A graticule on a sphere or an ellipsoid. The lines from pole to pole are lines of constant longitude, or meridians. The circles parallel to the equator are lines of constant latitude, or parallels. The graticule determines the latitude and longitude of position on the surface.

In geography, latitude is a geographic coordinate that specifies the north-south position of a point on the Earth's surface. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude is an angle (defined below) which ranges from 0° at the Equator to 90° (North or South) at the poles.

Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. Since the actual physical surface of the Earth is too complex for mathematical analysis two levels of abstraction are employed in the definition of these coordinates. In the first step the physical surface is modelled by the geoid, a surface which approximates the mean sea level over the oceans and its continuation under the land masses. The second step is to approximate the geoid by a mathematically simpler reference surface. The simplest choice for the reference surface is a sphere, but the geoid is more accurately modelled by an ellipsoid. The definitions of latitude and longitude on such reference surfaces are detailed in the following sections. Lines of constant latitude and longitude together constitute a graticule on the reference surface. The latitude of a point on the actual surface is that of the corresponding point on the reference surface, the correspondence being along the normal to the reference surface which passes through the point on the physical surface. Latitude and longitude together with some specification of height constitute a geographic coordinate system as defined in the specification of the ISO 19111 standard.^[1]

Since there are many different reference ellipsoids the latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst". This is of great importance in accurate applications, such as GPS, but in common usage, where high accuracy is not required, the reference ellipsoid is not usually stated.

In English texts the latitude angle, defined below, is usually denoted by the Greek letter phi (φ). It is measured in degrees, minutes and seconds or decimal degrees, north or south of the equator.

Measurement of latitude requires an understanding of the gravitational field of the Earth, either for setting up theodolites or for determination of GPS satellite orbits. The study of the Figure of the Earth together with its gravitational field is the science of Geodesy. These topics are not discussed in this article. (See for example the text books by Torge^[2] and Hofmann-Wellenhof and Moritz.^[3])

This article relates to coordinate systems for the Earth: it may be extended to cover the Moon, planets and other celestial objects by a simple change of nomenclature.

The following lists are available:

• List of countries by latitude
• List of cities by latitude

Latitude on the sphere[link]

A perspective view of the Earth showing how latitude (φ) and longitude (λ) are defined on a spherical model. The graticule spacing is 10 degrees.

The graticule on the sphere

The graticule, the mesh formed by the lines of constant latitude and constant longitude, is constructed by reference to the rotation axis of the Earth. The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface. Planes which contain the rotation axis intersect the surface in the meridians and the angle between any one meridian plane and that through Greenwich (the Prime Meridian) defines the longitude: meridians are lines of constant longitude. The plane through the centre of the Earth and orthogonal to the rotation axis intersects the surface in a great circle called the equator. Planes parallel to the equatorial plane intersect the surface in circles of constant latitude; these are the parallels. The equator has a latitude of 0°, the North pole has a latitude of 90° north (written 90° N or +90°), and the South pole has a latitude of 90° south (written 90° S or −90°). The latitude of an arbitrary point is the angle between the equatorial plane and the radius to that point.

The latitude defined in this way for the sphere is often termed the spherical latitude to avoid ambiguity with auxiliary latitudes defined in subsequent sections.

Named latitudes[link]

The orientation of the Earth at the December solstice.

Besides the equator, four other parallels are of significance:

Arctic Circle	66° 33′ 39″ N
Tropic of Cancer	23° 26′ 21″ N
Tropic of Capricorn	23° 26′ 21″ S
Antarctic Circle	66° 33′ 39" S

The plane of the Earth's orbit about the sun is called the ecliptic. The plane perpendicular to the rotation axis of the Earth is the equatorial plane. The angle between the ecliptic and the equatorial plane is called the inclination of the ecliptic, denoted by Failed to parse (Missing texvc executable; please see math/README to configure.): i

in the figure. The current value of this angle is 23° 26′ 21″.[4] It is also called the axial tilt of the Earth since it is equal to the angle between the axis of rotation and the normal to the ecliptic.

The figure shows the geometry of a cross section of the plane normal to the ecliptic and through the centres of the Earth and the Sun at the December solstice when the sun is overhead at some point of the Tropic of Capricorn. The south polar latitudes below the Antarctic Circle are in daylight whilst the north polar latitudes above the Arctic Circle are in night. The situation is reversed at the June solstice when the sun is overhead at the Tropic of Cancer. The latitudes of the tropics are equal to the inclination of the ecliptic and the polar circles are at latitudes equal to its complement. Only at latitudes in between the two tropics is it possible for the sun to be directly overhead (at the zenith).

The named parallels are clearly indicated on the Mercator projections shown below.

Map projections from the sphere

On map projections there is no simple rule as to how meridians and parallels should appear. For example, on the spherical Mercator projection the parallels are horizontal and the meridians are vertical whereas on the Transverse Mercator projection there is no correlation of parallels and meridians with horizontal and vertical, both are complicated curves. The red lines are the named latitudes of the previous section.

	Normal Mercator			Transverse Mercator

For map projections of large regions, or the whole world, a spherical Earth model is completely satisfactory since the variations attributable to ellipticity are negligible on the final printed maps.

Meridian distance on the sphere

On the sphere the normal passes through the centre and the latitude (φ) is therefore equal to the angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by m(φ) then

Failed to parse (Missing texvc executable; please see math/README to configure.): m(\phi)=\frac{\pi}{180}R\phi_{\rm degrees}= R\phi_{\rm radians}.

where R denotes the mean radius of the Earth. R is equal to 6371 km or 3959 miles. No higher accuracy is appropriate for R since higher precision results necessitate an ellipsoid model. With this value for R the meridian length of 1 degree of latitude on the sphere is 111.2 km or 69 miles. The length of 1 minute of latitude is 1.853 km, or 1.15 miles. (See nautical mile).

Latitude on the ellipsoid[link]

Ellipsoids[link]

In 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid.^[5] (This article uses the term ellipsoid in preference to the older term spheroid). Newton's theoretical result was confirmed by precise geodetic measurements in the eighteenth century. (See Meridian arc). The definition of an oblate ellipsoid is the three dimensional surface generated by the rotation of a two dimensional ellipse about its shorter axis (minor axis). 'Oblate ellipsoid of revolution' is abbreviated to ellipsoid in the remainder of this article: this is the current practice in geodetic literature. (Ellipsoids which do not have an axis of symmetry are termed tri-axial).

