spherical excess—The amount by which the sum of three angles of a triangle on a sphere exceeds 180 degrees. The magnitude of the excess depends upon the radius of curvature and the area of the triangle and is approximately one second of arc for each 75.6 square miles on the Earth ellipsoid. Spherical angles are generally used in geodetic surveying, and the difference between spherical and ellipsoidal angles is neglected. One-third of the spherical excess is subtracted from each angle, or Legendre’s theorem is applied in distribution of the spherical excess.

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Source: NSPS “Definitions of Surveying and Related Terms“, used with permission.

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