS Parameters worksheet. o Type in the ellipsoid name GRS 80 in cell B2 and the

ellipsoid parameters from the Ellipsoid Parameters

worksheet will be inserted.

For UTM

o Type in the ellipsoid name WGS84 in cell B2, and the ellipsoid parameters from the Ellipsoid Parameters worksheet will be inserted, or type in your regional values.

o Set the following zone parameters

l0 as appropriate for the zone. See the UTM Grid

worksheet for assistance.

f0 = 00’0”

E0 = 500,000 m N0 = 0 m for Northern Hemisphere or 500,000 m

for Southern k0 = 0.9996

Charles D. Ghilani

Penn State Surveying Program Transverse Mercator

Transverse Mercator You can use this spreadsheet for any Transverse Mercator map projection

including the State Plane Coordinate System and Universal Transverse Mercator.

For the State Plane Coordinate System, o Obtain the appropriate values for the zone parameters from

the Defining SPCS Parameters worksheet. o Type in the ellipsoid name GRS 80 in cell B2 and the

ellipsoid parameters from the Ellipsoid Parameters

worksheet will be inserted.

For UTM

o Type in the ellipsoid name WGS84 in cell B2, and the ellipsoid parameters from the Ellipsoid Parameters worksheet will be inserted, or type in your regional values.

o Set the following zone parameters

l0 as appropriate for the zone. See the UTM Grid

worksheet for assistance.

f0 = 00’0”

E0 = 500,000 m N0 = 0 m for Northern Hemisphere or 500,000 m

for Southern k0 = 0.9996

Charles D. Ghilani


Ellipsoid parameters Zone parameters

Name = GRS 80 Origin PA

a = 6,378,137.0 m fb = 39° 33'

1/f = 298.257222101 l0 = -77° 45'

e² = 0.006694380 Standard parallels

e = 0.081819191 fSouth = 40° 01'

fNorth = 41° 49'

E0 = 1,000,000.0 m

Nb = 300,000.0 m

Direct solution

Position (Enter south latitudes and western longitudes as negatives)

f = 39° 34' 00.00000"

l = -77° 45' 00.00000"

Solution: X = 1,000,000.000 m

Y = 301,850.725 m

k = 1.0001526096

Inverse solution

Position X = 1,000,000.000 m

Y = 301,850.725 m

Solution:

f = 0.690569 rad 39.566667° 39° 34' 00.00001" N

l = -1.356993 rad 77.750000° 77° 45' 00.00000" W

k = 1.00015261

Steps: This is a worksheet to compute

values for a single-zone map projection coordinate system in

Pennsylvania. It is only one of many suggested systems that could be designed.

Enter the appropriate ellipsoid name (GRS 80, WGS 84, or Clarke 1866)

in cell B2 and the parameters from the Ellipsoid sheet will be inserted. Note that U.S. State Plane

Coordinate System of 1983 uses GRS 80.



the standard parallels (f South and

f North), and the false easting E0 and



and longitude of the point were

southern latitude and western longitude are considered negative.



Steps: This is a worksheet to compute

values for a single-zone map projection coordinate system in

Pennsylvania. It is only one of many suggested systems that could be designed.

Enter the appropriate ellipsoid name (GRS 80, WGS 84, or Clarke 1866)

in cell B2 and the parameters from the Ellipsoid sheet will be inserted. Note that U.S. State Plane

Coordinate System of 1983 uses GRS 80.



the standard parallels (f South and

f North), and the false easting E0 and



and longitude of the point were

southern latitude and western longitude are considered negative.


Penn State Surveying Program 5/12/2014 Mercator Projection

Ellipsoid parameters Zone central meridian

Name = WGS 84 l0 = -180° 00'

a = 6,378,137.0 m

1/f = 298.257223563

Input values

f = 35° 10' 00.00000"

l = -75° 00' 00.00000"

Direct Equations:

x= 11,688,546.5333 m

y= 4,161,943.3640 m

k= 1.22191233

Inverse Equations:

x = 11,688,546.533 m t= 0.520725231

y = 4,161,943.364 m f0 = 0.610616 rad 34.985739°

Solution:

f = 0.613774 rad 35.166667° 35° 10' 00.00000" N

l = -1.308997 rad 75.000000° 74° 59' 60.00000" W

k= 1.22191233

Steps: Enter the ellipsoid name (GRS 80, WGS 84, Clarke 1866) in cell B2 and the

appropriate values from the Ellipsoid sheet will appear in the B3 and B4. Select the central meridian for the zone.

