Coordinate Systems

The core of geospatial data is geographic location information, and the most basic carrier of geographic location information is a spatial coordinate established in a specific coordinate system. A Spatial Reference System (SRS) or Coordinate Reference System (CRS) is a framework for accurately measuring positions on the Earth's surface as coordinates. It is the application of coordinate systems and the abstract mathematics of analytic geometry to geospatial space.

In GIS software, spatial coordinates are classified by coordinate system as geographic coordinates or projected coordinates. Geographic coordinates treat the Earth as an ellipsoid-like body and describe the position of a point on its surface. During map production, however, features usually need to be displayed on a plane, whether on paper maps or digital maps. This creates a conflict between the Earth's curved surface and the map plane. Projection is therefore required. Coordinates after projection are called projected coordinates, so projected coordinates are built on geographic coordinates.

The concept of a geographic coordinate system, or geodetic coordinate system, is relatively simple: it imagines the Earth as a huge, ellipsoid-like body and describes the exact position of a point on that surface. It is a spherical coordinate system that directly measures locations on the Earth, modeled as an ellipsoid, using latitude, the angle north or south of the equator, and longitude, the angle west or east of the prime meridian.

A projected coordinate system is a standardized Cartesian coordinate system that models the Earth, or more commonly a large region of the Earth, as a plane. Positions are measured from an arbitrary origin along the x and y axes, more or less aligned with cardinal directions. Each such system is based on a specific map projection that creates a plane from the curved Earth surface. These systems are usually defined and used strategically to minimize the distortions inherent in projection. Common examples include Universal Transverse Mercator (UTM).

Concepts

Ellipsoid

An Earth ellipsoid is a mathematical representation of the Earth's shape used in geodesy, astronomy, Earth science, and related fields. A reference ellipsoid is an Earth ellipsoid with defined geometric parameters.

A reference ellipsoid is a mathematical model that approximates the Earth's shape and defines the size and shape of the Earth in a datum. Common parameters include:

Chinese term	English term	Symbol	Meaning
Semi-major axis	Semi-major Axis	a	The Earth's equatorial radius, the maximum radius from the ellipsoid center to the equator, in meters
Flattening	Flattening	f	The degree of ellipsoid flattening, calculated as f = (a - b)/a, where b is the semi-minor axis
Semi-minor axis	Semi-minor Axis	b	The minimum radius from the ellipsoid center to a pole, in meters; obtained from b = a x (1 - f)
First eccentricity	First Eccentricity	e	The degree of deviation between the ellipsoid and a true sphere, calculated as e² = (a² - b²)/a²

Over nearly two centuries, scientists have calculated multiple groups of Earth ellipsoid parameters using geodetic and gravimetric observations. The following table lists commonly used examples; GRS 1980 is a commonly used ellipsoid parameter set in China.

Ellipsoid name	Semi-major axis (m)	Semi-minor axis (m)	Flattening, 1/f
Clarke 1866	6 378 206.4	6 356 583.8	294.978 698 2
Bessel 1841	6 377 397.155	6 356 078.965	299.152 843 4
International 1924	6 378 388	6 356 911.9	296.999 362 1
Krasovsky 1940	6 378 245	6 356 863	298.299 738 1
GRS 1980	6 378 137	6 356 752.3141	298.257 222 101
WGS 1984	6 378 137	6 356 752.3142	298.257 223 563
Sphere (6371 km)	6 371 000	6 371 000	∞

Datum

An ellipsoid only models the overall shape of the Earth. After selecting an ellipsoid, it must be anchored so that it can be used for real navigation. Every non-spherical ellipsoid has two poles, where the axis reaches the surface. These ellipsoid poles must be permanently related to actual points on the Earth. This is where a datum is used. Even if two reference systems use the same ellipsoid, they may still have different anchors, or datums, on the Earth.

Common ellipsoid and datum combinations:

Datum / coordinate reference frame	Common ellipsoid	Common coordinate system / EPSG example	Main region or use case
WGS 84	WGS 84	EPSG:4326	GPS, web maps, global positioning, and general GIS data exchange
CGCS2000	CGCS2000 ellipsoid, with parameters close to GRS80	EPSG:4490	Modern national geodetic coordinate system of China
Xian 1980	IAG 1975 / Xian 1980 ellipsoid	EPSG:4610	China 1980 coordinate system; common in historical surveying data
Beijing 1954	Krasovsky 1940	EPSG:4214	Early surveying in China, older topographic maps, and historical engineering data
NAD83	GRS80	EPSG:4269	Modern geodetic datum for North America, the United States, and Canada
NAD27	Clarke 1866	EPSG:4267	Historical North American data and older U.S. topographic maps
ETRS89	GRS80	EPSG:4258	Modern European geodetic reference frame
ITRF series	Usually GRS80	Depends on version	Global high-precision surveying, GNSS, and plate-motion research
ED50	International 1924 / Hayford	EPSG:4230	Historical European surveying data
OSGB36	Airy 1830	EPSG:4277	British National Grid and historical and official British mapping data
Tokyo Datum / Tokyo 1918	Bessel 1841	EPSG:4301	Older Japanese datum
JGD2000 / JGD2011	GRS80	EPSG:4612 / EPSG:6668	Modern Japanese geodetic coordinate systems
GDA94 / GDA2020	GRS80	EPSG:4283 / EPSG:7844	Modern Australian coordinate datums
Pulkovo 1942	Krasovsky 1940	EPSG:4284	Historical data from the former Soviet Union, Eastern Europe, and Russia
SAD69	GRS67	EPSG:4291	Historical surveying data in South America
SIRGAS 2000	GRS80	EPSG:4674	Modern South American geodetic reference frame
Indian 1975	Everest 1830 / Everest Modified	EPSG:4240, etc.	Historical data in India and parts of Southeast Asia
AGD66 / AGD84	Australian National Spheroid	EPSG:4202 / EPSG:4203	Older Australian coordinate datums

Common Combinations in China

Coordinate system / datum	Ellipsoid	Description
CGCS2000 National Geodetic Coordinate System	CGCS2000 ellipsoid	Modern coordinate datum currently recommended in China
Xian 1980 Coordinate System	IAG 1975 ellipsoid	Common historical surveying coordinate system in China
Beijing 1954 Coordinate System	Krasovsky 1940 ellipsoid	Common in old topographic maps and early engineering data
WGS 84	WGS 84 ellipsoid	Common for GPS, global data, and web maps

Projection

In cartography, a map projection is one of a broad set of transformation methods used to represent the curved surface of the Earth on a plane. In this process, positions on the Earth's surface, usually expressed as latitude and longitude, are transformed into a plane coordinate system. Map projection is a key step in producing two-dimensional maps and is a fundamental element of cartography.

