The solid angle is that fraction of the surface of a sphere that a particular object covers, as seen by an observer at the sphere’s centre. For a small region with area Δa, the numerical value of the solid angle is:
ΔΩ = Δa/r^{2}
where r is the radius of the sphere. A physical representation of the solid angle is shown in the following diagram:


For an observer at O, the galaxy will cover a small fraction of the surface of a sphere. The galaxy has a solid angle given by ΔΩ. 
Although the solid angle is a dimensionless quantity, it is usually expressed in units of steradians (sr). The solid angle is often a function of direction.
As an example, a sphere has a solid angle of 4π≃12.57 sr, a factor that appears in the formula for the surface area of a sphere (radius r):
SA = 4πr^{2}
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