Direct equations : Enter the latitude and longitude of the point. Southern latitudes and western longitudes are negative.

Inverse Equations: Enter the x and y coordinates of the point.

Unhide rows and columns to see intermediate computations.

Penn State Surveying Program 5/12/2014 Secant Mercator

Ellipsoid parameters Zone central meridian

Name = GRS 80

a = 6,378,137.0 m l0 = -180° 00'

1/f = 298.257222101 Standard Parallels

e² = 0.00669438 fN = 41° 30'

e = 0.081819191 fS = -41° 30'

Direct Equations: Input values

x= 8,767,097.7098 m f = 35° 00' 00.00000"

y= 3,104,773.1520 m l = -75° 00' 00.00000"

k= 0.914643913

Inverse Equations:

x = 8,767,097.710 m t= 0.52257

y = 3,104,773.152 m f0 = 0.60771 34.81945°

Solution:

f = 0.610865 rad 34° 59' 60.00000" N

l = -1.308997 rad 75° 00' 00.00000" W

k= 0.914643913

Steps: Enter the Ellipsoid name (GRS 80, WGS 84, Clarke 1866) into cell B2 and the

parameters from the Ellipsoid sheet will be entered. Select the central meridian for the zone.

Select the northern standard parallel of the projection. Direct Equations:

Enter the latitude and longitude of the point. Southern latitudes and western

longitudes are considered negative. Inverse Equations:

Enter the grid coordinates of the point.

Penn State Surveying Program 5/12/2014 Oblique Transverse Mercator

Ellipsoid Parameters Origin

Name = GRS 80 Zone = AK 5001

a = 6,378,137.0 m Axis az = -36° 52' 11.631525"

1/f = 298.257222101 f0 = 57° 00' 00.000000"

e² = 0.00669438 lc = -133° 40' 00.000000"

e = 0.081819191 k0 = 0.9999

e'² = 0.006739497 E0 = 5,000,000.0

N0 = -5,000,000.0

DIRECT PROBLEM

Point information

f = 57° 50' 59.0000"

l = -133° 30' 00.0000"

Direct Solution:

x = 828,571.2516 m

y = 669,733.5360 m

k = 0.9999513051

Direct Problem - Convergence Angle

g = 0.002507 rad 0.14362247 0° 08' 37.0409"

INVERSE PROBLEM

Point information

x = 828,571.252 m

y = 669,733.536 m Unhide rows to see intermediate computations.

Inverse Solution:

f = 1.0096681 rad 57.849722° 57° 50' 59.00000"

l = -2.3300146 rad -133.500000° -133° 30' 00.00000"

k = 0.9999513051

Inverse Problem - Convergence Angle

g = 0.002507 rad 0.14362247 0° 08' 37.0409"

Penn State Surveying Program 5/12/2014 Oblique Transverse Mercator

Unhide rows to see intermediate computations.

This worksheet computes coordinates for the Oblique Mercator projection. Not

all conditions are handled by this spreadsheet. Feel free to modify it to your

satisfaction. Equations for this procedure can be found in Map Projection

Manual – A Working Manual by James P. Snyder. The axis az cell contains the

angle of the azimuth east of north for the central line as it passes through the

center of the map (f c, lc). For the SPCS Alaska Zone 5001 enter a value of the

arctan(-3/4) or -36°52’11.631525”. Due to the fact that the SPCS system uses this

form of the equations, the more common usage of providing the geodetic

coordinates of two points on the central line was not implemented. For form of

the equations can be seen in the Snyder text.

You can unhide rows and columns to see all the intermediate computations.