A great many different reference ellipsoids have been used in the history of geodesy. In pre-satellite days they were devised to give a good fit to the geoid over the limited area of a survey but, with the advent of GPS, it has become natural to use reference ellipsoids (such as WGS84) with centres at the centre of mass of the Earth and minor axis aligned to the rotation axis of the Earth. These geocentric ellipsoids are usually within 100m of the geoid. Since latitude is defined with respect to an ellipsoid the position of a given feature is different on each ellipsoid: it is meaningless to specify the latitude and longitude of a geographical feature without specifying the ellipsoid used. The maps maintained by many national agencies are often based on the older ellipsoids so that is necessary to know how the latitude and longitude values may be transformed from one ellipsoid to another. For example GPS handsets must include software to carry out datum transformations which link WGS84 to the local reference ellipsoid with its associated grid reference system.

The geometry of the ellipsoid[link]

The overall shape of an ellipsoid of revolution is determined by the shape of the ellipse which is rotated about its minor (shorter) axis. Two parameters are required. One is invariably chosen to be the equatorial radius, which is the semi-major axis, a. The other parameter is usually taken as one of three possibilities: (1) the polar radius or semi-minor axis, b; (2) the (first) flattening, f; (3) the eccentricty, e. These parameters are not independent: they are related by

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} f&=\frac{a-b}{a}, \qquad e^2=2f-f^2,\qquad b=a(1-f)=a\sqrt{1-e^2}. \end{align}

A great many other parameters (see ellipse, ellipsoid) are used in the study of the ellipsoid in geodesy, geophysics and map projections but they can all may be expressed in terms of one or two members of the set a, b, f and e. Both f and e are small parameters which often appear in series expansions involved in practical calculations; they are of the order 1/300 and 0.08 respectively. Accurate values for a number of important ellipsoids are given in Figure of the Earth. It is conventional to define reference ellipsoids by giving the semi-major axis and the inverse flattening, 1/f. For example, the defining values for the WGS84 ellipsoid, used by all GPS devices, are^[6]

• a (equatorial radius): 6,378,137.0 m
• 1/f (inverse flattening): 298.257,223,563

from which are derived

• b (polar radius): 6,356,752.3142 m
• e² (eccentricity squared): 0.006,694,379,990,14

The difference of the major and minor semi-axes is approximately 21 km and as fraction of the semi-major axis it is given by the flattening. Thus the representation of the ellipsoid on a computer could be sized as 300px by 299px. Since this would be indistinguishable from a sphere shown as 300px by 300px illustrations invariably greatly exaggerate the flattening.

Geodetic and geocentric latitudes[link]

The definition of geodetic latitude (φ) and longitude (λ) on an ellipsoid. The normal to the surface does not pass through the centre.

The graticule on the ellipsoid is constructed in exactly the same way as on the sphere. The normal at a point on the surface of an ellipsoid does not pass through the centre, except for points on the equator or at the poles, but the definition of latitude remains unchanged as the angle between the normal and the equatorial plane. The terminology for latitude must be made more precise by distinguishing

Geodetic latitude: the angle between the normal and the equatorial plane. The standard notation in English publications is φ. This is the definition assumed when the word latitude is used without qualification. The definition must be accompanied with a specification of the ellipsoid.

Geocentric latitude: the angle between the radius (from centre to the point on the surface) and the equatorial plane. (Figure below). There is no standard notation: examples from various texts include ψ, q, φ', φ_c, φ_g. This article uses ψ.

Spherical latitude: the angle between the normal to a spherical reference surface and the equatorial plane.

Geographic latitude must be used with care. Some authors use it as a synonym for geodetic latitude whilst others use it as an alternative to the astronomical latitude.

Latitude (unqualified) should normally refer to the geodetic latitude.

The importance of specifying the reference datum may be illustrated by a simple example. On the reference ellipsoid for WGS84, the centre of the Eiffel Tower has a geodetic latitude of 48° 51′ 29″ N, or 48.8583° N and longitude of 2° 17′ 40″ E or 2.2944°E. The same coordinates on the datum ED50 define a point on the ground which is 140 m distant from Tower.^{[citation needed]} A web search may produce several different values for the latitude of the Tower; the reference ellipsoid is rarely specified.

The length of a degree of latitude[link]

In Meridian arc and standard texts^[2][7][8] it is shown that the meridian distance from a point at latitude φ to the equator is given by (φ in radians)

Failed to parse (Missing texvc executable; please see math/README to configure.): m(\phi) =\int_0^\phi M(\phi) d\phi = a(1 - e^2)\int_0^\phi \left (1 - e^2 \sin^2 \phi \right )^{-3/2} d\phi.

The function Failed to parse (Missing texvc executable; please see math/README to configure.): M(\phi)

in the first integral is the meridional radius of curvature. 

The distance from the equator to the pole is

Failed to parse (Missing texvc executable; please see math/README to configure.): m_p = m(\pi/2).\,

For WGS84 this distance is 10001.965729 km.

The evaluation of the meridian distance integral is central to many studies in geodesy and map projection. It is normally evaluated by expanding the integral by the binomial series and integrating term by term: see Meridian arc for details. The length of the meridian arc between two given latitudes is given by replacing the limits of the integral by the latitudes concerned. The length of a small meridian arc is given by^[7][8]

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} \delta m(\phi) &= M(\phi) \delta\phi = a(1 - e^2) \left (1 - e^2 \sin^2 \phi \right )^{-3/2} \delta\phi\,. \end{align}

When the latitude difference is 1 degree, corresponding to Failed to parse (Missing texvc executable; please see math/README to configure.): \pi /180 radians, the arc distance is approximately

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta^1_{\rm LAT}= \frac{\pi a(1 - e^2)}{180(1 - e^2 \sin^2 \phi )^{3/2}} \,

The distance in metres between latitudes (Failed to parse (Missing texvc executable; please see math/README to configure.): \phi - 0.5

deg) and (Failed to parse (Missing texvc executable; please see math/README to configure.):  \phi + 0.5
deg) on the WGS84 spheroid is given to within one centimetre by

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta^1_{\rm LAT}= 111132.954 - 559.822\cos 2\phi + 1.175\cos 4\phi.

