The Maxwell (or Maxwell-Boltzmann) distribution gives the distribution of speeds of molecules in thermal equilibrium as given by statistical mechanics. Defining a=sqrt(kT/m), where k is the Stephan-Boltzmann constant, T is the temperature, m is the mass of a molecule, and letting x denote the speed a molecule, the probability distribution over the range x in 0,inf) is

f(x,a) = 1/a^3sqrt(2/pi)x^2exp(-x^2/(2a^2))

Spiegel (1992) and von Seggern (1993) each use slightly different definitions of the constant a.

support 0 ⇐ x ⇐ Inf