Steradians

Part of speech: noun

Definitions

1. A unit of measure for solid angles in three-dimensional space, where one steradian corresponds to the angle formed at the center of a sphere by an area equal to the square of the sphere's radius
2. This measure defines the ratio of the area on the surface of a sphere to the radius squared, thus quantifying spatial angles
3. In geometric terms, one steradian is the solid angle that encloses an area on a sphere equal to the square of its radius, facilitating calculations in three-dimensional geometry

Etymology: "Steradians" is the plural of "steradian", the SI unit of solid angle, and the singular is a compound built from "stereo-", from Greek "stereos" meaning solid, and "radian", the unit of plane angle. Where a radian measures the angle subtended by an arc equal to the radius of a circle, the steradian extends that idea into three dimensions: it measures the solid angle subtended by a patch of area equal to the square of the radius on a sphere's surface. The name therefore records both ideas at once. A flat angle is measured in radians, and a cone-shaped or three-dimensional angle needs a "solid" counterpart, so the prefix was attached to the existing unit. Because the steradian is a full sphere's worth of angle divided into roughly 12.57 units (4π), it is useful in fields such as optics, radiometry and astronomy, where light spreads out over three-dimensional directions.