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Projected coordinate system

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1062:. The area is divided into 100 km squares, each of which is denoted by a two-letter code. Within each 100 km square, a numerical grid reference is used. Since the Eastings and Northings are one kilometre apart, a combination of a Northing and an Easting will give a four-digit grid reference describing a one-kilometre square on the ground. The convention is the grid reference numbers call out the lower-left corner of the desired square. In the example map above, the town Little Plumpton lies in the square 6901, even though the writing which labels the town is in 6802 and 6902, most of the buildings (the orange boxed symbols) are in square 6901. 565: 1099:
Northing values. Each successive increase in precision (from 6 digit to 8 digit to 10 digit) pinpoints the location more precisely by a factor of 10. Since, in the UK at least, a 6-figure grid reference identifies a square of 100-metre sides, an 8-figure reference would identify a 10-metre square, and a 10-digit reference a 1-metre square. In order to give a standard 6-figure grid reference from a 10-figure GPS readout, the 4th, 5th, 9th and 10th digits must be omitted, so it is important not to read just the first 6 digits.
1083:, and thus our six-figure grid reference for the church becomes 696017. This reference describes a 100-metre by 100-metre square, and not a single point, but this precision is usually sufficient for navigation purposes. The symbols on the map are not precise in any case, for example the church in the example above would be approximately 100x200 metres if the symbol was to scale, so in fact, the middle of the black square represents the map position of the real church, independently of the actual size of the church. 1108: 64: 45: 1035:, the above coordinate is in grid 11U (representing UTM Zone 11 5xxxxxx mN), and grid cell NS within that (representing the second digit 5xxxxxmE x6xxxxxm N), and as many remaining digits as are needed are reported, yielding an MGRS grid reference of 11U NS 949 361 (or 11U NS 9493 3617 or 11U NS 94934 36174). 835:, e.g., at which the ellipsoid and flat map surfaces coincide, at which point the projection formulas generate a coordinate of (0,0). To ensure that the northing and easting coordinates on a map are not negative (thus making measurement, communication, and computation easier), map projections may set up a 1098:
receivers enables determination of accurate grid references without needing a map, but it is important to know how many digits the GPS displays to avoid reading off just the first six digits. A GPS unit commonly gives a ten-digit grid reference, based on two groups of five numbers for the Easting and
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After the War, UTM gradually gained users, especially in the scientific community. Because UTM zones do not align with political boundaries, several countries followed the United Kingdom in creating their own national or regional grid systems based on custom projections. The use and invention of such
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The grid lines on Ordnance Survey maps divide the UK into one-kilometre squares, east of an imaginary zero point in the Atlantic Ocean, west of Cornwall. The grid lines point to a Grid North, varying slightly from True North. This variation is zero on the central meridian (north-south line) of the
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values, that offset the true origin. For example, in UTM, the origin of each northern zone is a point on the equator 500km west of the central meridian of the zone (the edge of the zone itself is just under 400km to the west). This has the desirable effect of making all coordinates within the zone
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used in UTM, the parameters associated are the latitude and longitude of the natural origin, the false northing and false easting, and an overall scale factor. Given the parameters associated with particular location or grin, the projection formulas for the transverse Mercator are a complex mix of
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by controlling the measurement framework for latitude and longitude (GCS). Thus, there will be a significant difference between the coordinate of a location in "UTM NAD83 Zone 14N" and for the same location in "UTM NAD27 Zone 14N", even though the UTM formulas are identical, because the underlying
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The more digits added to a grid reference, the more precise the reference becomes. To locate a specific building in Little Plumpton, a further two digits are added to the four-digit reference to create a six-digit reference. The extra two digits describe a position within the 1-kilometre square.
