steradiankaari

Steradiankaari, or steradian in Finnish, is the SI unit of solid angle used to quantify the apparent size of an object or surface from a given point in three-dimensional space. It is the three-dimensional analogue of the radian, but for angles subtended on a sphere rather than along a line.

Formally, the solid angle Ω is defined as the ratio of the surface area A on a sphere of radius r subtended by the object to r^2: Ω = A / r^2. For a unit sphere (r = 1), Ω equals the area A. The steradian is the unit of this measure, denoted by sr. The entire sphere subtends 4π steradians, so 4π sr corresponds to a full 360-degree sweep around a point.

In terms of practical conversions, one steradian is equivalent to approximately 3282.806 square degrees, since 1 sr = (180/π)^2 deg^2. Consequently, a full sphere equals about 12.5664 sr or roughly 41,253 deg^2. A common small-angle approximation for a circular aperture with angular radius θ (in radians) is Ω ≈ π θ^2. The exact solid angle of a circular cap of radius θ is Ω = 2π (1 − cos θ). In spherical coordinates, the differential solid angle is dΩ = sin θ dθ dφ.

Steradians are used across physics and astronomy to express quantities such as radiance, flux through a surface, and telescope field of view. They are considered a unit of measure for a dimensionless quantity, since they describe an angular extent rather than a physical length, and the term steradiankaari is the Finnish-language designation for this concept.