Penn State Surveying Program 5/12/2014 Albers Equal-Area Conic

Ellipsoid parameters Zone parameters

Name = GRS 80 Origin fb = 23° 00'

a = 6,378,137.0 m l0 = -96° 00'

1/f = 298.257222101 Standard parallels

e² = 0.006694380 fSouth = 29° 30'

e = 0.081819191 fNorth = 45° 30'

E0 = 0.0 m

Nb = 0.0 m

Direct solution

Position

f = 35° 00' 00.00000" 35.000000° 0.610865 rad

l = -75° 00' 00.00000" -75.000000° -1.308997 rad

Solution:

X = 1,885,428.3905 m

Y = 1,535,969.2858 m

k = 0.9915542073 h = 1.008517732

Inverse solution

Position

X = 1,885,428.391 m

Y = 1,535,969.286 m

Solution:

f = 0.610865 rad 35.0000° 35° 00' 00.00000" N

l = -1.308997 rad 75.0000° 75° 00' 00.00000" W

k = 0.991554207 h = 1.008517732

Enter the appropriate Ellipsoid name (GRS

80), WGS 84, Clarke 1886) in cell B2 and the appropriate ellipsoid parameters will appear in cells B3 and B4.

Enter the latitude and longitude of the grid origin.

Enter the zone information including the latitudes of the standard parallels, false

easting (Eb), and false northing (N0).

Direct solution: Enter the latitude and

longitude of the point where southern latitudes and western longitudes are negative.

Inverse solution: Enter the grid xy

coordinates of the point.

You can unhide rows and columns to see

intermediate computations.

Penn State Surveying Program 5/12/2014 Albers Equal-Area Conic

Enter the appropriate Ellipsoid name (GRS

80), WGS 84, Clarke 1886) in cell B2 and the appropriate ellipsoid parameters will appear in cells B3 and B4.

Enter the latitude and longitude of the grid origin.

Enter the zone information including the latitudes of the standard parallels, false

easting (Eb), and false northing (N0).

Direct solution: Enter the latitude and

longitude of the point where southern latitudes and western longitudes are negative.

Inverse solution: Enter the grid xy


You can unhide rows and columns to see

intermediate computations.

Penn State Surveying Program 5/12/2014 Observation Reduction

Ellipsoid parameters

Name = GRS 80

a = 6,378,137.0 m

1/f = 298.257222101

Distance Reduction

Endpoint coordinates

From To

Name Red Blue

x (m) 412,513.256 m 412,786.921 m

y (m) 67,869.759 m 71,783.356 m

k 0.999906680838 0.999905298308

Elevation 375.592 m 354.785 m

Geoid height -31.760 m -31.743 m

Horizontal distance 5,100.747 m m

f, of occuped station 39° 02' 21.63632"

Grid distance 5,100.000 m

Arc-to-Chord correction

Lambert Conformal Conic

Station 1 Station 2

f = 42° 42°

f' = 00' 01'

f" = 00.0000" 00.0000"

l = -77° -77°

l' = 45' 39'

l" = 00.00000" 12.00000"

d" -1.33"

Transverse Mercator

E0 = 600,000 m

Station 1 Station 2

E = 126,703.0681 129,253.0681

N = 22,902.2324 27,318.9620 m

d" 2.10"

Steps: Enter in an ellipsoid name (GRS

80, WGS 84, or Clarke 1866) in cell B2. The ellipsoidal

parameters will be determined from the ellipsoidal sheet.

Complete the cells below using

the “Lambert Conformal Conic” and “SPCS 83 using TM”

worksheets for assistance. Copy values from the other sheets

and use the “Paste Special – paste

values” feature in the Edit menu. Intermediate computed values

can be seen by “unhiding” the hidden rows and columns.

Penn State Surveying Program 5/12/2014 Observation Reduction

Steps: Enter in an ellipsoid name (GRS

80, WGS 84, or Clarke 1866) in cell B2. The ellipsoidal

parameters will be determined from the ellipsoidal sheet.