Because a sphere cannot be projected perfectly onto a plane, all map projections inevitably distort the curved surface in some way. Depending on the map's intended use, some distortions may be acceptable while others are not. Therefore, many map projections exist; each preserves certain properties of the sphere while sacrificing others. The study of map projections focuses mainly on their distortion properties. In practice, the number of possible map projection types is unlimited.

More broadly, projection is also a concept in several areas of pure mathematics, including differential geometry, projective geometry, and manifolds. In cartography, however, the term "map projection" specifically refers to projections used for making maps.

One way to classify map projections is by the type of surface used for projection. In this classification, the projection process is considered as placing a hypothetical projection surface, comparable in size to the region of interest, onto part of the Earth so that features on the Earth's surface can be transferred to that projection surface, which is then unfolded and scaled into a flat map. The most common projection surfaces are cylindrical, such as Mercator, conic, such as Albers, and planar, such as stereographic. Many mathematical projections, however, do not strictly fit into any of these three categories. Other categories described in academic literature include pseudoconic, pseudocylindrical, pseudoazimuthal, retroazimuthal, and polyconic projections.

Another way to classify projections is by the geographic properties they preserve. Common categories include:

• Preserving direction, as in azimuthal or zenithal projections; this property is usually achieved only from one or two points, or between every point and a specific point.
• Locally preserving shape, as in conformal or orthomorphic projections.
• Preserving area, as in equal-area projections, which preserve relative areas across the map.
• Preserving distance, as in equidistant projections; this property is usually achieved only between one or two points, or between every point and a specific point.
• Preserving shortest routes, a property achieved only by perspective projections.

Because a sphere is not a developable surface, it is impossible to construct a map projection that is both equal-area and conformal everywhere.

Datum

A reference ellipsoid is a mathematical model that approximates the Earth's shape and defines the Earth's size and shape in a datum.

A datum includes:

• Ellipsoid parameters, such as semi-major axis, semi-minor axis, and flattening
• A reference origin, either geocentric or local
• Coordinate transformation relationships used when converting between datums

1. Ellipsoid parameters are described above.

2. The reference origin defines the datum's spatial position on the Earth. It determines how the ellipsoid is aligned within the Earth coordinate system. There are two main types:

• A. Geocentric datum

  • The origin is at the Earth's center of mass

  • Suitable for global positioning systems, such as WGS84 and CGCS2000

  • Advantage: compatible with global surveying systems and can connect precisely with satellite positioning

• B. Local datum

  • The origin is set at a ground survey control point in a specific region

  • The ellipsoid position has translations and rotations relative to the Earth's center of mass

  • Example: Beijing 1954 used in China, based on the Krasovsky ellipsoid

3. Coordinate transformation parameters

When coordinate data under one datum must be converted to another datum, inter-datum transformation is required. This is usually implemented with a seven-parameter coordinate transformation or a geocentric coordinate transformation model.

Seven-parameter model, or Helmert transformation:

Parameter name	English term	Meaning
ΔX, ΔY, ΔZ	Translation	Translation along the X, Y, and Z axes, in meters
Rx, Ry, Rz	Rotation	Rotation angles about the three coordinate axes, in seconds
S	Scale factor	Coordinate scale factor, in ppm, or parts per million

This transformation can convert a local datum coordinate to a global coordinate system such as WGS84, for example:

WGS84 coordinates = local coordinates x rotation matrix x scale factor + translation

Example:

China's CGCS2000 and WGS84 coordinate systems are theoretically equivalent and do not require transformation. However, when transforming between older coordinate systems such as Beijing 1954 and Xian 1980, a seven-parameter transformation or another refined model must be used.

Geographic Coordinate System (GCS)

A geographic coordinate system (GCS) defines positions on the Earth using the surface of a three-dimensional ellipsoid. This coordinate system is based on angular measurements from the Earth's center to points on the surface. In most cases, a geographic coordinate system uses degrees (°) as the measurement unit for latitude and longitude. A GCS mainly consists of three parts:

• Datum: an approximate model of the Earth's shape, usually represented by an ellipsoid model.
• Prime meridian: the starting reference line for longitude measurement.
• Angular unit: the unit used to express latitude and longitude, such as degrees.

In practice, common datums include WGS84, or World Geodetic System 1984, mainly used for GPS with SRID 4326; China CGCS2000, used for digital mapping in China with SRID 4490; and NAD83, or North American Datum 1983, mainly used for surveying and mapping in North America.

WGS84 coordinate system parameters, World Geodetic System 1984:

Parameter	English term	Value / description
Coordinate system type	Coordinate System Type	Geographic Coordinate System
Ellipsoid name	Ellipsoid Name	WGS84
Semi-major axis (a)	Semi-major Axis (a)	6,378,137.000 m
Flattening (f)	Flattening (f)	1 / 298.257223563
Flattening value, approx.	Flattening Value	0.003352810664747
Semi-minor axis (b)	Semi-minor Axis (b)	≈ 6,356,752.3142 m
First eccentricity squared (e²)	First Eccentricity² (e²)	≈ 0.00669437999014
Origin	Datum Origin	Earth's center of mass
Coordinate unit	Coordinate Unit	Degrees (°)
Common projection	Common Projection	UTM (Universal Transverse Mercator), Mercator
EPSG code	EPSG Code	EPSG:4326
Main usage	Main Usage	GPS, marine surveying, international aeronautical charts, etc.