The variation of this distance with latitude (on WGS84) is shown in the table along with the length of a degree of longitude:

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta^1_{\rm LONG}= \frac{\pi a\cos\phi}{180(1 - e^2 \sin^2 \phi)^{1/2}}\,.

A calculator for any latitude is provided by the U.S. government's National Geospatial-Intelligence Agency(NGA).^[9]

Auxiliary latitudes[link]

There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and the theory of map projections:

• geocentric latitude,
• reduced (or parametric) latitude,
• rectifying latitude,
• authalic latitude,
• conformal latitude,
• isometric latitude.

The definitions given in this section all relate to locations on the reference ellipsoid but the first two auxiliary latitudes, like the geodetic latitude, can be extended to define a three dimensional geographic coordinate system as discussed below. The remaining latitudes are not used in this way; they are used only as intermediate constructs in map projections of the reference ellipsoid to the plane: their numerical values are not of interest. For example no one would need to calculate the authalic latitude of the Eiffel Tower.

The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, a, and the eccentricity, e. The forms given are, apart from notational variants, those in the standard reference for map projections, namely "Map projections — a working manual" by J.P.Snyder.^[10] Derivations of these expressions may be found in Adams^[11] and web publications by Rapp^[7] and Osborne^[8]

Geocentric latitude[link]

The definition of geodetic (or geographic) and geocentric latitudes.

The geocentric latitude is the angle between the equatorial plane and the radius from the centre to a point on the surface. The relation between the geocentric latitude (ψ) and the geodetic latitude (φ) is derived in the above references as

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi(\phi)=\tan^{-1}\left[(1-e^2)\tan\phi\right]\;\!.

The geodetic and geocentric latitudes are equal at the equator and poles. The value of the squared eccentricity is approximately 0.007 (depending on the choice of ellipsoid) and the maximum difference of (φ-ψ) is approximately 11.5 minutes of arc at a geodetic latitude of 45°5′.

Reduced (or parametric) latitude[link]

Definition of the reduced latitude (β) on the ellipsoid.

The reduced or parametric latitude, β, is defined by the radius drawn from the centre of the ellipsoid to that point Q on the surrounding sphere (of radius a) which is the projection parallel to the Earth's axis of a point P on the ellipsoid at latitude Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle\phi . It was introduced by Legendre^[12] and Bessel^[13] who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, Failed to parse (Missing texvc executable; please see math/README to configure.): u(\phi) , is also used in the current literature. The reduced latitude is related to the geodetic latitude by^[7][8]

Failed to parse (Missing texvc executable; please see math/README to configure.): \beta(\phi)=\tan^{-1}\left[\sqrt{1-e^2}\tan\phi\right]\,\!

The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates p, the distance from the minor axis, and z, the distance above the equatorial plane, the equation of the ellipse is

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{p^2}{a^2} + \frac{z^2}{b^2} =1 .

The Cartesian coordinates of the point are parameterized by

Failed to parse (Missing texvc executable; please see math/README to configure.): p=a\cos\beta, \qquad z=b\sin\beta;

Cayley^[14] suggested the term parametric latitude because of the form of these equations.

The reduced latitude is not used in the theory of map projections. Its most important application is in the theory of ellipsoid geodesics. (Vincenty, Karney^[15]).

Rectifying latitude[link]

The rectifying latitude, μ, is the meridian distance scaled so that its value at the poles is equal to 90 degrees or π/2 radians:

 Failed to parse (Missing texvc executable; please see math/README to configure.): \mu(\phi)=\frac{\pi}{2}\frac{m(\phi)}{m_p}\,\!

where the meridian distance from the equator to a latitude φ is (see Meridian arc)

Failed to parse (Missing texvc executable; please see math/README to configure.): m(\phi)= a(1 - e^2)\int_0^\phi \left (1 - e^2 \sin^2 \phi \right )^{-3/2} d\phi,

and the length of the meridian quadrant from the equator to the pole is

Failed to parse (Missing texvc executable; please see math/README to configure.): m_p = m(\pi/2).\,

Using the rectifying latitude to define a latitude on a sphere of radius

Failed to parse (Missing texvc executable; please see math/README to configure.): R=\frac{2m_p}{\pi}

defines a projection from the ellipsoid to the sphere such that all meridians have true length and uniform scale. The sphere may then be projected to the plane with an equirectangular projection to give a double projection from the ellipsoid to the plane such that all meridians have true length and uniform meridian scale. An example of the use of the rectifying latitude is the Equidistant conic projection. (Snyder,^[10] Section 16). The rectifying latitude is also of great importance in the construction of the Transverse Mercator projection.

Authalic latitude[link]

The authalic (Greek for same area) latitude, ξ, gives an area-preserving transformation to a sphere.

Failed to parse (Missing texvc executable; please see math/README to configure.): \xi(\phi)=\sin^{-1}\left(\frac{q(\phi)}{q_p}\right)\,\!

where

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} q(\phi)&= \frac{(1 - e^2)\sin\phi}{1 - e^2 \sin^2 \phi} -\frac{1-e^2}{2e}\ln \left(\frac{1-e\sin\phi}{1+e\sin\phi}\right),\\ &= \frac{(1 - e^2)\sin\phi}{1 - e^2 \sin^2 \phi} +\frac{1-e^2}{e}\tanh^{-1}(e\sin\phi), \end{align}

and

Failed to parse (Missing texvc executable; please see math/README to configure.): q_p = q(\pi/2) =1-\frac{1-e^2}{2e}\ln \left(\frac{1-e}{1+e}\right) =1+\frac{1-e^2}{e}\tanh^{-1}e, \,

and the radius of the sphere is taken as

Failed to parse (Missing texvc executable; please see math/README to configure.): R_q=a\sqrt{q_p/2}.\,

An example of the use of the authalic latitude is the Albers equal-area conic projection. (Snyder,^[10] Section 14).

Conformal latitude[link]

The conformal latitude, χ, gives an angle-preserving (conformal) transformation to the sphere.