774:, a map projection is used to convert geodetic coordinates to plane coordinates on a map; it projects the datum ellipsoidal coordinates and height onto a flat surface of a map. The datum, along with a map projection applied to a grid of reference locations, establishes a 731:), a coordinate system definition will specify the parameters to be used, such as a center point, standard parallels, scale factor, false origin, and such. With these parameters, the underlying formulas of the projection convert latitude and longitude directly into the ( 817:
Map projection formulas depend on the geometry of the projection as well as parameters dependent on the particular location at which the map is projected. The set of parameters can vary based on the type of project and the conventions chosen for the projection. For the
662:. GIS requires locations to be specified as precise coordinates and performs numerous calculations on them, making cartesian geometry preferable to spherical trigonometry when computing horsepower was at a premium. In recent years, the rise of global GIS datasets and 911:, and greatest at the map edges. The difference between grid north and true north is very small and can be ignored for most navigation purposes. The difference exists because the correspondence between a flat map and the round Earth is necessarily imperfect. 1004:
and other computer databases, they can be difficult for humans to remember and communicate. Thus, since the mid 20th century, there have been alternative encodings that shorten the numbers or convert the numbers into some form of alphanumeric string.
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For the church in Little Plumpton, this gives the digits 6 and 7 (6 on the left to right axis (Eastings) and 7 on the bottom to top axis (Northings). These are added to the four-figure grid reference after the two digits describing the same
1075:) a further 10x10 grid within the current grid square. Any of the 100 squares in the superimposed 10×10 grid can be accurately described using a digit from 0 to 9 (with 0 0 being the bottom left square and 9 9 being the top right square). 682:
is the most common mechanism for publishing such definitions in a machine-readable form, and forms the basis for many GIS and other location-aware software programs. A projected SRS specification consists of three parts:
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in many systems such as UTM. Any coordinate system definition must include a planar surface, an origin point, a set of orthogonal axes to define the direction of each measurement, and a unit of measure (usually the
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to bind the coordinate system to real locations on the earth, an origin point, and a choice of unit of measure. Hundreds of projected coordinate systems have been specified for various purposes in various regions.
666:, along with an abundance of processing speed in personal computers, have led to a resurgence in the use of GCS. That said, projected coordinate systems are still very common in the GIS data stored in the 678:
Because the purpose of any coordinate system is to accurately and unambiguously measure, communicate, and perform calculations on locations, it must be defined precisely. The
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latitude and longitude values are different. In some GIS software, this part of the definition is called the choice of a particular geographic coordinate system.
1119: 634:, modern warfare practices required soldiers to quickly and accurately measure and report their location, leading to the printing of grids on maps by the U.S. 1020:
provide a precision that is not needed in most circumstances, they may be unnecessary for some uses. This permits users to shorten the example coordinates to
603:(SPCS), which was developed in the United States during the 1930s for surveying and engineering, because calculations such as distance are much simpler in a 1031:
Alphanumeric encodings typically use codes to replace the most significant digits by partitioning the world up into large grid squares. For example, in the
1616: 245: 993:, meaning that is almost 600km east of the false origin for Zone 11 (95km east of the true central meridian at 117°W) and 5.6 million meters north of the 723:
that creates a planar surface for the coordinate system that is connected to locations on the Earth. In addition to the general type of projection (e.g.,
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of the 18th century. However, their use as the basis for specifying precise locations, rather than latitude and longitude, is a 20th century innovation.
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was mapped in a custom projection with its own grid and coding system, but this resulted in confusion. This led to the development of the
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Buchroithner, Manfred; Pfahlbusch, René (2017). "Geodetic grids in authoritative maps – new findings about the origin of the UTM Grid".
