Knudsen Number Calculator
Calculate the Knudsen number, the ratio that tells you whether a gas flow behaves as a continuum or must be treated at the molecular level.
What the Knudsen number is
The Knudsen number (Kn) is a dimensionless ratio used in fluid mechanics to determine whether a gas can be treated as a continuous fluid or must be analyzed as individual colliding molecules. It matters in microfluidics, vacuum systems, high-altitude aerodynamics, and nanotechnology.
The formula
The Knudsen number is calculated as Kn = λ / L, where λ is the mean free path of the gas molecules (the average distance a molecule travels between collisions) and L is a characteristic physical length of the system, such as a pore or channel width.
As a rule of thumb: Kn < 0.01 indicates continuum flow (standard fluid dynamics applies), 0.01-0.1 is the slip-flow regime, 0.1-10 is the transition regime, and Kn > 10 is free-molecular flow. This calculator is intended for general engineering and educational reference.