Steradian

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The steradian (ste from Greek stereos, solid) is the SI derived unit of solid angle, and the 3-dimensional equivalent of the radian. The symbol is sr.

The steradian is defined as "the solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r²." Since the surface area of this sphere is 4πr², then the definition implies that a sphere measures 4π steradians. A steradian can also be called a squared radian.

A steradian also equal to the spherical area of a polygon having an angle excess of 1 radian, to 1/4&pi of a complete sphere, or to 57.2957795 degrees squared.

Full solid angle is 4π sr. That is, a sphere measures 4π sr. A hemisphere measures 2π sr. Cut a hemisphere into two equal lunes, and each one will measure π sr. Cut one of these lunes into a pair of equal surfaces, then each one will be an octant of a sphere, and will measure π/2 sr.

The steradian was formerly an SI supplementary unit, but this category was abolished from the SI system in 1995.