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but is not generally used for land navigating for walkers or cyclists, etc. The growing availability and decreasing cost of handheld
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Locations in a projected coordinate system, like any cartesian coordinate system, are measured and reported as easting/northing or (
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Grid references comprising larger numbers for greater precision could be determined using large-scale maps and an accurate
1978: 1898: 1728: 1171: 1161: 1143: 1125: 1047: 1001: 803: 795: 791: 612: 600: 553: 521: 517: 505: 253: 585: 1892: 1887: 1881: 1224: 942:) pairs. The pair is usually represented conventionally with easting first, northing second. For example, the peak of 688: 667: 604: 489: 922:. Since the meridians converge at the poles, true east and west directions change rapidly in a condition similar to 1765: 1639: 1602: 549: 1012:
may be used where the general location is already known to participants and may be assumed. Because the (leading)
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positive values, being east and north of the origin. Because of this, they are often referred to as the
532:; the term is still common in some domains such as the military that encode coordinates as alphanumeric 525: 444: 361: 111: 564: 654:(MGRS) was then created as an encoding scheme for UTM coordinates to make them easier to communicate. 2028: 1786: 1243: 663: 351: 321: 261: 211: 137: 2033: 1983: 1943: 1576: 1199: 1189: 807: 728: 508:
WGS 84 Zone 26N," is defined by a choice of map projection (with specific parameters), a choice of
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When the first standardized coordinate systems were created during the 20th century, such as the
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maps, each Easting and Northing grid line is given a two-digit code, based on the
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has recently become predominant to clearly differentiate it from other types of
83: 1860: 1804: 1733: 1151: 1038: 915: 903:, indicate the difference between grid north, true north, and magnetic north. 884: 880: 872: 569: 1562: 964: 951: 1965: 1850: 1794: 1348:"OGC Abstract Specification Topic 2: Referencing by coordinates Corrigendum" 1091: 1050:(United Kingdom) and other national grid systems use similar approaches. In 679: 647: 545: 162: 88: 1954: 1775: 1254: 341: 158: 147: 782:
projections are generally preferred. Common map projections include the
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systems especially proliferated during the 1980s with the emergence of
221: 78: 55: 1174:(SPCS): another composite system of more than 120 coordinate systems ( 1686: 1164:(OSNG): a transverse mercator projection centered on 2°W that covers 1147: 986: 875:
term referring to the direction northwards along the grid lines of a
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zones on an equirectangular world map with irregular zones in red
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While such precise numbers are easy to store and calculate in
30:"Easting and northing" redirects here. Not to be confused with 1375:"Using the EPSG geodetic parameter dataset, Guidance Note 7-1" 1095: 771: 750:. This binds the coordinate system to actual locations on the 691:
that allows for the measurement of each location as a tuple (
1565:. Bivouac.com – Canadian Mountain Encyclopedia. 2006-11-17. 544:. The term is used in international standards such as the 1128:(UTM): not a single coordinate system, but a series of 60 615:
was released in 1938, based on earlier experiments during
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with an origin point just off the southwest coast of the
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To establish the position of a geographic location on a