CGCS2000 coordinate system parameters, China Geodetic Coordinate System 2000:

Parameter	English term	Value / description
Coordinate system type	Coordinate System Type	Geographic Coordinate System
Ellipsoid name	Ellipsoid Name	GRS80, with parameters very close to WGS84
Semi-major axis (a)	Semi-major Axis (a)	6,378,137.000 m
Flattening (f)	Flattening (f)	1 / 298.257222101
Flattening value, approx.	Flattening Value	0.003352810681182
Semi-minor axis (b)	Semi-minor Axis (b)	≈ 6,356,752.3141 m
First eccentricity squared (e²)	First Eccentricity² (e²)	≈ 0.00669438002290
Origin	Datum Origin	Earth's center of mass
Coordinate unit	Coordinate Unit	Degrees (°)
Common projection	Common Projection	Gauss-Krüger projection
EPSG code	EPSG Code	EPSG:4490
Main usage	Main Usage	National surveying datum of China, remote sensing, land resources, and navigation applications

NAD83 coordinate system parameters, North American Datum 1983:

Parameter	English term	Value / description
Coordinate system type	Coordinate System Type	Geographic Coordinate System
Ellipsoid name	Ellipsoid Name	GRS80, Geodetic Reference System 1980
Semi-major axis (a)	Semi-major Axis (a)	6,378,137.000 m
Flattening (f)	Flattening (f)	1 / 298.257222101
Flattening value, approx.	Flattening Value	0.003352810681182
Semi-minor axis (b)	Semi-minor Axis (b)	≈ 6,356,752.3141 m
First eccentricity squared (e²)	First Eccentricity² (e²)	≈ 0.00669438002290
Origin	Datum Origin	Earth's center of mass, adjusted to align with the North American plate
Coordinate unit	Coordinate Unit	Degrees (°)
Common projection	Common Projection	Lambert Conformal Conic, UTM, State Plane Coordinate System (SPCS)
EPSG code, main version	EPSG Code	EPSG:4269, original NAD83
Main usage	Main Usage	Surveying, engineering design, and government geospatial data standards in the United States, Canada, and Mexico

Projected Coordinate System (PCS)

A projected coordinate system (PCS) is usually described as a planar two-dimensional coordinate system, also called a Cartesian coordinate system or plane coordinate system. It projects three-dimensional geographic coordinates on the Earth's surface onto a two-dimensional plane for display in various graphical interfaces. Unlike geographic coordinate systems, projected coordinate systems can preserve constancy of length, angle, or area in two dimensions within their design constraints. They are usually based on a specific geographic coordinate system and datum.

There are many types of projected coordinate systems, each with particular desirable properties. Some projections are suitable for specific regions of the Earth and maintain high accuracy there; some focus on preserving object shape; others are better for accurate area or distance measurement. In these systems, positions are identified by x and y coordinates on a grid.

For example, many popular online map platforms, such as Tianditu, ArcGIS Online, Google Maps, and OpenStreetMap imagery, use a projected coordinate system called Web Mercator Auxiliary Sphere. Its WKID, or Well-Known ID, is 3857. It is widely used in web map services because it provides relatively balanced performance worldwide.

EPSG:3857 coordinate system parameters, Web Mercator Projection:

Parameter	English term	Value / description
Coordinate system type	Coordinate System Type	Projected Coordinate System
Projection name	Projection Name	Web Mercator / Pseudo-Mercator
EPSG code	EPSG Code	3857, formerly 900913
Datum / ellipsoid used	Datum / Ellipsoid	WGS84 ellipsoid, but not true geodetic curvature
Units	Units	Meters
Origin, central meridian	Central Meridian	0° meridian
Latitude bounds	Latitude Bounds	±85.05112878°, avoiding divergence near the poles
X coordinate range	X Extent	-20037508.34 m ~ +20037508.34 m
Y coordinate range	Y Extent	-20037508.34 m ~ +20037508.34 m
Projection formula	Projection Formula	Spherical Mercator Projection
Accuracy	Accuracy	Good in low and mid latitudes; large errors at high latitudes and polar regions
Common uses	Usage	Web map services, such as Google Maps, Leaflet, CesiumJS, etc.

Coordinate System Representation

In GIS, the same coordinate system can be represented in different forms. Common forms include PROJ.4, OGC WKT, OGC WKT2, ESRI WKT, JSON, and PostGIS.

For the WGS84 geographic coordinate system, the representations are:

PROJ.4

#+proj=longlat +datum=WGS84 +no_defs +type=crs

OGC WKT

GEOGCS["WGS 84",DATUM["WGS_1984",SPHEROID["WGS 84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],AUTHORITY["EPSG","6326"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4326"]]