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} \chi(\phi)&=2\tan^{-1}\left[ \left(\frac{1+\sin\phi}{1-\sin\phi}\right) \left(\frac{1-e\sin\phi}{1+e\sin\phi}\right)^{\!\textit{e}} \;\right]^{1/2} -\frac{\pi}{2}\\[2ex] &=2\tan^{-1}\left[ \tan\left(\frac{\phi}{2}+\frac{\pi}{4}\right) \left(\frac{1-e\sin\phi}{1+e\sin\phi}\right)^{\!\textit{e}/2} \;\right] -\frac{\pi}{2} \;\!\end{align}

. The conformal latitude defines a transformation from the ellipsoid to a sphere of arbitrary radius such that the angle of intersection between any two lines on the ellipsoid is the same as the corresponding angle on the sphere (so that the shape of small elements is well preserved). A further conformal transformation from the sphere to the plane gives a conformal double projection from the ellipsoid to the plane. This is not the only way of generating such a conformal projection. For example, the 'exact' version of the Transverse Mercator projection on the ellipsoid is not a double projection. (It does, however, involve a generalisation of the conformal latitude to the complex plane).

Isometric latitude[link]

The isometric latitude is conventionally denoted by ψ (not to be confused with the geocentric latitude): it is used in the development of the ellipsoidal versions of the normal Mercator projection and the Transverse Mercator projection. The name "isometric" arises from the fact that at any point on the ellipsoid equal increments of ψ and longitude λ give rise to equal distance displacements along the meridians and parallels respectively. The graticule defined by the lines of constant ψ and constant λ, divides the surface of the ellipsoid into a mesh of squares (of varying size). The isometric latitude is zero at the equator but rapidly diverges from the geodetic latitude, tending to infinity at the poles. The conventional notation is given in Snyder^[10] (page 15):

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} \psi(\phi) &=\ln\left[\tan\left( \frac{\pi}{4}+\frac{\phi}{2}\right) \right] + \frac{e}{2}\ln\left[ \frac{1-e\sin\phi}{1+e\sin\phi} \right]\\ &=\sinh^{-1}(\tan\phi) -e\tanh^{-1}(e\sin\phi). \end{align}

For the normal Mercator projection (on the ellipsoid) this function defines the spacing of the parallels: if the length of the equator on the projection is E (units of length or pixels) then the distance, y, of a parallel of latitude φ from the equator is

Failed to parse (Missing texvc executable; please see math/README to configure.): y(\phi)=\frac{E}{2\pi}\psi(\phi).

Numerical comparison of auxiliary latitudes[link]

The following plot shows the magnitude of the difference between the geodetic latitude, (denoted as the 'common' latitude on the plot), and the auxiliary latitudes other than the isometric latitude (which diverges to infinity at the poles). In every case the geodetic latitude is the greater. The differences shown on the plot are in arc minutes. The horizontal resolution of the plot fails to make clear that the maxima of the curves are not at 45° but calculation shows that they are within a few arc minutes of 45°. Some representative data points are given in the table following the plot. Note the closeness of the conformal and geocentric latitudes. This was exploited in the days of hand calculators to expedite the construction of map projections. (Snyder,^[10] page 108).

Approximate difference from geodetic latitude (Failed to parse (Missing texvc executable; please see math/README to configure.): \phi\,\! )
Failed to parse (Missing texvc executable; please see math/README to configure.): \phi\,\!	Reduced Failed to parse (Missing texvc executable; please see math/README to configure.): \phi-\beta\,\!	Authalic Failed to parse (Missing texvc executable; please see math/README to configure.): \phi-\xi\,\!	Rectifying Failed to parse (Missing texvc executable; please see math/README to configure.): \phi-\mu\,\!	Conformal Failed to parse (Missing texvc executable; please see math/README to configure.): \phi-\chi\,\!	Geocentric Failed to parse (Missing texvc executable; please see math/README to configure.): \phi-\psi\,\!
0°	0.00′	0.00′	0.00′	0.00′	0.00′
15°	2.91′	3.89′	4.37′	5.82′	5.82′
30°	5.05′	6.73′	7.57′	10.09′	10.09′
45°	5.84′	7.78′	8.76′	11.67′	11.67′
60°	5.06′	6.75′	7.59′	10.12′	10.13′
75°	2.92′	3.90′	4.39′	5.85′	5.85′
90°	0.00′	0.00′	0.00′	0.00′	0.00′

Latitude and coordinate systems[link]

The geodetic latitude, or any of the auxiliary latitudes defined on the reference ellipsoid, constitutes with longitude a two-dimensional coordinate system on that ellipsoid. To define the position of an arbitrary point it is necessary to extend such a coordinate system into three dimensions. Three latitudes are used in this way: the geodetic, geocentric and reduced latitudes are used in geodetic coordinates, spherical polar coordinates and ellipsoidal coordinates respectively.

Geodetic coordinates[link]

Geodetic coordinates P(φ, λ,h)

At an arbitrary point P consider the line PN which is normal to the reference ellipsoid. The geodetic coordinates P(φ, λ,h) are the latitude and longitude of the point N on the ellipsoid and the distance PN. This height differs from the height above the geoid or a reference height such as that above mean sea level at a specified location. The direction of PN will also differ from the direction of a vertical plumb line. The relation of these different heights requires knowledge of the shape of the geoid and also the gravity field of the Earth.

Spherical polar coordinates[link]

Geocentric coordinate related to spherical polar coordinates P(r, θ, λ)

The geocentric latitude ψ is the complement of the polar angle θ in conventional spherical polar coordinates in which the coordinates of a point are P(r, θ, λ) where r is the distance of P from the centre O, θ is the angle between the radius vector and the polar axis andλ is longitude. Since the normal at a general point on the ellipsoid does not pass through the centre it is clear that points on the normal, which all have the same geodetic latitude, will have differing geocentic latitudes. Spherical polar coordinate systems are used in the analysis of the gravity field.

Ellipsoidal coordinates[link]

Ellipsoidal coordinates P(u,β,λ)

The reduced latitude can also be extended to a three dimensional coordinate system. For a point P not on the reference ellipsoid (semi-axes OA and OB) construct an auxiliary ellipsoid which is confocal (same foci F, F') with the reference ellipsoid: the necessary condition is that the product ae of semi-major axis and eccentricity is the same for both ellipsoids. Let u be the semi-minor axis (OD) of the auxiliary ellipsoid. Further let β be the reduced latitude of P on the auxiliary ellipsoid. The set (u,β,λ) define the ellipsoid coordinates. (Torge^[2] Section 4.2.2). These coordinates are the natural choice in models of the gravity field for a uniform distribution of mass bounded by the reference ellipsoid.

