For the 3D uniform Fermi gas, with fermions of spin-½, the number of particles as a function of the energy  is obtained by substituting the Fermi energy by a variable energy :
from which the density of states (number of energy states per energy per volume)  can be obtained. It can be calculated by differentiating the number of particles with respect to the energy:
This result provides an alternative way to calculate the total energy of a Fermi sphere of  fermions (which occupy all  energy states within the Fermi sphere):