JSON

{"$schema": "https://proj.org/schemas/v0.5/projjson.schema.json","type": "GeographicCRS","name": "WGS 84","datum_ensemble": {"name": "World Geodetic System 1984 ensemble","members": [{"name": "World Geodetic System 1984 (Transit)","id": {"authority": "EPSG","code": 1166}},{"name": "World Geodetic System 1984 (G730)","id": {"authority": "EPSG","code": 1152}},{"name": "World Geodetic System 1984 (G873)","id": {"authority": "EPSG","code": 1153}},{"name": "World Geodetic System 1984 (G1150)","id": {"authority": "EPSG","code": 1154}},{"name": "World Geodetic System 1984 (G1674)","id": {"authority": "EPSG","code": 1155}},{"name": "World Geodetic System 1984 (G1762)","id": {"authority": "EPSG","code": 1156}},{"name": "World Geodetic System 1984 (G2139)","id": {"authority": "EPSG","code": 1309}}],"ellipsoid": {"name": "WGS 84","semi_major_axis": 6378137,"inverse_flattening": 298.257223563},"accuracy": "2.0","id": {"authority": "EPSG","code": 6326}},"coordinate_system": {"subtype": "ellipsoidal","axis": [{"name": "Geodetic latitude","abbreviation": "Lat","direction": "north","unit": "degree"},{"name": "Geodetic longitude","abbreviation": "Lon","direction": "east","unit": "degree"}]},"scope": "Horizontal component of 3D system.","area": "World.","bbox": {"south_latitude": -90,"west_longitude": -180,"north_latitude": 90,"east_longitude": 180},"id": {"authority": "EPSG","code": 4326}}

PostGIS

INSERT into spatial_ref_sys (srid, auth_name, auth_srid, proj4text, srtext) values ( 4326, 'EPSG', 4326, '+proj=longlat +datum=WGS84 +no_defs +type=crs', 'GEOGCS["WGS 84",DATUM["WGS_1984",SPHEROID["WGS 84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],AUTHORITY["EPSG","6326"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4326"]]');

Coordinate Systems in iXGIS

iXGIS currently supports only part of the coordinate systems in the EPSG database. Custom coordinate systems are still under development.

Coordinate System Standardization

A Spatial Reference Identifier (SRID) is a unique value used to explicitly identify projected, unprojected, and local spatial coordinate system definitions. Almost all major spatial vendors have created their own SRID implementations or reference authoritative SRID implementations. Two major examples are EPSG and ESRI.

EPSG Coordinate Database

The EPSG Geodetic Parameter Dataset, also called the EPSG Registry, is a public registry of geodetic datums, spatial reference systems, Earth ellipsoids, coordinate transformations, and related units of measure. It was started in 1985 by members of the European Petroleum Survey Group (EPSG). Each entity is assigned an EPSG code between 1024 and 32767 and a standard machine-readable Well-Known Text (WKT) representation. The dataset is maintained by the IOGP Geomatics Committee.

EPSG codes make coordinate system conversion and matching easier and more accurate across software and datasets. EPSG coordinate systems cover many types, from geographic coordinate systems such as WGS 84, EPSG:4326, to projected coordinate systems such as UTM, where different zones have different EPSG codes.

EPSG coordinate systems are widely used not only in geographic information systems (GIS), but also in surveying, petroleum exploration, environmental monitoring, and many other fields. Standardization greatly improves the compatibility and exchangeability of geospatial data from different sources. By using EPSG codes, users can ensure that their coordinate systems have high accuracy and consistency, which is essential for precise spatial analysis and decision-making.

EPSG lookup website: https://epsg.io/

EPSG Code	Name	Ellipsoid	Datum	CS type	Projection	Origin	Axes	Unit
4326	GCS WGS 84	GRS 80	WGS 84	Spherical coordinates (lat, lon)	N/A	Central meridian	Equator / prime meridian	Radian
26717	UTM Zone 17N NAD 27	Clarke 1866	NAD 27	Plane coordinates (x, y)	Mercator: central meridian 81°W, scale 0.9996	500 km west (81°W, 0°N)	Equator, longitude 81°W	Meter
6576	SPCS Tennessee Zone NAD 83 (2011) ftUS	GRS 80	NAD 83 (2011 epoch)	Plane coordinates (x, y)	Lambert Conic: central 86°W, 34°20'N, standard parallels 35°15'N and 36°25'N	600 km west of central point	Grid east of central point, 86°W	US survey foot

ESRI Identifiers

ESRI also defines a set of SRID codes called WKIDs. They correspond to EPSG codes in this way: if an Esri WKID is lower than 32767, it corresponds to an EPSG ID. WKIDs of 32767 or higher are defined by Esri, and the object may not be in the EPSG Geodetic Parameter Dataset. If the object is later added to the EPSG dataset, Esri updates the WKID to match EPSG, but the previous value remains valid.

There are also additional limitations. Esri does not follow the axis directions used by EPSG; at least in ArcGIS Desktop, the order is always longitude-latitude or easting-northing (xy).

Common Coordinate Systems

China National Coordinate System (CGCS2000)

The 2000 National Geodetic Coordinate System, officially named China Geodetic Coordinate System 2000 and abbreviated as CGCS2000, is China's unified national geodetic coordinate system established according to the Surveying and Mapping Law of the People's Republic of China.

Its EPSG code is 4490.

Since the founding of the People's Republic of China, the Beijing 1954 coordinate system and the Xian 1980 coordinate system were established in the 1950s and 1980s respectively. Through topographic maps at various scales, these coordinate systems played important roles in the national economy, social development, and scientific research. Due to the technical limitations of that time, they relied mainly on traditional techniques. The Beijing 1954 coordinate system used the Krasovsky ellipsoid, but Chinese data was not used in its calculation and positioning, making the system less suitable for China and unable to meet the needs of high-precision positioning, Earth science, space science, and strategic weapon development. In the 1970s, after more than twenty years of work, Chinese surveyors completed the nationwide first- and second-order astronomic-geodetic network. After overall adjustment and adoption of reference ellipsoid parameters recommended by the 1975 International Geological Congress, China established the Xian 1980 coordinate system, which played an important role in economic construction, national defense construction, and scientific research.

As society advanced, demand for the national geodetic coordinate system continued to increase, especially in national economic development, national defense, social development, and scientific research. It became urgent to adopt a geocentric coordinate system with the Earth's center of mass as the origin for the national geodetic coordinate system. A geocentric coordinate system helps maintain and rapidly update the coordinate system using modern space technology, improves surveying efficiency, and accurately determines high-precision three-dimensional coordinates of geodetic control points.

