Maxwell distribution | Vose Software

Maxwell distribution

Format: Maxwell(a)


The Maxwell distribution, sometimes known as the Maxwell–Boltzmann, distribution, describes particle speeds in gases, where the particles do not constantly interact with each other but move freely between short collisions.



The Maxwell–Boltzmann distribution applies to ideal gases close to thermodynamic equilibrium. It forms the basis of the kinetic theory of gases, which explains many fundamental gas properties, including pressure and diffusion.


The a parameter only changes the scale. The distribution always has the same shape.

Named after James Clerk Maxwell and Ludwig Boltzmann.

The distribution is the magnitude of a 3-dimensional vector whose components are independent and normally distributed with mean 0 and standard deviation a :


Thus, the Maxwell and Chi Squared distributions are related as follows:



ModelRisk functions added to Microsoft Excel for the Maxwell distribution

VoseMaxwell generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseMaxwellObject constructs a distribution object for this distribution.

VoseMaxwellProb returns the probability density or cumulative distribution function for this distribution.

VoseMaxwellProb10 returns the log10 of the probability density or cumulative distribution function.

VoseMaxwellFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseMaxwellFitObject constructs a distribution object of this distribution fitted to data.

VoseMaxwellFitP returns the parameters of this distribution fitted to data.


Maxwell distribution equations