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than the three-dimensional trigonometry of GCS. In the
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McGraw-Hill. p. 34. 907:map, which is at two degrees West of the 1479: 1477: 1475: 1342: 1340: 1106: 563: 37:For broader coverage of this topic, see 1311: 1219:Hellenic Geodetic Reference System 1987 823:algebraic and trigonometric functions. 54: 1369: 1367: 1056:British national grid reference system 27:Cartesian geographic coordinate system 1522:. John Wiley & Sons. p. 35. 1519:A Guide to Understanding Land Surveys 1136:6° wide), each a system with its own 548:and ISO 19111 (also published by the 470:projected coordinate reference system 7: 1188:(LV95): covers Switzerland, using a 277: 424:Universal Transverse Mercator (UTM) 386:European Terrestrial Ref. Sys. 1989 1071:Imagine (or draw or superimpose a 926:. Grid north solves this problem. 296:Ordnance Survey Great Britain 1936 262:Discrete Global Grid and Geocoding 153:Horizontal position representation 48:Layout of a UTM coordinate system. 25: 1433:. McGraw-Hill. pp. 225–229. 468: – also called a 212:Global Nav. Sat. Systems (GNSSs) 62: 1379:EPSG Geodetic Parameter Dataset 897:United States Geological Survey 680:EPSG Geodetic Parameter Dataset 480: – is a type of 376:N. American Vertical Datum 1988 1831:Military Grid Reference System 1815:International Map of the World 1516:Estopinal, Stephen V. (2009). 1198:(ITM): jointly created by the 1138:Transverse Mercator projection 1033:Military Grid Reference System 820:transverse Mercator projection 660:geographic information systems 652:Military Grid Reference System 406:Internet link to a point 2010 336:Geodetic Reference System 1980 254:Quasi-Zenith Sat. Sys. (QZSS) 1: 2039:Geographic coordinate systems 1899:Ordnance Survey National Grid 1577:"Grids and Reference Systems" 1458:10.1080/15230406.2015.1128851 1172:State Plane Coordinate System 1168:with its own encoding scheme. 1162:Ordnance Survey National Grid 1144:Universal Polar Stereographic 1126:Universal Transverse Mercator 1048:Ordnance Survey National Grid 1042:A typical map with grid lines 796:State Plane Coordinate System 788:Universal Transverse Mercator 746:, which includes a choice of 699:), which are also called the 601:State Plane Coordinate System 554:geographic information system 522:State Plane Coordinate System 518:Universal Transverse Mercator 506:Universal Transverse Mercator 484:that represents locations on 396:Chinese obfuscated datum 2002 1884:(north-east Atlantic region) 1286:as mathematical abstraction) 739:) coordinates of the system. 687:An abstract two-dimensional 668:Spatial Data Infrastructures 611:, the first version of the 586:Geographic coordinate system 528:, they were commonly called 346:Geographic point coord. 1983 1979:ITU-T country calling codes 1893:National Topographic System 1888:Irish grid reference system 1882:ICES Statistical Rectangles 1563:"Truncated Grid References" 1225:Israeli Transverse Mercator 831:Every map projection has a 689:Cartesian coordinate system 605:Cartesian coordinate system 599:Among the earliest was the 592:, proliferating during the 538:projected coordinate system 466:projected coordinate system 306:Systema Koordinat 1942 goda 2060: 1984:ITU-T mobile calling codes 1352:Open Geospatial Consortium 1319:Chang, Kang-tsung (2016). 1117: 763: 550:Open Geospatial Consortium 366:World Geodetic System 1984 36: 29: 2002:Maidenhead Locator System 1950:United Kingdom post codes 1196:Irish Transverse Mercator 1103:Examples of projected CRS 895:, including those of the 879:. It is contrasted with 778:for plotting locations. 