The SI unit of solid angle, representing a cone with a surface area equal to the square of its radius.The steradian is the SI unit of solid angle, the three-dimensional analogue of the ordinary radian. Just as a radian measures an angle in a plane by the ratio of arc length to radius, a steradian measures a cone of directions in space by the ratio of the area it cuts out on a sphere to the square of the sphere's radius. One steradian corresponds to a cone that, with its apex at the center of a sphere, intercepts a patch of surface area equal to the radius squared. Since the total surface area of a sphere is 4πr², a full sphere subtends 4π steradians, about 12.57.
The term 'steradian' was introduced in the late 19th century, with the name proposed by the French physicist and mathematician Joseph Plateau in 1875, though the concept had been used earlier. It was formally adopted as an SI derived unit in 1960.
Imagine a point source of light at the center of a sphere. The solid angle it illuminates is the area of the sphere's surface that the light hits, divided by the square of the sphere's radius. If that area equals r², the solid angle is exactly one steradian. This definition makes solid angle dimensionless, though it is given the unit name 'steradian' for clarity. In practice, you compute solid angles by integrating over angular coordinates, often in spherical coordinates, where an infinitesimal solid angle is sin(θ) dθ dφ.
Steradians are essential in photometry and radiometry for quantifying luminous intensity (candela is lumens per steradian), in antenna design for beam solid angle, and in computer graphics for calculating light falloff and field-of-view.
A typical human eye's field of view covers roughly 2–3 steradians, which is only about a fifth of the full sphere.