Coordinate conversions[link]

The relations between the above coordinate systems, and also Cartesian coordinates are not presented here. The transformation between geodetic and Cartesian coordinates may be found in Geodetic system. The relation of Cartesian and spherical polars is given in Spherical coordinate system. The relation of Cartesian and ellipsoidal coordinates is discussed in Torge.^[2]

Astronomical latitude[link]

The astronomical latitude (Φ) is defined as the angle between the equatorial plane and the true vertical at a point on the surface: the true vertical, the direction of a plumb line, is the direction of the gravity field at that point. (The gravity field is the resultant of the gravitational acceleration and the centrifugal acceleration at that point. See Torge.^[2]) The astronomic latitude is readily accessible by measuring the angle between the zenith and the celestial pole or alternatively the angle between the zenith and the sun when the elevation of the latter is obtained from the almanac.

In general the direction of the true vertical at a point on the surface does not coincide with the either the normal to the reference ellipsoid or the normal to the geoid. The deflections between the astronomic and geodetic normals are only of the order of a few seconds of arc but they are nevertheless important in high precision geodesy.^[2][3]

Astronomical latitude is not to be confused with declination, the coordinate astronomers used in a simlilar way to describe the locations of stars north/south of the celestial equator (see equatorial coordinates), nor with ecliptic latitude, the coordinate that astronomers use to describe the locations of stars north/south of the ecliptic (see ecliptic coordinates).

See also[link]

Footnotes[link]

External links[link]

Look up latitude in Wiktionary, the free dictionary.

Find more about Latitude on Wikipedia's sister projects:
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• A Comprehensive Library of Cartographic Projection Functions (Preliminary Draft) at the Internet ArchivePDF (1.88 MB)
• GEONets Names Server, access to the National Geospatial-Intelligence Agency's (NGA) database of foreign geographic feature names.
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Kanye West
West at the SWU Music & Arts Festival, 2011
Background information
Birth name	Kanye Omari West
Born	(1977-06-08) June 8, 1977 (age 35) Atlanta, Georgia, United States
Origin	Chicago, Illinois, United States
Genres	Hip hop
Occupations	rapper, singer, songwriter, record producer, music video director, film director, fashion designer
Instruments	Vocals, keyboards, sampler, percussion, synthesizer
Years active	1996–present
Labels	GOOD Music, Roc-A-Fella, Def Jam
Associated acts	Go Getters, Child Rebel Soldier, Jay-Z, The Throne, Common, John Legend, Kid Cudi, Rihanna, Jeff Bhasker, Pusha T, Mos Def, Mr Hudson, Talib Kweli, Big Sean, A-Trak, Pharrell, Lupe Fiasco, RZA
Website	kanyewest.com

Kanye Omari West ( /ˈkɑːnjeɪ/; born June 8, 1977)^[1] is an American musician, film director and fashion designer. West first rose to fame as a producer for Roc-A-Fella Records, where he eventually achieved recognition for his work on Jay-Z's album The Blueprint, as well as hit singles for musical artists including Alicia Keys, Ludacris, and Janet Jackson. His style of production originally used pitched-up vocal samples from soul songs incorporated with his own drums and instruments. However, subsequent productions saw him broadening his musical palette and expressing influences encompassing '70s R&B, baroque pop, trip hop, arena rock, folk, alternative, electronica, synthpop, and classical music.^[2]

West released his debut album The College Dropout in 2004, his second album Late Registration in 2005, his third album Graduation in 2007, his fourth album 808s & Heartbreak in 2008, and his fifth album My Beautiful Dark Twisted Fantasy in 2010. West released a collaborative album, Watch the Throne with Jay-Z in 2011, which is the duo's first collaborative album. His five solo albums, all of which have gone platinum, have received numerous awards and critical acclaim.^[3] As of 2012, West has won a total of eighteen Grammy Awards, making him one of the most awarded artists of all-time.^[4] All albums have been very commercially successful, with My Beautiful Dark Twisted Fantasy becoming his fourth consecutive No. 1 album in the U.S. upon release.^[5] West has had 5 songs exceed 3 million in digital sales as of July 2011, with "Gold Digger" selling 3,086,000, "Stronger" selling 4,402,000, "Heartless" selling 3,742,000, "E.T." selling over 4,000,000 and "Love Lockdown" selling over 3,000,000^[6][7] placing him third in overall digital sales of the past decade.^[8][9] He has sold over 30 million digital songs in the United States making him one of the best-selling digital artists of all-time.^[10]

West also runs his own record label GOOD Music, home to artists such as John Legend, Common and Kid Cudi.^[11] West's mascot and trademark is "Dropout Bear," a teddy bear which has appeared on the covers of three of his five solo albums as well as various single covers and in his music videos.^[12] About.com ranked Kanye West No. 8 on their "Top 50 Hip-Hop Producers" list.^[13] On May 16, 2008, Kanye West was crowned by MTV as the year's No. 1 "Hottest MC in the Game."^[14] On December 17, 2010, Kanye West was voted as the MTV Man of the Year by MTV.^[15] Billboard ranked Kanye West No. 3 on their list of Top 10 Producers of the Decade.^[16] West has also been included in the Time 100 list of the most influential people in the world as well as being listed in a number of Forbes' annual lists.^[17]

Kanye will release the full-length album entitled Cruel Summer with GOOD Music signed artists sometime in 2012.

Early life[link]

Kanye West was born in Atlanta, Georgia,^[18] where he lived with his parents. When he was three years old, his parents divorced, and he and his mother moved to Chicago, Illinois.^[19] His father was Ray West, a former Black Panther who was one of the first black photojournalists at The Atlanta Journal-Constitution, and is now a Christian counselor.^[19] West's mother, Dr. Donda West, was a Professor of English at Clark Atlanta University, and the Chair of the English Department at Chicago State University before retiring to serve as West's manager. He was raised in a middle-class background, attending Polaris High School^[20] in suburban Oak Lawn, Illinois after living in Chicago.^[21] When asked about his grades in high school, West replied, "I got A's and B's. And I'm not even frontin'".^[22]

West attended art classes at the American Academy of Art in Chicago, and also enrolled at Chicago State University, but dropped out to focus on his music career.^[23] While attending school, West produced for local artists. He later gained fame by producing hit singles for major hip hop/R&B artists, including Jay-Z, Talib Kweli, Cam'ron, Paul Wall, Common, Mobb Deep, Jermaine Dupri, Scarface, The Game, Alicia Keys, Janet Jackson, John Legend among others. He also "ghost-produced" for his mentor Deric Angelettie, according to his song "Last Call" and the credits of Nas' "Poppa Was a Playa".^[23]

Music career[link]

1996–2003: Career beginnings[link]

Kanye West's first career productions came on Chicago rapper Grav's 1996 debut album Down to Earth. West produced eight tracks on the album. While the album did not attract much attention and would be the only album released by Grav, West would soon be producing for higher profile artists. In 1998–1999 he produced for well-known artists such as Jermaine Dupri, Foxy Brown, Goodie Mob, and the group Harlem World.

