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/r²

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 = 4πr²