The origin of the 2000 National Geodetic Coordinate System is at the center of mass of the entire Earth, including oceans and atmosphere. Its Z axis points from the origin to the Earth's reference pole at epoch 2000.0. This direction is calculated by the International Time Bureau from the initial direction at epoch 1984.0 and ensures that temporal evolution produces no residual global rotation of the crust. The X axis points from the origin to the intersection of the Greenwich reference meridian and the Earth's equatorial plane at epoch 2000.0. The Y axis forms a right-handed orthogonal coordinate system with the Z and X axes. The system is established on a scale in the sense of general relativity.

2000 National Geodetic Coordinate System

Basic information:

• Semi-major axis a = 6378137 m
• Flattening f = 1/298.257222101
• Geocentric gravitational constant GM = 3.986004418 x 10^14 m^3/s^2
• Angular velocity of rotation ω = 7.292115 x 10^-5 rad/s

PROJ.4 representation:

+proj=longlat +ellps=GRS80 +no_defs +type=crs

JavaScript (Proj4js) representation:

proj4.defs("EPSG:4490","+proj=longlat +ellps=GRS80 +no_defs +type=crs");

OGC WKT representation:

GEOGCS["China Geodetic Coordinate System 2000",
    DATUM["China_2000",
           SPHEROID["CGCS2000",6378137,298.257222101,
               AUTHORITY["EPSG","1024"]],
           AUTHORITY["EPSG","1043"]],
    PRIMEM["Greenwich",0,
        AUTHORITY["EPSG","8901"]],
    UNIT["degree",0.0174532925199433,
        AUTHORITY["EPSG","9122"]],
    AUTHORITY["EPSG","4490"]]

References:

2000 National Geodetic Coordinate System

What is the 2000 National Geodetic Coordinate System?

China National Projected Coordinate System CGCS2000

The China national projected coordinate system CGCS2000 / Gauss-Kruger projected coordinate system is obtained by projecting the CGCS2000 geographic coordinate system. It uses the Gauss-Krüger projection, also called the transverse conformal tangent elliptical cylindrical projection.

The Gauss-Krüger projection is a transverse conformal tangent elliptical cylindrical projection. Its principle is to place an elliptical cylinder tangent to the Earth ellipsoid along a meridian. In this projection, graticules extending 3° or 6° east and west from the central meridian are projected conformally onto the elliptical cylinder. The cylinder is then unfolded into a plane to obtain the map. The method was first designed in the 1820s by the German mathematician, astronomer, and physicist Carl Friedrich Gauss, and later supplemented and improved by the German geodesist Johann Heinrich Louis Krüger, hence the name Gauss-Krüger projection.

In the Gauss-Krüger projection, the central meridian and equator are perpendicular straight lines. Meridians are curves concave toward and symmetric about the central meridian, while parallels are curves convex toward and symmetric about the equator. Meridians and parallels intersect at right angles. This projection causes angular deformation in the sense of map distortion analysis. In the Gauss-Krüger projection, the length scale on the central meridian is 1, so there is no length deformation there. The length scale on other meridians is greater than 1, creating positive length deformation. Deformation increases with distance from the central meridian and reaches its maximum at the intersections of the edge meridians and the equator. Even in those areas, the maximum length and area deformations are only about +0.14% and 0.27%, respectively, for a 6° zone, so the overall deformation is very small.

To control projection distortion, the Gauss-Krüger projection uses 6° and 3° zone projection methods so that distortion stays within specified limits.

In China, 1:250,000 to 1:500,000 topographic maps use 6° zone projection, while 1:10,000 and larger-scale topographic maps use 3° zone projection. The 6° zoning method starts at the Greenwich zero meridian and divides the world eastward into 6° projection zones, for a total of 60 zones numbered 1 to 60. China lies between 72°E and 136°E and includes 11 projection zones, zones 13 to 23. The 3° zoning method starts at 1°30'E, with one zone every 3°, giving 120 zones worldwide.

In the Gauss-Krüger projection, the plane rectangular coordinate system is set as follows: the central meridian of each projection zone is the vertical coordinate axis, or X axis, and the equator is the horizontal coordinate axis, or Y axis. To avoid negative Y values, the X axis is shifted 500 km west, creating a new rectangular coordinate system. In this adjusted coordinate system, original Y coordinates are increased by 500 km. Since China is in the Northern Hemisphere, X axis values are positive.

The whole system consists of 60 or 120 projection zones, and each zone has the same plane rectangular coordinate system. To distinguish these coordinate systems, the corresponding projection zone number is added to the easting values at the north and south margins of topographic maps. For ease of use, maps draw lines parallel to the central meridian and the equator every 1 km, 2 km, or 10 km, forming the topographic map grid, or kilometer grid.

EPSG:4491 to EPSG:4512 are 6° zone projections for China. EPSG:4496 is one example of a 6° zone projection.

PROJCS["CGCS2000 / 3-degree Gauss-Kruger CM 108E",GEOGCS["China Geodetic Coordinate System 2000",DATUM["China_2000",SPHEROID["CGCS2000",6378137,298.257222101,AUTHORITY["EPSG","1024"]],AUTHORITY["EPSG","1043"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4490"]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",0],PARAMETER["central_meridian",108],PARAMETER["scale_factor",1],PARAMETER["false_easting",500000],PARAMETER["false_northing",0],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AUTHORITY["EPSG","4545"]]

# PROJ.4 representation for 4545
+proj=tmerc +lat_0=0 +lon_0=108 +k=1 +x_0=500000 +y_0=0 +ellps=GRS80 +units=m +no_defs +type=crs

EPSG:4513 to EPSG:4554 are 3° zone projections for China.