Complete the cells below using

the “Lambert Conformal Conic” and “SPCS 83 using TM”

worksheets for assistance. Copy values from the other sheets

and use the “Paste Special – paste

values” feature in the Edit menu. Intermediate computed values

can be seen by “unhiding” the hidden rows and columns.

Penn State Surveying Program 33 Transverse Mercator (James Stem)Ellipsoid parameters Zone central meridian Note: Western longitudes considered positive

Name = GRS 80 State NJ

a = 6378137 Zone 2900

1/f = 298.2572221009 CM 74 30 1.300270293 radians

e² = 0.00669438 k0 10,000 0.9999

e = 0.081819191 f0 38 50 0.677769526 radians

l0 74 30 1.300270293 radians

E0 150,000.0000

N0 0.0000

Ellipsoidal Defining Constants

n = 0.00167922 u2 = -0.002518828 v2 = 0.002518827

r = 6,367,449.1458 u4 = 2.64354E-06 v4 = 3.70095E-06

U0 = ############## u6 = -3.45263E-09 v6 = 7.44781E-09

U2 = 0.000021259204 u8 = 4.89183E-12 v8 = 1.7036E-11

U4 = ##############

U6 = 0.000000000626

V0 = 0.005022893948

V2 = 0.000029370625

V4 = 0.000000235059

V6 = 0.000000002181

w0 = 0.675309935

S0 = 4,299,571.6693

Direct Equations

Point ° ' " dd radians

f = 39 2 21.63632 39.03934 0.681365081 t = 0.8109216

l = 74 46 8.80133 74.76911 1.304967174 h² = 0.0040658

L = 0.003648132 A2 = 2,589,266.5278 A1 = -6,385,984.668 C1 = -0.810922

w = 0.67890165 A4 = 0.3649220604 A3 = 0.0577453252 C3 = 0.3374102

S = 4,322,439.4412 A6 = 0.0652984706 A5 = -0.0541867591 C5 = 0.0894937

R = 6,385,984.6680 A7 = -0.0350926415 F2 = 0.5020329

F4 = 0.1951707

SOLUTION:

x = 126,703.06805 m

y = 22,902.23235 m DD ° ' "

g = -0.002958362 -0.169501673 0 -10 -10.2060

k = 0.999906681

Inverse Equations

x = 126,703.06805 m -23,296.9320

y = 22,902.23235 m 22,902.2324

DD ° ' "

w = 0.678907062 38.9 38 53 54.6336

ff = 0.681370499 39 39 2 22.7539 foot point latitude

Rf = 6,385,984.782

Q = -0.003648135 tf = 0.810930605 D3 = -0.551169863

B2 = -0.407113841 hf² = 0.004065795 D5 = 0.439025922

B3 = -0.386547115 G2 = 0.502032898

B4 = -0.579396808 G4 = 0.085027415

B5 = 0.281979948 L = -0.003648116

B6 = 0.38611103

B7 = -0.252365944

SOLUTION: DD ° ' "

f = 0.681365081 39 39 2 21.63632

l = 1.304967174 74.8 74 46 8.80133

g = -0.002958362 -0.17 0 -10 -10.2060

k = 0.999906681

This sheet was developed to perform SPCS 83

computations for states using the Transverse

Mercator projection.

Steps:

Enter the appropriate ellipsoid parameters.

You can use the Ellipsoid sheet to cut and

paste these values.

Enter the zone parameter values. These

can be obtained on the SPCS Defining

Parameters sheet.

Direct Equations: Enter the latitude and

longitude of the point. Only positive

values should be entered. Western

longitudes are considered positive.

Inverse Equations: Enter the grid xy


Penn State Surveying Program 34 Transverse Mercator (James Stem)This sheet was developed to perform SPCS 83

computations for states using the Transverse

Mercator projection.

Steps:

Enter the appropriate ellipsoid parameters.

You can use the Ellipsoid sheet to cut and

paste these values.

Enter the zone parameter values. These

can be obtained on the SPCS Defining

Parameters sheet.

Direct Equations: Enter the latitude and

longitude of the point. Only positive

values should be entered. Western

longitudes are considered positive.

Inverse Equations: Enter the grid xy


survey map projections

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