In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's base). The angle between the radii lying within the bounding semidisks is the dihedral . If is a semidisk that forms a ball when completely revolved about the z-axis, revolving only through a given produces a spherical wedge of the same angle . Beman (2008) remarks that "a spherical wedge is to the sphere of which it is a part as the angle of the wedge is to a perigon." A spherical wedge of radians (180ð) is called a hemisphere, while a spherical wedge of radians (90ð) is sometimes called a ' (two octants); a spherical wedge of radians (360ð) constitutes a complete ball.
The volume of a spherical wedge can be intuitively related to the definition in that while the volume of a ball of radius is given by , the volume a spherical wedge of the same radius is given by
Extrapolating the same principle and considering that the surface area of a sphere is given by , it can be seen that the surface area of the lune corresponding to the same wedge is given by
Hart (2009) states that the "volume of a spherical wedge is to the volume of the sphere as the number of degrees in the [angle of the wedge] is to 360". Hence, and through derivation of the spherical wedge volume formula, it can be concluded that, if is the volume of the sphere and is the volume of a given spherical wedge,
Also, if is the area of a given wedge's lune, and is the area of the wedge's sphere,