PROJCS["CGCS2000 / 3-degree Gauss-Kruger zone 40",GEOGCS["China Geodetic Coordinate System 2000",DATUM["China_2000",SPHEROID["CGCS2000",6378137,298.257222101,AUTHORITY["EPSG","1024"]],AUTHORITY["EPSG","1043"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4490"]],PROJECTION["Transverse_Mercator"],PARAMETER["latitude_of_origin",0],PARAMETER["central_meridian",120],PARAMETER["scale_factor",1],PARAMETER["false_easting",40500000],PARAMETER["false_northing",0],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AUTHORITY["EPSG","4528"]]

EPSG:4528 is one example of a 3° zone projection.

In some European and American countries, the Gauss-Krüger projection is also called the transverse conformal Mercator projection. It and the Universal Transverse Mercator projection (UTM) used for topographic maps in some countries both belong to the transverse conformal cylindrical projection family. The difference is that UTM is a transverse conformal secant cylindrical projection. Within a projection zone, it has two standard lines, parallel to the central meridian, where the length scale is 1, while the length scale on the central meridian is 0.9996. Therefore, distortion differences within the zone are smaller, and the maximum length deformation does not exceed 0.04%.

Zone Diagram

EPSG codes, central meridians, and longitude ranges for China are shown below:

Zone N	EPSG code	Central meridian (°E)	Longitude range (°E)
13	4491	75	72-78
14	4492	81	78-84
15	4493	87	84-90
16	4494	93	90-96
17	4495	99	96-102
18	4496	105	102-108
19	4497	111	108-114
20	4498	117	114-120
21	4499	123	120-126
22	4500	129	126-132
23	4501	135	132-138

Zone Conversion

If the central meridian of a Gauss-Krüger projection is known, the zone number for 3° zoning and 6° zoning can be calculated as follows:

3° zoning: zone number = local central meridian / 3

6° zoning: zone number = (local central meridian + 3) / 6

If the local 3° or 6° zone number is known, the local central meridian can be calculated as follows:

3° zoning: central meridian = zone number x 3

6° zoning: central meridian = zone number x 6 - 3

In China, 1:10,000 topographic maps use Gauss-Krüger 3° zone projected coordinates, while 1:25,000 to 1:500,000 topographic maps use 6° zones. Generally, on standard topographic maps in China, the first two digits of the X coordinate indicate the zone number, and the remaining digits indicate the X coordinate. The zone number is usually printed in a larger font than the coordinate digits.

China GCJ-02

For data security and confidentiality, WGS84 coordinates processed by a nonlinear topographic-map confidentiality algorithm, commonly called Mars encryption, are known as the State Bureau coordinate system or Mars coordinate system.

The offset between GCJ-02 and WGS84 is roughly 50 to 700 m.

Most domestic map basemaps and vector data in China, including not only coordinate data from LBS services but also Android phone positioning data, use GCJ-02. To align GCJ-02 basemaps and data with WGS84 basemaps and data, coordinate correction algorithms are usually used to unify the coordinate systems.

Various correction algorithms in JavaScript, Java, Python, and other languages can be found online. In data processing and WebGIS development, coordinate correction and data fusion are important steps.

Based on analysis of original data and offset data, the offset algorithm is likely to use parameters of the Krasovsky ellipsoid, convert offsets along the corresponding meridians and parallels of the original coordinate into radians, and add them to the original coordinate to form the shifted coordinate.

This algorithm is strong because it preserves the linear monotonicity of GCJ-02 relative to WGS84, and also preserves the linear monotonicity of GCJ-02 under pseudo-Mercator projection relative to WGS84 under pseudo-Mercator projection. It both maintains the real spatial relative positions after offsetting and allows the data to be corrected back without loss.

World WGS84

The World Geodetic System (WGS) is the standard used for cartography, geodesy, and satellite navigation, including GPS. The current version, WGS 84 (EPSG:4326), defines an Earth-centered, Earth-fixed coordinate system and geodetic datum, and also describes related Earth Gravitational Models (EGM) and World Magnetic Models (WMM). The standard is published and maintained by the National Geospatial-Intelligence Agency.

In the early 1980s, the geodetic community and the U.S. Department of Defense recognized the need for a new World Geodetic System. The older WGS 72 system could no longer meet current and expected future application requirements in data volume, information content, geographic coverage, or product accuracy. A new working group therefore improved data quality, expanded data coverage, increased data types, and improved technical capabilities. Doppler observations, satellite laser ranging, and very-long-baseline interferometry (VLBI) became important new information sources. Satellite radar altimetry also provided an excellent new data source. An advanced least-squares method called collocation allowed different types of Earth gravity field measurements, such as geoid, gravity anomaly, deflection, and dynamic Doppler measurements, to be integrated into a consistent solution.

This new World Geodetic System was named WGS 84 and is the reference system used by the Global Positioning System (GPS). WGS 84 is a geocentric system with global accuracy within 1 m. The International Terrestrial Reference System (ITRS), a geocentric reference system series maintained by the International Earth Rotation Service (IERS), is also geocentric in its geodetic realization. It is internally consistent at the centimeter level while remaining meter-level consistent with WGS 84.

The WGS 84 reference ellipsoid is based on the GRS 80 ellipsoid. Because it was independently derived and has a small difference in inverse flattening, the semi-minor axis differs by 0.105 mm. The table below compares the main ellipsoid parameters.

Ellipsoid reference	Semi-major axis a	Semi-minor axis b	Inverse flattening 1/f
GRS 80	6378137.0 m	≈ 6356752.314140 m	298.257222100882711...
WGS 84[5]	6378137.0 m	≈ 6356752.314245 m	298.2572236

The origin of the WGS 84 coordinate system is at the Earth's center of mass, with positional uncertainty considered to be less than 2 cm. In WGS 84, the zero-longitude meridian is defined as the IERS reference meridian, which is about 5.3 arcseconds, or 102 m (335 ft), east of the Greenwich meridian, roughly at the latitude of the Royal Observatory in the United Kingdom. This offset exists because the local gravity field at Greenwich does not point precisely toward the Earth's center of mass, but is deflected about 102 m west of it. Longitude positions in WGS 84 are consistent with longitude positions in the 1927 North American Datum (NAD27), which is located near 85°W in the east-central United States.

