Fermions are subatomic particles that have odd, half-integral angular momentum (¹/₂, ³/_{2, etc.}), and obey Fermi-Dirac statistics. Fermi-Dirac statistics deals with the energy distribution of fermions. Theory proposes that all matter is composed of fundamental fermions, and that fermions obey the Pauli exclusion principle, which forbids more than one fermion from occupying the same quantum state. This principle explains the buildup of electrons in an atom in successive orbitals. Fermions are produced and annihilated in particle-antiparticle pairs.

Fermions include leptons (Electrons, muons), baryons ( neutrons, protons, lambda particles),
and nuclei of odd mass number such as helium-3.

The Fermi-Dirac distribution equation which is used to compute the average number of fermions in a particular energy state was developed in 1926 by the physicists Enrico Fermi and P.A.M. Dirac.
number(fermions) = 1 / ( e^x  + 1)

Where e is the base of the natural logarithms, and x = y + energy divided by Boltzman's Constant * temperature.

Note that the Fermi-Dirac distribution equation is very similar to the Bose-Einstein distribution equation which is used to compute the average number of bosons in a particular energy state.
number(fermions) = 1 / ( e^x  - 1)

Where e is the base of the natural logarithms, and x = y + energy divided by Boltzman's Constant * temperature.

At high temperatures and low concentrations, both of these distribution laws tend toward the classical particle distribution law.
number(particles) = A*e^x

In Fermi-Dirac and  Bose-Einstein statistics "y" is a function of temperature and particle concentration,.
In the classical particle distribution law "y" = 1.