West got his big break in the year 2000, when he began to produce for artists on Roc-a-Fella Records. He produced the well-received Jay-Z song "This Can't Be Life" off of the album The Dynasty: Roc La Familia. West would later state that to create the beat for "This Can't Be Life", he sped up the drum beat from Dr. Dre's song "Xxplosive".^[24]

After producing for Jay-Z earlier, West’s sound was featured heavily on Jay-Z's critically acclaimed album The Blueprint, released September 11, 2001.^[25] His work was featured on the lead single "Izzo (H.O.V.A.)", "Heart of the City (Ain't No Love)" and a diss track against Nas and Mobb Deep named "Takeover"; West has worked with Mobb Deep and Nas since the track's release.^[25]

After meeting great commercial success and critical acclaim for his productions on The Blueprint, West became a sought after producer in the hip-hop industry, even before he became known as a rapper and solo artist. In the years 2002–2003 he would produce for artists such as Nas, Scarface, Talib Kweli, Mos Def, T.I., Ludacris, DMX, and Monica. He also continued producing for Roc-a-Fella Records artists and contribued four tracks to Jay-Z's follow up album to The Blueprint, The Blueprint²: The Gift & the Curse.

After great successes as a producer, West now looked to pursue a career as a rapper and solo artist, but struggled to get a record deal. Chris Anokute, then A&R at Def Jam, said that when West regularly dropped by the office to pick up his producer checks he would play demos of solo material to Anokute in his cubicle and bemoan the fact that no one was taking him seriously as a rapper.^[26] Jay-Z admitted that Roc-A-Fella was initially reluctant to support West as a rapper, claiming that he saw him as a producer first and foremost.^[27] Multiple record companies felt he was not as marketable as rappers who portray the "street image" prominent in hip hop culture.^[24] Beginning his career as a rapper, Kanye West recorded the third verse on the song "The Bounce" off of Jay-Z's The Blueprint²: The Gift & the Curse, an album he produced for, from the same label he was signed to as a rapper.

[edit] 2004–05: The College Dropout and Late Registration

On October 23, 2002, West was involved in a near fatal car crash while driving home from the recording studio.^[28] The crash provided inspiration for West's first single, "Through the Wire".^[29] West's faith is apparent in many of his songs, such as "Jesus Walks", which became a staple at his benefit performances, such as the Live 8 concert. These songs were featured on West's debut album, The College Dropout, which was released on Roc-A-Fella Records in February 2004, and went on to receive critical acclaim. The album also defined the style for which West would become known, including wordplay and sampling.^[29] The album was eventually certified triple platinum. Guest appearances included Jay-Z, Ludacris, GLC, Consequence, Talib Kweli, Mos Def, Common, and Syleena Johnson. The album also featured the singles, "All Falls Down" and "The New Workout Plan", as well as Twista's number one single, "Slow Jamz".^[30] During 2003 West also co-produced songs for British singer Javine Hylton, even appearing in the music video to Real Things playing the love interest of Javine.

West was involved in a financial dispute over Royce Da 5'9"'s song "Heartbeat", produced by West and released on Build & Destroy: The Lost Sessions. West maintains that Royce never paid for the beat, but recorded to it and released it; hearing him on the beat, the original customers decided not to buy it from West. After the disagreement, West vowed to never work with Royce again.^[31] Other Kanye West-produced hit singles during the period The College Dropout was released included "I Changed My Mind" by Keyshia Cole, "Overnight Celebrity" by Twista and "Talk About Our Love" by Brandy.^[29]

West and Jamie Foxx performing "Gold Digger" at the Democratic Convention in Denver, Colorado

Taking a more eclectic route, West collaborated with American film score composer Jon Brion to construct his second album, Late Registration, which was released on August 30, 2005.^[32] Like its predecessor, the sophomore effort garnered universal acclaim from music critics.^[33] Late Registration topped countless critic polls and was revered as the best album of the year by numerous publications, including USA Today, Spin, and Time.^[34][35] Rolling Stone awarded the album the highest position on their end of the year record list and hailed it as a "sweepingly generous, absurdly virtuosic hip-hop classic."^[36] The record earned the number one spot on the Village Voice's Pazz & Jop critics' poll of 2005 for the second consecutive year.^[37] Late Registration was also a commercial success, selling over 860,000 copies in its first week alone and topping the Billboard 200.^[38] Grossing over 2.3 million units sold in the United States alone by year's end, Late Registration was considered by industry observers as the sole majorly successful album release of the fall of 2005, a season that was plagued by steadily declining CD sales.^[39] The second album earned eight Grammy Award nominations including Album of the Year and Record of the Year for the song "Gold Digger".^[40] The album is certified triple platinum.^[41]

On August 22, 2005, the MTV special All Eyes On Kanye West aired, in which West spoke out against homophobia in hip-hop. He claimed that hip-hop has always been about "speaking your mind and about breaking down barriers, but everyone in hip-hop discriminates against gay people."^[42] He then reflected on a personal experience. He said that he had a "turning point" when he realized one of his cousins was gay. He said regarding this experience: "This is my cousin. I love him and I've been discriminating against gays." He drew comparison between African Americans' struggle for civil rights and today's gay rights movement. The following year, in an interview with Entertainment Weekly, West further expounded his experiences with and views on the relationship between the black and gay communities.^[43]

In September 2005, West announced that he would release his Pastelle Clothing line in spring 2006:^[44] "Now that I have a Grammy under my belt and Late Registration is finished, I am ready to launch my clothing line next spring." In that year, West produced the hit singles "Go" by Common and "Dreams" by The Game.^[45]

[edit] 2007–09: Graduation and 808s & Heartbreak

West performing in Kuala Lumpur, Malaysia, April 2007.

