Living Textbook | Geographic coordinate system | By ITC, University of Twente (2025)

2D geographic coordinates

The most widely used global coordinate system consists of lines of geographic latitude (phi or ϕ or φ) and longitude (lambda or λ) such as2D Geographic Coordinates. Lines of equal latitude are calledparallels. They form circles on the surface of theellipsoid. Lines of equal longitude are calledmeridiansand form ellipses (meridian ellipses) on the ellipsoid (Figure 1).

The latitude (ϕ) of a point P (Figure 2) is the angle between the ellipsoidal normal through P’ and the equatorial plane. Latitude is zero on the Equator (ϕ = 0∘), and increases towards the two poles to maximum values of ϕ = +90^∘(N90^∘) at the North Pole and ϕ = -90^∘(S90^∘) at the South Pole.

The longitude (λ) of the point is the angle between the meridian ellipse that passes through Greenwich and the meridian ellipse containing the point in question. It is measured on the equatorial plane from the meridian of Greenwich (λ = 0^∘), either eastwards through λ = +180^∘(E180^∘) or westwards through λ = -180^∘(W180^∘).

Latitude and longitude represent the geographic coordinates (ϕ,λ) of a point P’ (Figure2) with respect to the selected reference surface. They are always given in angular units. For example, the coordinates for the City Hall in Enschede are:

Thegraticuleon a map represents the projected position of the geographic coordinates (ϕ, λ) at constant intervals or, in other words, the projected position of selected meridians and parallels. The shape of the graticule depends largely on the characteristics of the map projection and the scale of the map.

3D Geographic coordinates

3D geographic coordinates (ϕ, λ, h)are obtained by introducingellipsoidal height (h)into the system. The ellipsoidal height (h) of a point is the vertical distance of the point in question above theellipsoid. It is measured in distance units along the ellipsoidal normal from the point to the ellipsoid surface. 3D geographic coordinates can be used to define a position on the surface of the Earth (Point P in Figure 2).

Geocentric coordinates

An alternative method for defining a 3D position on the surface of the Earth is to usegeocentric coordinates (X, Y, Z), also known as3D Cartesian coordinates. The system’s origin lies at theEarth’s centre of mass, with the X and Y axes on the plane of the Equator.

The X-axis passes through the meridian of Greenwich and the Z-axis coincides with the Earth’s axis of rotation. The three axes are mutually orthogonal and form a right-handed system. Geocentric coordinates can be used to define a position on the surface of the Earth (point P in Figure 3).

The rotational axis of the Earth, however, changes position over time (referred to as polar motion). To compensate for this, the mean position of the pole in the year 1903 (based on observations between 1900 and 1905) is used to define what is referred to as the “Conventional International Origin” (CIO).