steradianin

Steradianin is a unit of solid angle, defined as the solid angle subtended at the center of a sphere by a portion of the sphere's surface whose area is equal to the square of the sphere's radius. The symbol for steradianin is sr. It is a dimensionless quantity, meaning it has no physical units attached to it, but it is useful for describing three-dimensional angles.

The concept of the steradianin arises from the need to measure the extent of a three-dimensional region as seen from a point. Just as a radian measures a planar angle by comparing arc length to radius, a steradianin measures a solid angle by comparing surface area to the square of the radius. A full sphere subtends a solid angle of 4π steradianins at its center.

Steradianin is used in various fields of physics and engineering, particularly in photometry and radiometry, where it is used to describe luminous intensity and radiant intensity. For example, the intensity of light emitted from a source in a particular direction is often expressed in candelas per steradianin. Similarly, the power radiated by a source per unit solid angle is measured in watts per steradianin. In astronomy, steradianin is used to quantify the apparent size of celestial objects.