In 2007, it was announced that West would be starring in a series directed by Larry Charles. He has been working on the pilot episode for the past two years with Larry Charles and Rick Rubin. He also had this to say on January 14: "I wouldn't do something as cliché as a reality show. At least give me the credit for being more creative than that. It's a situational half-hour comedy. It's fictional, and loosely based on my life.^[46] " West also collaborated with Japanese hip-hop group Teriyaki Boyz to produce the single "I Still Love H.E.R.", a reference to Common's 1994 single "I Used to Love H.E.R.". Further to this, during a radio appearance in early 2007, West, like many of his peers, recorded an impromptu freestyle to the popular song "Throw Some D's." The song that to all other rappers was about automobile rims, was used by West to comically refer to D-cup breasts. Because of the unexpected success of the song, West went on to make a video for the freestyle, in which he is seen playing his 'Old Ass Cousin'.^[47]

West was also featured in a new song called "Classic (Better Than I've Ever Been)". It was believed to be a single for, Graduation, because he is featured on the track, but Nike quickly explained that it was for the Nike Air Force 1's anniversary. It was meant only to be an exclusive track for the company.^[48]

On March 25, 2007, he and his father Ray West supported World Water Day by having a "Walk for Water" rally.^[49] After a two-year break, West has returned to being a fashion columnist in lifestyle magazine Complex.^[50] On July 7, 2007, West performed with The Police and John Mayer at the American leg of Live Earth.^[51] West hosted the August 17 edition of British comedy- variety show The Friday Night Project.^[52]

In July 2007, West changed the release date of Graduation, his third album, from September 18, 2007, to the same release date as 50 Cent's album Curtis, September 11, 2007.^[53] 50 Cent later claimed that if Graduation were to sell more records than Curtis, he would stop releasing solo albums. However, 50 Cent would later dispel his comments.^[54] The album has been certified double platinum. Guest appearances included T-Pain, Mos Def, and Lil Wayne.^[55]

On August 26, 2007, West appeared as himself on the HBO television show Entourage which he used as a platform to premier his new single "Good Life" during the end credits. On September 9, 2007, West performed at the 2007 MTV Video Music Awards, losing in every category he was nominated for; he gave an angry speech immediately afterward. (see "Controversies" section)

Following the MTV stint, West was nominated in eight Grammy Award categories for the 50th annual Grammy Awards.^[57] He won four of them,^[58] including Best Rap Album for Graduation and Best Rap Solo Performance for "Stronger" from Graduation. During the four-hour televised Grammy Awards ceremony, West also performed two songs: "Stronger" (with Daft Punk) and "Hey Mama" (in honor of his recently deceased mother).^[59]

West kicked off the Glow in the Dark Tour in Seattle at the Key Arena on April 16. The tour was originally scheduled to end in June in Cincinnati but was extended into August. Over the course of the tour West was joined by a varying group of opening acts, including Lupe Fiasco, Rihanna, N.E.R.D., DJ Craze, and Gnarls Barkley. On June 15, West was scheduled to perform a late night set at the Bonnaroo Music Festival. His performance started almost two hours late and ran for half of its alloted time, angering many fans in the audience. West later wrote an outraged entry on his blog, blaming the festival organizers as well as Pearl Jam's preceding set, which ran longer than expected.

On September 7, West debuted a new song "Love Lockdown" at the 2008 MTV Video Music Awards. "Love Lockdown" features no rapping and only singing using an auto-tune device. This song appears on West's fourth studio album, 808s & Heartbreak. The new album was expected to be released on December 16, but West announced on his blog on September 24, 2008, that he had finished the album and would be releasing it sometime in November, earlier than previously scheduled. In early October, West made a surprise appearance at a T.I. concert in Los Angeles, where he stated that 808s & Heartbreak was scheduled to be released on November 25, though it was actually released on the 24th, and that the second single is "Heartless". The album was another number one album for West, even though the first week numbers fell well short of Graduation with 450,145 sold.^[60]

West performing in 2008

West performed at the American Music Awards ceremony on November 23.^[61] That same night he won two AMA awards, including Favorite Rap/Hip-Hop Album for Graduation and Favorite Rap/Hip-Hop Male Artist. West performed at the Democratic National Convention in Denver in August 2008, along with Wyclef Jean and N.E.R.D. in support of Barack Obama. On January 20, 2009, Kanye West performed at the Youth Inaugural Ball hosted by MTV for Obama's inauguration.

On February 17, 2009, West was named one of Top 10 Most Stylish Men in America by GQ.^[62] The next day, February 18, 2009, West won International Male Solo Artist at The Brit Awards 2009. West was not in attendance but accepted his award with a video speech, saying "Barack is the 'Best Interracial Male' but I'm proud to be the Best International Male in the world.^[63]

In April 2009, Kanye West recorded a song called "Hurricane" with 30 Seconds to Mars to appear on their album This Is War, but was not released due to legal issues with both record companies. The song was eventually released on the deluxe version of This Is War, titled "Hurricane 2.0".^[64][65][66]

[edit] 2010–present: My Beautiful Dark Twisted Fantasy and Watch the Throne

West performing at The Big Chill

In May 2010, West made an animated television guest appearance on Fox's animated television series The Cleveland Show (a spin-off of Family Guy) as the voice behind "Kenny West", a rival of Cleveland Brown's son.^[67] In his first episode he performed in a rap battle with Cleveland's son. The producers stated working with West was a very good experience and a reason they chose him was because they knew he was a fan of Family Guy.^[68] Kenny West re-appeared in the season 2 premiere of The Cleveland Show.

