The article has only treated the case in which particles have a parabolic relation between energy and momentum, as is the case in non-relativistic mechanics. For particles with energies close to their respective rest mass, the equations of special relativity are applicable. Where single-particle energy is given by:
For this system, the Fermi energy is given by:
where the  equality is only valid in the ultrarelativistic limit, and
The relativistic Fermi gas model is also used for the description of massive white dwarfs which are close to the Chandrasekhar limit. For the ultrarelativistic case, the degeneracy pressure is proportional to .