Solid angle

A solid angle measures how much of the surrounding space a region subtends at a point. Its value equals the area that region covers on a unit sphere centered at that point.

Steradian: The SI unit of solid angle, equal to the area of one square unit on a unit sphere. It gives the unit-sphere area a standard measurement unit.
Radiant intensity: Radiant power emitted per unit solid angle in a specified direction. It measures how emitted power is distributed across directions.
Plane angle: A measure of the opening between two rays in a plane, commonly expressed in radians. Solid angle extends the same angular idea from a plane to three-dimensional directions.
Angular size: The apparent extent of an object measured as an angle from an observation point. Angular size is a one-dimensional measure; solid angle captures extent across two angular directions.
Full sphere: The entire surface of a sphere centered at a point. It spans all directions and therefore has a solid angle of 4π steradians.
Spherical cap: A region of a sphere bounded by a plane cutting through it. A circular cone cuts a spherical cap whose area determines its solid angle.
Luminance: The luminous intensity emitted or reflected per unit projected area in a direction. Its directional measurement uses solid angle to describe light reaching an observer.
Unit sphere: A sphere of radius one centered at the origin of a coordinate system. Its surface area provides the defining measure for a solid angle.
Projected solid angle: A directional-area measure weighted by the cosine between each direction and a reference axis. Radiation across a surface often depends on this cosine-weighted form rather than solid angle alone.
Hemisphere: Half of a sphere divided by a plane through its center. It occupies half of all directions, or 2π steradians.

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