West spent the first half of 2010 in Honolulu, Hawaii, working on his new album with the working title "Good Ass Job", later named My Beautiful Dark Twisted Fantasy, released on November 22, 2010.^[69] West has cited Maya Angelou, Gil Scott-Heron and Nina Simone as his musical inspirations for this album. Outside production is said to come from RZA, Q-Tip, Pete Rock, and DJ Premier.^[70][71] West also had Justin Vernon flown into his studio on Oahu after seemingly expressing interest in sampling one of Bon Iver's songs; Vernon proceeded to feature on a number of new tracks, including "Lost In The World," which features Vernon's vocal line from Woods.^[72]

On May 28, the Dwele-assisted first single from the album, entitled "Power", leaked to the Internet. On June 30, the track was officially released via iTunes. The upcoming music video was quoted as being "apocalyptic, in a very personal way" by the director Marco Brambilla.^[73]

On September 12, 2010, West performed a new song, "Runaway" featuring Pusha T, at the 2010 MTV Video Music Awards.^[74] Shortly after the performance, Kanye revealed he was working on a 35 minute short film based around the song. The movie is said to be influenced by film noir and concerns a fallen phoenix whom Kanye falls in love with.^[75] On October 15, 2010, Kanye West was ranked 3rd in BET's "Top Ten Rappers of the 21st Century" list.^[76]

West performing at a benefit at the Museum of Modern Art in 2011

Watch the Throne, a collaborative studio album by West and Jay-Z,^[77] was released by Def Jam Recordings on August 8, 2011.^[78] It has been under production since August 2010 as part of West's GOOD Friday initiative of releasing new songs every Friday between August 20 and Christmas 2010.^[79] West said through a recent interview with MTV that the album is "going to be very dark and sexy, like couture hip hop."^[79][80][81] He appeared at the Macy's Thanksgiving Day Parade, performing the track "Lost in the World" from My Beautiful Dark Twisted Fantasy.^[82] On January 6, 2011, Kanye announced via Twitter that the first official single from Watch the Throne would be a song called "H•A•M" produced by Lex Luger. The song was released on January 11, 2011.^[83]

On April 17, 2011, West closed the Coachella Festival with a headlining set that received glowing praise from fans and critics alike.^[84][85] On July 20, a track titled "Otis" from the album was released in the iTunes Store. It samples "Try a Little Tenderness" by Otis Redding.^[86] On October 19, 2011, via his Twitter, West announced plans for a Spring 2012 GOOD Music album release.^[87] On April 6, 2012, "Mercy", the lead single from the GOOD Music compilation album, Cruel Summer, was released.^[88] The song, produced by newly signed in-house producer Lifted, features West along with Big Sean, Pusha T and southern rapper 2 Chainz.^[89]

Other ventures[link]

Business ventures[link]

In August 2008, West revealed plans to open 10 Fatburger restaurants in the Chicago area; the first was set to open in September 2008 in Orland Park. The second followed in January 2009, while a third location is yet to be revealed, although the process is being finalized. His company, KW Foods LLC, bought the rights to the chain in Chicago.^[90] Additionally, West planned to launch his fashion career, and applied for internships with major European fashion houses.^[91] He was due to release his own clothing line called Past Tell in 2009. He also collaborated with Nike to release his own shoe, Air Yeezys.

On January 22, 2009, during Paris Fashion Week, West introduced his first shoe line designed for Louis Vuitton. The line was released in summer 2009.

On October 1, 2011, Kanye West premiered his women's fashion label, DW Kanye West^[92] at Paris Fashion Week. He received support from DSquared2 duo Dean and Dan Caten, Olivier Theyskens, Jeremy Scott, Azzedine Alaïa, and the Olsen twins, who were also in attendance during his show. His debut fashion show received mixed-to-negative reviews,^[93][94] ranging from reserved observations by Style.com^[95] to excoriating commentary by The Wall Street Journal,^[96] the New York Times,^[97] the International Herald Tribune, Elleuk.com, The Daily Telegraph, Harper's Bazaar and many others.^{[98][99][100]}

Philanthropy[link]

West started the "Kanye West Foundation" in Chicago in 2003. On August 24, 2007, West hosted the inaugural benefit concert to launch the foundation's partnership with Strong American Schools. It is focused on helping Latino and African American children stay in school and continue education through grade school, high school, and college. The foundation also helps children pursue music in school. West has contributed over $500,000 to his foundation. The foundation has also been called the "Donda West Foundation".

Kanye West has appeared and participated in many fundraisers, benefit concerts, and has done community work for Hurricane Katrina relief, the Kanye West Foundation, the Millions More Movement, 100 Black Men of America, a Live Earth concert benefit, World Water Day rally and march, Nike runs, and a MTV special helping young Iraq War veterans who struggle through debt and PTSD a second chance after returning home.^[101]

Musical style and influences[link]

West working in the studio with his mentor No I.D. (left)

At the start of his career, Kanye West's production style often used pitched-up vocal samples, usually from soul songs, with his own drums and instruments.^[25] His first major release featuring his trademark vocal sampling style was "This Can't Be Life", a track from Jay-Z’s The Dynasty: Roc La Familia. West said he sped up the drum beat of Dr. Dre's "Xxplosive" to use as a replacement for his drums on "This Can't Be Life".^[24]

West has said that Wu-Tang Clan producer RZA influenced him in his style,^[21][102] and has said on numerous occasions that Wu-Tang rappers Ghostface Killah and Ol' Dirty Bastard were some of his all-time favorites, "Wu-Tang? Me and my friends talk about this all the time... We think Wu-Tang had one of the biggest impacts as far as a movement. From slang to style of dress, skits, the samples. Similar to the [production] style I use, RZA has been doing that."^[103] RZA himself has spoken quite positively of the comparisons, stating in an interview for Rolling Stone, "All good. I got super respect for Kanye. He came up to me about a year or two ago. He gave me mad praising and blessings... For people to say Wu-Tang inspire Kanye, Kanye is one of the biggest artists in the world. That goes back to what we say: 'Wu-Tang is forever.' Kanye is going to inspire people to be like him."^[104] After hearing his work on The Blueprint, RZA claimed that a torch-passing had occurred between him and West, saying, "The shoes gotta be filled. If you ain't gonna do it, somebody else is gonna do it. That's how I feel about rap today."^[104]

West accompanied by an eleven-piece chamber orchestra

While his use of sampling has lessened over time, West's production continues to feature distinctive and intricate string arrangements. This characteristic arose from him listening to the English trip hop group Portishead, whose 1998 live album Roseland NYC Live, with the New York Philharmonic Orchestra inspired him to incorporate string sections into his hip hop production.^[2] Though he was unable to afford live instruments beyond violin riffs provided by Israeli violinist Miri Ben-Ari around the time of his debut album, its subsequent commercial success allowed him to hire his very own eleven-piece string orchestra. For a time, West stood as the sole current pop star to tour with a string section.^[2]