356:North American Datum 1983 326:South American Datum 1969 1295:Spatial reference system 1156:Stereographic projection 1090:. This might be used in 1018:least significant digits 1010:truncated grid reference 930:Grid reference encodings 839:, specified in terms of 542:spatial reference system 482:spatial reference system 474:planar coordinate system 217:Global Pos. System (GPS) 184:Spatial reference system 39:Spatial reference system 1543:"Moving the South Pole" 1270:Graticule (cartography) 1206:to cover the island of 1186:Swiss coordinate system 1014:most significant digits 989:) in UTM Zone 11 is at 812:Swiss coordinate system 800:Lambert Conformal Conic 725:Lambert Conformal Conic 1939:New Zealand post codes 1115: 1043: 991:(0594934mE, 5636174mN) 965:50.86944°N 115.65083°W 883:(the direction of the 577: 49: 1935:(Republic of Ireland) 1922:Australian post codes 1429:Raisz, Erwin (1948). 1265:Geographical distance 1214:Bermuda National Grid 1118:Further information: 1110: 1041: 792:British National Grid 764:Further information: 613:British National Grid 572:region, showing the 567: 526:British National Grid 490:Cartesian coordinates 478:grid reference system 112:Geographical distance 47: 1633:Administrative codes 1381:. Geomatic Solutions 1244:Discrete global grid 970:50.86944; -115.65083 899:and Great Britain's 802:(some states in the 674:System specification 664:satellite navigation 536:. However, the term 286:Sea Level Datum 1929 138:Geodetic coordinates 1974:ITU-R country codes 1944:Postal Index Number 1431:General Cartography 1200:Republic of Ireland 1190:Mercator projection 1178:), each covering a 961: /  784:transverse mercator 729:Transverse Mercator 316:European Datum 1950 274:Standards (history) 174:Reference ellipsoid 122:Figure of the Earth 2006:Historical : 1841:Open Location Code 1676:MARC country codes 1548:2011-07-16 at the 1116: 1044: 798:for some states), 590:Hellenistic period 578: 194:Vertical positions 50: 2016: 2015: 1908: 1907: 1836:Natural Area Code 1766:FIFA country code 1756:Aircraft prefixes 1729:IANA country code 1711:ICAO airport code 1706:IATA airport code 1640:FIPS country code 1529:978-0-470-23058-9 1330:978-1-259-92964-9 944:Mount Assiniboine 594:Enlightenment Era 462: 461: 410: 409: 189:Spatial relations 179:Satellite geodesy 134: 16:(Redirected from 2051: 1783: 1761:IOC country code 1672:(United Kingdom) 1652:FIPS county code 1619: 1612: 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1256: 1253: 1251: 1250:East north up 1248: 1245: 1242: 1241: 1237: 1232: 1229: 1226: 1223: 1220: 1217: 1215: 1212: 1209: 1205: 1201: 1197: 1194: 1191: 1187: 1184: 1181: 1177: 1173: 1170: 1167: 1166:Great Britain 1163: 1160: 1157: 1153: 1149: 1145: 1142: 1139: 1135: 1131: 1127: 1124: 1123: 1121: 1113: 1109: 1102: 1100: 1097: 1093: 1089: 1084: 1082: 1076: 1074: 1065: 1063: 1061: 1057: 1053: 1049: 1040: 1036: 1034: 1029: 1019: 1015: 1011: 1006: 1003: 998: 996: 988: 984: 980: 974: 945: 941: 937: 929: 927: 925: 921: 917: 912: 910: 904: 902: 898: 894: 890: 886: 882: 878: 874: 870: 866: 859: 857: 855: 851: 846: 845:false easting 842: 838: 834: 826: 824: 821: 815: 813: 809: 805: 801: 797: 793: 789: 785: 781: 777: 773: 767: 759: 753: 749: 745: 741: 738: 734: 730: 726: 722: 718: 715: 711: 706: 702: 698: 694: 690: 686: 685: 684: 681: 673: 671: 669: 665: 661: 655: 653: 649: 645: 641: 637: 633: 628: 626: 622: 618: 614: 610: 606: 602: 597: 595: 591: 587: 583: 576:grid in blue. 575: 571: 566: 559: 557: 555: 551: 547: 543: 539: 535: 531: 527: 523: 519: 514: 511: 507: 503: 499: 495: 491: 487: 483: 479: 475: 471: 467: 455: 450: 448: 443: 441: 436: 435: 433: 432: 425: 422: 420: 417: 415: 412: 411: 405: 403: 400: 399: 395: 393: 390: 389: 385: 383: 380: 379: 375: 373: 370: 369: 365: 363: 360: 359: 355: 353: 350: 349: 345: 343: 340: 339: 335: 333: 330: 329: 325: 323: 320: 319: 315: 313: 310: 309: 305: 303: 300: 299: 295: 293: 290: 289: 285: 283: 280: 279: 271: 270: 263: 260: 258: 252: 250: 244: 242: 236: 234: 230:BeiDou (BDS) 228: 226: 220: 218: 215: 213: 210: 209: 203: 202: 195: 192: 190: 187: 185: 182: 180: 177: 175: 172: 170: 167: 164: 160: 156: 154: 151: 149: 146: 144: 141: 139: 136: 132: 