Knudsen Number Calculator

The Knudsen number is a dimensionless ratio that compares a gas molecule's mean free path with a representative physical length of the system. It is written as Kn = mean free path divided by characteristic length. Mean free path is the average distance a molecule travels between collisions, while characteristic length may be a channel width, particle diameter, nozzle throat, spacecraft dimension, or another scale that controls the flow. Because both quantities use the same unit, their units cancel and the result has no unit. The ratio indicates whether ordinary continuum fluid mechanics is appropriate. For Knudsen numbers below 0.01, intermolecular collisions dominate and the gas normally behaves as a continuum. Between 0.01 and 0.1, slip flow develops and velocity at a solid boundary may no longer be assumed to be exactly zero. From 0.1 to 10, transitional behavior requires rarefied-gas models or kinetic methods. Above 10, collisions with boundaries dominate over molecule-to-molecule collisions and the flow is classified as free molecular. These boundaries are useful engineering conventions rather than abrupt physical changes. Geometry, surface accommodation, temperature gradients, and the accuracy required by a project can shift the modeling decision. The characteristic length must also represent the phenomenon being studied. A microchannel usually uses hydraulic diameter or channel height, while an external-flow problem may use body length. Choosing an unrelated dimension can produce a numerically correct ratio that is physically misleading. Mean free path changes with pressure, temperature, and molecular collision diameter. Lower pressure generally increases mean free path, making rarefaction more important. This explains why vacuum systems, high-altitude vehicles, microelectromechanical devices, aerosol transport, and semiconductor processing often operate outside the continuum regime. Enter both lengths in metres here, or convert them from any common unit first. The calculator divides the values directly, reports the ratio, and applies the standard regime bands. It is useful for an initial model selection, but detailed designs should use property data and boundary conditions appropriate to the actual gas.