The Maxwell (or Maxwell-Boltzmann) distribution gives the distribution of speeds of molecules in thermal equilibrium as given by statistical mechanics. Defining

a = √ k/Tm

where k is the Boltzmann constant, T is the temperature, m is the mass of a molecule, and letting x denote the speed a molecule, the probability and cumulative distributions over the range [0, ∞]

Mathematically, the Maxwell–Boltzmann distribution is the chi distribution with three degrees of freedom (the components of the velocity vector in Euclidean space), with a scale parameter measuring speeds in units proportional to the square root of
T/m

The Maxwell Distribution app has iPad, iPhone and Apple Watch versions.