The WGS 84 reference ellipsoid is an oblate spheroid with equatorial radius a = 6378137 m and flattening f = 1/298.257223563. The Earth's gravitational constant, including the mass of the atmosphere, is defined precisely as GM = 3.986004418 x 10^14 m^3/s^2, and the Earth's angular velocity is defined as ω = 72.92115 x 10^-6 rad/s.

Based on these parameters, other important Earth parameters can be calculated, such as the polar semi-minor axis b = a x (1 - f) = 6356752.3142 m, and the square of the first eccentricity e^2 = 6.69437999014 x 10^-3.

World Web Mercator

Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator, WGS 84/Pseudo-Mercator, or WGS 84/Pseudo Mercator is a variant of the Mercator map projection derived from WGS84 with deformation. It is also the de facto standard for web mapping applications. It became prominent when Google Maps adopted it in 2005. Today, almost all major online map providers use it, including Tianditu, Amap, Baidu Maps, Google Maps, Bing Maps, OpenStreetMap, and Esri Maps. Its official EPSG identifier is EPSG:3857; historical identifiers include EPSG:900913, EPSG:3785, ESRI:102113, and ESRI:102100.

The Web Mercator projection is a slight variant of the standard Mercator projection and is mainly used for web basemaps. Although it uses the same formula as the standard Mercator projection for small-scale maps, Web Mercator uses spherical formulas at all scales, while traditional large-scale Mercator maps usually use ellipsoidal projection formulas. This difference is almost imperceptible at global scale, but in local areas it can cause the map to deviate slightly from a true ellipsoidal Mercator map at the same scale. Especially far from the equator, the ground deviation can reach 40 km.

Although the Web Mercator projection applies spherical Mercator formulas, geographic coordinates must be in the WGS 84 ellipsoid datum. This difference causes slight projection distortion. General misunderstanding of the difference between Web Mercator and standard Mercator has led to considerable confusion and misuse. For these reasons, the National Geospatial-Intelligence Agency under the U.S. Department of Defense has stated that this map projection is not suitable for any official use.

Unlike most spherical map projections, Web Mercator uses the equatorial radius of the WGS 84 ellipsoid rather than a compromise between equatorial and polar radii. Compared with most maps, this makes maps at standard scale appear slightly enlarged.

Sphere and ellipsoid mixed

This projection is neither strictly ellipsoidal nor strictly spherical. EPSG defines it as using a spherical development of ellipsoidal coordinates. The underlying geographic coordinates are defined using the WGS84 ellipsoid model of the Earth's surface, but the projection behaves as though it were defined on a sphere. This approach is uncontroversial for small-scale maps, such as world maps, but has little precedent for large-scale maps, such as city or provincial maps.

Advantages and disadvantages

Web Mercator is a spherical Mercator projection, so it has the same properties as spherical Mercator: north is everywhere up, meridians are equally spaced vertical lines, angles are locally correct assuming spherical coordinates, and areas expand with distance from the equator, so polar regions are greatly exaggerated. Ellipsoidal Mercator has the same properties but models the Earth as an ellipsoid.

However, unlike ellipsoidal Mercator, Web Mercator is not fully conformal. This means that angles between lines on the surface are not drawn as exactly the same angles on the map, although the difference is not visible to the naked eye. Lines deviate because Web Mercator specifies that coordinates should be provided as measured on the WGS 84 ellipsoid model. By projecting coordinates measured on the ellipsoid as if they were measured on a sphere, angular relationships change slightly. This is standard practice for standard spherical Mercator projection, but unlike Web Mercator, spherical Mercator is usually not used for local-area maps such as street maps, so the positional accuracy needed for drawing is typically lower than the angular deviation caused by spherical formulas. The advantage of Web Mercator is that spherical computation is simpler than ellipsoidal computation and requires only a fraction of the computing resources.

PROJCRS["WGS 84 / Pseudo-Mercator",
    BASEGEOGCRS["WGS 84",
        ENSEMBLE["World Geodetic System 1984 ensemble",
            MEMBER["World Geodetic System 1984 (Transit)", ID["EPSG",1166]],
            MEMBER["World Geodetic System 1984 (G730)",    ID["EPSG",1152]],
            MEMBER["World Geodetic System 1984 (G873)",    ID["EPSG",1153]],
            MEMBER["World Geodetic System 1984 (G1150)",   ID["EPSG",1154]],
            MEMBER["World Geodetic System 1984 (G1674)",   ID["EPSG",1155]],
            MEMBER["World Geodetic System 1984 (G1762)",   ID["EPSG",1156]],
            MEMBER["World Geodetic System 1984 (G2139)",   ID["EPSG",1309]],
            ELLIPSOID["WGS 84", 6378137, 298.257223563, LENGTHUNIT["metre", 1, ID["EPSG",9001]], ID["EPSG",7030]],
            ENSEMBLEACCURACY[2], ID["EPSG",6326]],
        ID["EPSG",4326]],
    CONVERSION["Popular Visualisation Pseudo-Mercator",
        METHOD["Popular Visualisation Pseudo Mercator", ID["EPSG",1024]],
        PARAMETER["Latitude of natural origin",  0, ANGLEUNIT["degree", 0.0174532925199433, ID["EPSG",9102]], ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin", 0, ANGLEUNIT["degree", 0.0174532925199433, ID["EPSG",9102]], ID["EPSG",8802]],
        PARAMETER["False easting",               0, LENGTHUNIT["metre", 1,                  ID["EPSG",9001]], ID["EPSG",8806]],
        PARAMETER["False northing",              0, LENGTHUNIT["metre", 1,                  ID["EPSG",9001]], ID["EPSG",8807]],
        ID["EPSG",3856]],
    CS[Cartesian, 2, ID["EPSG",4499]],
    AXIS["Easting (X)", east],
    AXIS["Northing (Y)", north],
    LENGTHUNIT["metre", 1, ID["EPSG",9001]],
    ID["EPSG",3857]]

Universal Transverse Mercator (UTM) Coordinate System

UTM (Universal Transverse Mercator) is a globally used plane rectangular coordinate system.

