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A spherical cap is the region of a sphere that lies above or below a given plane. It is defined by a circle not passing through the center of the sphere. The area A of a spherical cap is given by $A = 2\pi Rh$, where $R$ is the sphere's radius and $h$ is the height of the cap.

A spherical lune is the surface on a sphere bounded by two half-great circles that share endpoints. Its area is proportional to the angle between the two half-circles and the radius of the sphere squared. The area A of a spherical lune can be expressed as $A = 2\theta R^2$, where $\theta$ is the angle in radians and $R$ is the sphere's radius.

A spherical polygon is formed by a sequence of points on the surface of a sphere, connected by great circle arcs. Each interior angle of a spherical polygon exceeds the corresponding angle of a flat polygon, and the sum of its interior angles is greater than $(n-2) imes 180$ degrees, where $n$ is the number of sides.

A spherical triangle is a figure on the surface of a sphere, bounded by three great circle arcs which are the intersection of three planes that intersect the sphere. Properties include having the sum of its angles exceeding 180 degrees and being curved, unlike planar triangles.