where is the Planck function, is the azimuthal angle, is the polar angle, and is a differential element of solid angle. The units are J Hz-1 m-2 s-1. For emission from an antenna, the observed flux density is weighted by antenna pattern,
(2)
where is the modified antenna pattern. If the source is large compared to the beam, is roughly constant over the beam, so
(3)
where is the beam solid angle. If the source is small compared to the beam,
(4)
The radio astronomical unit of flux is the Jansky.
is the Planck function,
is the azimuthal angle,
is the polar angle, and 
is a differential element of solid angle. The units are J Hz-1 m-2 s-1. 
is the modified antenna pattern. If the source is large compared to the beam, 
is the beam solid angle. If the source is small compared to the beam,
