Mean Free Path Calculator
Enter molecular diameter, pressure and temperature to compute the mean free path of gas molecules.
Input Data
Results
At a glance:The mean free path λ is the average distance a molecule travels in a gas before colliding with another molecule. For identical hard spheres it is λ = k_B·T / (√2·π·d²·p), with k_B the Boltzmann constant, T temperature, d molecular diameter and p pressure. It increases with temperature (more volume, fewer collisions per distance) and decreases with pressure and molecule size. At atmospheric pressure λ is only tens of nanometres; in high vacuum it can be metres, which is why vacuum systems behave differently.
Formula
Mean free path: λ = k_B·T / (√2·π·d²·p)
$$\lambda = \frac{1}{\sqrt{2}\,\pi d^{2} n}$$$$\lambda = \frac{k_B T}{\sqrt{2}\,\pi d^{2} p}$$$$z = \frac{\bar{v}}{\lambda}$$How to Use
- Enter the molecular diameter d (nm).
- Enter the pressure p (Pa).
- Enter the temperature T (K).
- The calculator returns the mean free path λ.
Case Studies
Air at STP
d ≈ 0.37 nm, p = 101325 Pa, T = 273 K.
λ ≈ 6.6×10⁻⁸ m (≈66 nm).
Collisions are extremely frequent near atmospheric pressure.
FAQ
Why does mean free path increase in a vacuum?
λ is inversely proportional to pressure: as p drops, molecules are farther apart and collisions are rarer, so the average distance between collisions grows. In ultra-high vacuum λ can exceed the size of the container.
Does temperature really affect it?
Yes, λ ∝ T at fixed pressure because the gas occupies more volume when hotter, lowering the number density of molecules.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.