The Knudsen number can be related to the Mach number and the Reynolds number.
Using the dynamic viscosity
with the average molecule speed (from Maxwell–Boltzmann distribution)
the mean free path is determined as follows:
Dividing through by L (some characteristic length), the Knudsen number is obtained:
where
:  is the average molecular speed from the Maxwell–Boltzmann distribution [L T],
: T is the thermodynamic temperature [θ],
: μ is the dynamic viscosity [M L T],
: m is the molecular mass [M],
: k is the Boltzmann constant [M L T θ],
:  is the density [M L].
The dimensionless Mach number can be written as
where the speed of sound is given by
where
: U is the freestream speed [L T],
: R is the Universal gas constant (in SI, 8.314 47215 J K mol) [M L T θ mol],
: M is the molar mass [M mol],
:  is the ratio of specific heats [1].
The dimensionless Reynolds number can be written as
Dividing the Mach number by the Reynolds number:
and by multiplying by  yields the Knudsen number:
The Mach, Reynolds and Knudsen numbers are therefore related by