The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a
cartesian spatial reference system
A spatial reference system (SRS) or coordinate reference system (CRS) is a framework used to precisely measure locations on the surface of the Earth as coordinates. It is thus the application of the abstract mathematics of coordinate systems and ...
that represents locations in the vicinity of the Earth (including its
surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is t ...
, interior,
atmosphere
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. ...
, and surrounding outer space) as ''X'', ''Y'', and ''Z'' measurements from its
center of mass. Its most common use is in tracking the orbits of
satellite
A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioiso ...
s and in
satellite navigation
A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows satellite navigation devices to determine their location ( longitude, latitude, and altitude/ elevation) to hi ...
systems for measuring locations on the surface of the Earth, but it is also used in applications such as tracking crustal motion.
The distance from a given point of interest to the center of Earth is called the geocentric distance, , which is a generalization of the ''
geocentric radius'', , not restricted to points on the
reference ellipsoid
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximatio ...
surface.
The geocentric altitude is a type of
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
defined as the difference between the two aforementioned quantities: ;
it is not to be confused for the ''
geodetic altitude''.
Conversions between ECEF and geodetic coordinates (latitude and longitude) are discussed at
geographic coordinate conversion
In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion is composed of a number of different types of convers ...
.
Structure
As with any
spatial reference system
A spatial reference system (SRS) or coordinate reference system (CRS) is a framework used to precisely measure locations on the surface of the Earth as coordinates. It is thus the application of the abstract mathematics of coordinate systems and ...
, ECEF consists of an abstract
coordinate system (in this case, a conventional three-dimensional right-handed system), and a
geodetic datum
A geodetic datum or geodetic system (also: geodetic reference datum, geodetic reference system, or geodetic reference frame) is a global datum reference or reference frame for precisely representing the position of locations on Earth or other p ...
that binds the coordinate system to actual locations on the Earth.
The ECEF that is used for the
Global Positioning System (GPS) is the geocentric WGS 84, which currently includes its own ellipsoid definition.
Other local datums such as
NAD 83 may also be used. Due to differences between datums, the ECEF coordinates for a location will be different for different datums, although the differences between most modern datums is relatively small, within a few meters.

The ECEF coordinate system has the following parameters:
* The ''origin'' at the center of the chosen ellipsoid. In WGS 84, this is
center of mass of the Earth.
* The ''Z axis'' is the line between the North and South Poles, with positive values increasing northward. In WGS 84, this is the
international reference pole
International is an adjective (also used as a noun) meaning "between nations".
International may also refer to:
Music Albums
* ''International'' (Kevin Michael album), 2011
* ''International'' (New Order album), 2002
* ''International'' (The T ...
(IRP), which does not exactly coincide with the Earth's rotational axis
The slight "wobbling" of the rotational axis is known as
polar motion
Polar motion of the Earth is the motion of the Earth's rotational axis relative to its crust. This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called ''Earth-centered, Earth-fixed'' or ECEF reference ...
, and can actually be measured against an ECEF.
* The ''X axis'' is in the plane of the
equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can al ...
, passing through the origin and extending from 180° longitude (negative) to the
prime meridian
A prime meridian is an arbitrary meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its anti-meridian (the 180th meridian in a 360°-system) form a great ...
(positive); in WGS 84, this is the
IERS Reference Meridian
The IERS Reference Meridian (IRM), also called the International Reference Meridian, is the prime meridian (0° longitude) maintained by the International Earth Rotation and Reference Systems Service (IERS). It passes about 5.3 arcseconds east o ...
.
* The ''Y axis'' is also in the plane of the equator, passing through extending from 90°W longitude (negative) to 90°E longitude (positive)
An example is th
NGS datafor a brass disk near Donner Summit, in California. Given the dimensions of the ellipsoid, the conversion from lat/lon/height-above-ellipsoid coordinates to X-Y-Z is straightforward—calculate the X-Y-Z for the given lat-lon on the surface of the ellipsoid and add the X-Y-Z vector that is perpendicular to the ellipsoid there and has length equal to the point's height above the ellipsoid. The reverse conversion is harder: given X-Y-Z we can immediately get longitude, but no closed formula for latitude and height exists. See "
Geodetic system
A geodetic datum or geodetic system (also: geodetic reference datum, geodetic reference system, or geodetic reference frame) is a global datum reference or reference frame for precisely representing the position of locations on Earth or other pla ...
." Using Bowring's formula in 1976 ''Survey Review'' the first iteration gives latitude correct within 10 degree as long as the point is within 10,000 meters above or 5,000 meters below the ellipsoid.
In astronomy
Geocentric coordinates can be used for locating
astronomical object
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
s in the
Solar System
The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
in
three dimensions along the
Cartesian X, Y, and Z axes. They are differentiated from
topocentric coordinates, which use the observer's location as the reference point for bearings in
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
and
azimuth
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north.
Mathematicall ...
.
For
nearby stars
This list covers all known stars, brown dwarfs, and sub-brown dwarfs within of the Sun. So far, 131 such objects have been found, of which only List of nearest bright stars, 22 are bright enough to be visible without a telescope. The visible ...
, astronomers use
heliocentric
Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth ...
coordinates, with the center of the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared rad ...
as the origin. The
plane of reference
In celestial mechanics, the plane of reference (or reference plane) is the plane used to define orbital elements (positions). The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longi ...
can be aligned with the Earth's
celestial equator
The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract projec ...
, the
ecliptic
The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agai ...
, or the
Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked ey ...
's
galactic equator. These 3D
celestial coordinate system
Astronomical coordinate systems are organized arrangements for specifying positions of satellites, planets, stars, galaxies, and other celestial objects relative to physical reference points available to a situated observer (e.g. the true horizo ...
s add actual distance as the Z axis to the
equatorial,
ecliptic
The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agai ...
, and
galactic coordinate system
The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way Galaxy, and the fundamental plane parallel to an a ...
s used in
spherical astronomy
Spherical astronomy, or positional astronomy, is a branch of observational astronomy used to locate astronomical objects on the celestial sphere, as seen at a particular date, time, and location on Earth. It relies on the mathematical methods of ...
.
See also
*
Earth-centered inertial
Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and are fixed with respect to the stars. "I" in "ECI" stands for inertial (i.e. "not accelerating"), in contrast to the "Earth-centered - Earth ...
(ECI)
*
Geodetic system
A geodetic datum or geodetic system (also: geodetic reference datum, geodetic reference system, or geodetic reference frame) is a global datum reference or reference frame for precisely representing the position of locations on Earth or other pla ...
*
International Terrestrial Reference System and Frame (ITRS)
*
Orbital state vectors
In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are
Cartesian vectors of position (\mathbf) and velocity (\mathbf) that together with their time (epoch) (t) uniquely determine the trajectory ...
*
Planetary coordinate system
References
External links
ECEF datum transformationNotes on converting ECEF coordinates to WGS-84 datum
Datum Transformations of GPS Positions Application NoteClearer notes on converting ECEF coordinates to WGS-84 datum
orientation of the coordinate system and additional information
GeographicLibincludes a utility CartConvert which converts between
geodetic
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
and geocentric (ECEF) or local Cartesian (ENU) coordinates. This provides accurate results for all inputs including points close to the center of the earth.
EPSG:4978
{{DEFAULTSORT:Ecef
Global Positioning System