131:circumference 128: 123: 120: 118: 115: 113: 110: 109: 103: 102: 95: 92: 90: 87: 85: 82: 80: 77: 76: 70: 69: 65: 61: 60: 57: 53: 46: 40: 33: 32:East north up 19: 1914:Postal codes 1581:. Retrieved 1571: 1557: 1552:, NASA Quest 1538: 1518: 1511: 1499:. Retrieved 1492:the original 1449: 1445: 1439: 1430: 1409:. Retrieved 1405: 1395: 1383:. Retrieved 1378: 1355:. Retrieved 1351: 1320: 1314: 1300:Spatial grid 1283: 1231:Swedish grid 1175: 1129: 1085: 1077: 1069: 1045: 1030: 1009: 1007: 999: 939: 935: 933: 913: 905: 873:navigational 868: 864: 863: 853: 849: 844: 840: 837:false origin 836: 832: 830: 816: 775: 769: 742:A choice of 736: 732: 719:A choice of 704: 700: 696: 692: 677: 656: 632:World War II 629: 598: 579: 537: 533: 530:grid systems 529: 515: 497: 493: 477: 473: 469: 465: 463: 206:Technologies 161: / 73:Fundamentals 2029:Cartography 2008:QRA locator 1866:WMO squares 1779:place codes 1642:(FIPS 10-4) 1411:21 December 1385:15 December 968: / 956:115°39′03″W 924:gimbal lock 776:grid system 760:Projections 617:World War I 84:Geodynamics 2034:Navigation 2023:Categories 1861:what3words 1805:Geohash-36 1734:ISO 3166-1 1660:(FIPS 5-2) 1654:(FIPS 6-4) 1357:2018-12-25 1306:References 1152:Antarctica 985:border in 953:50°52′10″N 916:South Pole 885:North Pole 881:true north 865:Grid north 860:Grid north 570:Aksai Chin 556:software. 1966:Telephony 1851:UN/LOCODE 1795:C-squares 1681:SGC codes 1670:GSS codes 1648:(FIPS 55) 1466:131732222 1092:surveying 1066:Precision 786:(used in 780:Conformal 648:Wehrmacht 163:Longitude 89:Geomatics 2044:Geocodes 1955:ZIP Code 1933:Eircodes 1929:(Brazil) 1895:(Canada) 1875:Regional 1776:Geodesic 1683:(Canada) 1546:Archived 1255:Geocodes 1238:See also 1221:(Greece) 1154:using a 854:northing 808:Mercator 806:), and 705:northing 623:and the 619:by the 584:and the 342:ISO 6709 240:(Europe) 238:Galileo 224:(Russia) 222:GLONASS 159:Latitude 148:Geodesic 106:Concepts 18:Northing 1946:(India) 1821:Mapcode 1800:Geohash 1749:numeric 1744:alpha-3 1739:alpha-2 1687:UN M.49 1583:4 March 1501:5 March 1208:Ireland 1022:949-361 995:equator 983:Alberta 977:on the 914:At the 871:) is a 850:easting 714:US foot 701:easting 630:During 560:History 402:Geo URI 372:NAVD 88 282:NGVD 29 256:(Japan) 248:(India) 232:(China) 94:History 79:Geodesy 56:Geodesy 1810:GEOREF 1787:Global 1526:  1464:  1327:  1233:(RT90) 1148:Arctic 987:Canada 887:) and 794:, the 790:, the 524:, and 488:using 392:GCJ-02 382:ETRS89 362:WGS 84 352:NAD 83 332:GRS 80 292:OSGB36 246:NAVIC 127:radius 1495:(PDF) 1488:(PDF) 1462:S2CID 1246:(DGG) 1227:(NIG) 1180:state 1176:zones 1130:zones 1088:Romer 1073:Romer 752:Earth 710:meter 486:Earth 476:, or 322:SAD69 302:SK-42 117:Geoid 1901:(UK) 1846:QDGC 1689:(UN) 1666:(EU) 1664:NUTS 1585:2014 1524:ISBN 1503:2014 1413:2021 1387:2021 1325:ISBN 1284:grid 1202:and 1150:and 1134:gore 1046:The 946:(at 856:. 852:and 843:and 804:SPCS 712:or 703:and 621:Army 580:The 574:MGRS 546:EPSG 312:ED50 129:and 1927:CEP 1856:UTM 1454:doi 1112:UTM 1096:GPS 1002:GIS 997:. 814:). 772:map 2025:: 1474:^ 1460:. 1450:44 1448:. 1421:^ 1404:. 1377:. 1366:^ 1350:. 1339:^ 938:, 869:GN 735:, 727:, 716:). 695:, 627:. 520:, 496:, 472:, 464:A 1618:e 1611:t 1604:v 1587:. 1532:. 1505:. 1468:. 1456:: 1415:. 1389:. 1360:. 1333:. 1282:( 1210:. 1192:. 1158:. 1140:. 981:/ 940:y 936:x 867:( 810:( 737:y 733:x 697:y 693:x 498:y 494:x 492:( 453:e 446:t 439:v 133:) 125:( 41:. 34:. 20:)

Index

Northing
East north up
Spatial reference system

Geodesy

Geodesy
Geodynamics
Geomatics
History
Geographical distance
Geoid
Figure of the Earth
radius
circumference
Geodetic coordinates
Geodetic datum
Geodesic
Horizontal position representation
Latitude
Longitude
Map projection
Reference ellipsoid
Satellite geodesy
Spatial reference system
Spatial relations
Vertical positions
Global Nav. Sat. Systems (GNSSs)
Global Pos. System (GPS)
GLONASS (Russia)

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