Mean Free Path Calculator
How far a molecule gets between collisions.
Work out Mean Free Path. How far a molecule gets between collisions. Handles the awkward cases, not just the tidy ones.
N₂ about 370 pm, O₂ 360, H₂ 270, CO₂ 400.
1 atm is 101,325 Pa. Scientific notation works for vacuum work — 1e-3.
Optional — gives the collision frequency.
Mean free path
66.7933 nm
181× the molecule's own diameter
λ = kT / (√2 π d² P). At atmospheric pressure a nitrogen molecule travels about 65 nm between collisions — around 180 times its own diameter, and roughly a billion collisions every second. That is why a smell takes minutes to cross a room even though the molecules are moving at 500 m/s: the journey is a random walk with a step size under a tenth of a micrometre, not a straight line. The path scales inversely with pressure, which is the whole basis of vacuum technology. Once the mean free path exceeds the size of the chamber, molecules fly from wall to wall without meeting each other, and the gas stops behaving like a fluid at all — that is the molecular flow regime.
How the Mean Free Path Calculator works
Enter a molecular diameter, pressure and temperature to get the mean free path and the collision frequency. At atmospheric pressure a nitrogen molecule manages about 65 nanometres and a billion collisions a second, which is why smells travel so slowly.
Also known as: collision frequency calculator · mean free path formula · kinetic theory mean free path · vacuum mean free path calculator
Frequently asked questions
What is the mean free path?
The average distance a molecule travels between collisions: λ = kT / (√2 π d² P). For air at room temperature and pressure it is about 65 nm.
If molecules move at 500 m/s, why do smells take minutes to cross a room?
Because the journey is a random walk, not a straight line. With a step size under a tenth of a micrometre and a billion direction changes a second, net progress is far slower than the speed suggests.
How does pressure affect it?
Inversely and directly — halve the pressure and the mean free path doubles. That relationship is the entire basis of vacuum technology.
What is molecular flow?
The regime where the mean free path exceeds the size of the chamber, so molecules fly from wall to wall without meeting each other. The gas stops behaving like a fluid, which changes how pumps and gauges have to work.
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