Editing Steradian (section)

== Definition ==

A steradian can be defined as the solid angle [[subtended angle|subtended]] at the centre of a [[unit sphere]] by a unit [[area]] (of any shape) on its surface. For a general sphere of [[radius]] {{math|''r''}}, any portion of its surface with area {{math|1=''A'' = ''r''<sup>2</sup>}} subtends one steradian at its centre.<ref>"Steradian", ''McGraw-Hill Dictionary of Scientific and Technical Terms'', fifth edition, Sybil P. Parker, editor in chief. McGraw-Hill, 1997. {{ISBN|0-07-052433-5}}.</ref>

A solid angle in the form of a circular cone is related to the area it cuts out of a sphere:
: <math>\Omega = \frac{A}{r^2}\ \text{sr} \, = \frac{2\pi h}{r}\ \text{sr},</math>
where
*{{math|Ω}} is the solid angle
*{{mvar|A}} is the [[surface area]] of the [[spherical cap]], <math>2\pi rh</math>,
*{{mvar|r}} is the radius of the sphere,
*{{mvar|h}} is the height of the cap, and
*sr is the unit, steradian, sr = rad{{sup|2}}.

Because the surface area {{math|''A''}} of a sphere is {{math|4''πr''<sup>2</sup>}}, the definition implies that a sphere subtends {{math|4''π''}} steradians (≈&nbsp;12.56637&nbsp;sr) at its centre, or that a steradian subtends {{math|1/4''π'' ≈ 0.07958}} of a sphere. By the same argument, the maximum solid angle that can be subtended at any point is {{math|4''π'' sr}}.