It uses the Transverse Mercator projection and divides the Earth's surface by longitude into 60 zones, with each zone forming an independent coordinate system to reduce deformation.

Note: UTM is only a projection plus zoning rule. In real use, an ellipsoid and datum must also be specified. The most common examples are WGS 84 / UTM, EPSG:326xx and EPSG:327xx.

Standard UTM covers only:

• 80°S to 84°N
• Polar regions, south of 80°S and north of 84°N, do not use UTM; they usually use Universal Polar Stereographic (UPS) projection.

Worldwide WGS 84 / UTM 6° zone table:

• Each zone spans 6° of longitude; zone number $N = 1\sim60$.
• Central meridian: $\lambda_0 = 6N - 183^\circ$, with west negative and east positive.
• Longitude range: $\lambda_0 - 3^\circ \sim \lambda_0 + 3^\circ$.
• EPSG rules:
  • Northern Hemisphere: EPSG:32601-32660 = WGS 84 / UTM zone 1N-60N epsg.io+2spatialreference.org+2
  • Southern Hemisphere: EPSG:32701-32760 = WGS 84 / UTM zone 1S-60S docs.up42.com

---

EPSG:32649 example:

Eastern Hemisphere UTM Zone Quick Reference

Zone	Central longitude	Longitude range	EPSG (Northern Hemisphere)	EPSG (Southern Hemisphere)
32	9°E	6°E-12°E	32632	32732
33	15°E	12°E-18°E	32633	32733
34	21°E	18°E-24°E	32634	32734
31	3°E	0°-6°E	32631	32731
35	27°E	24°E-30°E	32635	32735
36	33°E	30°E-36°E	32636	32736
37	39°E	36°E-42°E	32637	32737
38	45°E	42°E-48°E	32638	32738
39	51°E	48°E-54°E	32639	32739
40	57°E	54°E-60°E	32640	32740
41	63°E	60°E-66°E	32641	32741
42	69°E	66°E-72°E	32642	32742
43	75°E	72°E-78°E	32643	32743
44	81°E	78°E-84°E	32644	32744
45	87°E	84°E-90°E	32645	32745
46	93°E	90°E-96°E	32646	32746
47	99°E	96°E-102°E	32647	32747
48	105°E	102°E-108°E	32648	32748
49	111°E	108°E-114°E	32649	32749
50	117°E	114°E-120°E	32650	32750
51	123°E	120°E-126°E	32651	32751
52	129°E	126°E-132°E	32652	32752
53	135°E	132°E-138°E	32653	32753
54	141°E	138°E-144°E	32654	32754
55	147°E	144°E-150°E	32655	32755
56	153°E	150°E-156°E	32656	32756
57	159°E	156°E-162°E	32657	32757
58	165°E	162°E-168°E	32658	32758
59	171°E	168°E-174°E	32659	32759
60	177°E	174°E-180°E	32660	32760

Western Hemisphere UTM Zone Quick Reference

The worldwide 6° UTM zones and EPSG codes are listed below:

Zone	Central meridian	Longitude range	EPSG (Northern Hemisphere)	EPSG (Southern Hemisphere)
1	177°W	180°W-174°W	32601	32701
2	171°W	174°W-168°W	32602	32702
3	165°W	168°W-162°W	32603	32703
4	159°W	162°W-156°W	32604	32704
5	153°W	156°W-150°W	32605	32705
6	147°W	150°W-144°W	32606	32706
7	141°W	144°W-138°W	32607	32707
8	135°W	138°W-132°W	32608	32708
9	129°W	132°W-126°W	32609	32709
10	123°W	126°W-120°W	32610	32710
11	117°W	120°W-114°W	32611	32711
12	111°W	114°W-108°W	32612	32712
13	105°W	108°W-102°W	32613	32713
14	99°W	102°W-96°W	32614	32714
15	93°W	96°W-90°W	32615	32715
16	87°W	90°W-84°W	32616	32716
17	81°W	84°W-78°W	32617	32717
18	75°W	78°W-72°W	32618	32718
19	69°W	72°W-66°W	32619	32719
20	63°W	66°W-60°W	32620	32720
21	57°W	60°W-54°W	32621	32721
22	51°W	54°W-48°W	32622	32722
23	45°W	48°W-42°W	32623	32723
24	39°W	42°W-36°W	32624	32724
25	33°W	36°W-30°W	32625	32725
26	27°W	30°W-24°W	32626	32726
27	21°W	24°W-18°W	32627	32727
28	15°W	18°W-12°W	32628	32728
29	9°W	12°W-6°W	32629	32729
30	3°W	6°W-0°W	32630	32730

World Map-Only Coordinate Systems

The following are coordinate systems used only for cartographic display. They do not have strict coordinate-system projection rules.

+proj code	Name	Characteristics	Example
robin	Robinson	World basemap used by National Geographic in 1998; a compromise between shape and area	proj4('+proj=robin +lon_0=0', 'EPSG:4326', pt)
moll	Mollweide	Equal-area; flatter in shape than Robinson; often used for raster data	+proj=moll +lon_0=0
vandg	Van der Grinten	Circular boundary and polar compression; visually close to Winkel Tripel	+proj=vandg +lon_0=0
mill	Miller Cylindrical	Modified Mercator; avoids excessive polar stretching; visually similar to Robinson	+proj=mill +lon_0=0
sinu	Sinusoidal	Equal-area; used by NASA Blue Marble; low distortion near the equator	+proj=sinu +lon_0=0