Steradian

The steradian is the SI derived unit of solid angle. One steradian subtends an area equal to the square of a sphere’s radius on its surface.

Solid angle: A three-dimensional angular measure describing the extent of a region of space as seen from a point. The steradian is the SI unit used to measure this quantity.
Spherical surface area: The area of a sphere’s surface, equal to four times pi times its radius squared. Dividing a spherical patch’s area by radius squared gives its solid angle in steradians.
Radiant intensity: Radiant power emitted per unit solid angle in a specified direction. Its denominator is measured in steradians, linking source power to angular spread.
Degree (angle): A plane-angle unit equal to one three-hundred-sixtieth of a full turn. Degrees measure planar spread, whereas steradians measure spread across directions in three dimensions.
Radian: The SI derived unit of plane angle, defined by an arc length equal to a circle’s radius. Its arc-to-radius definition parallels the steradian’s area-to-radius-squared definition.
Solid angle of a cone: The solid angle enclosed by a cone with a specified half-angle. It shows how a steradian measure follows from a cone’s footprint on a sphere.
Radiance: Radiant power per projected area per unit solid angle. Steradians quantify the directional part of this central radiometric quantity.
Square degree: A non-SI unit of solid angle based on the square of one degree. It measures the same kind of quantity as the steradian but uses a different scale.
Sphere: The set of points in three-dimensional space at a fixed distance from a center. The unit’s definition measures a patch on a sphere centered at the angle’s vertex.
Differential solid angle: An infinitesimal element of solid angle, commonly written as dΩ. Integrating these elements over directions produces a solid angle measured in steradians.

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SI derived unitBroader topic: It shows that a named derived unit can also have dimension one.