page_title: Earth radius
section_title: Prime vertical
hierarchical_section_title: Earth radius / Location-dependent radii / Radii of curvature / Principal sections / Prime vertical
caption_attribution_description: English: Three different radii as a function of Earth's latitude. R is the geocentric radius; M is the meridional radius of curvature; and N is the prime vertical radius of curvature.
context_page_description: Earth radius is the distance from the center of Earth to a point on its surface. Its value ranges from 6,378 km at the equator to 6,357 km at a pole. A nominal Earth radius is sometimes used as a unit of measurement in astronomy and geophysics, denoted in astronomy by the symbol R⊕. In other contexts, it is denoted or sometimes.
  The Earth is not a perfect sphere but approximately an oblate spheroid with a larger radius at the equator than at the poles. When only one radius is stated, the International Astronomical Union prefers that it be the equatorial radius. The International Union of Geodesy and Geophysics recommends three values: the arithmetic mean of the radii measured at the equator and the poles; the authalic radius, which is the radius of a sphere with the same surface area; and the volumetric radius, which is the radius of a sphere having the same volume as the ellipsoid. All three values are about 6,371 kilometres.
  There are many other ways to define and measure the Earth radius. Some appear below.
context_section_description: If one point had appeared due east of the other, one finds the approximate curvature in the east–west direction.
  This radius of curvature in the prime vertical which is perpendicular (normal or orthogonal) to M at geodetic latitude φ is:
  This radius is also called the transverse radius of curvature. At the equator, N = R. B. R. Bowring   gives a geometric proof that this is the perpendicular distance from the surface to the polar axis.
caption: Three different radii as a function of Earth's latitude. R is the geocentric radius; M is the meridional radius of curvature; and N is the prime vertical radius of curvature.
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