Mean Free Path Calculator — Gas Molecules
The mean free path (λ) is the average distance a gas molecule travels between successive collisions. It depends on temperature, pressure and molecular size. This calculator uses the hard-sphere kinetic-theory formula for seven common gases, or any custom molecular diameter.
Gas
°C
kPa
Average distance a molecule travels between collisions
- 1
Temperature in kelvin
T = 20 + 273.15 = 293.15 - 2
Pressure in pascals
P = 101.325 × 1 000 = 101,325 - 3
Mean free path λ (m): k_B × T ÷ (√2 × π × d² × P)
6.567 × 10^-8k_B = 1.381 × 10⁻²³ J/K; d is the molecular collision diameter. - 4
λ converted to nanometres
6.567 × 10^-8 × 10⁹ = 65.67
How does this calculator work?
λ = k_B T / (√2 π d² P). Enter temperature (°C), pressure (kPa) and gas type to get the mean free path in nanometres. At standard conditions, air molecules travel about 68 nm between collisions. Lower pressure or higher temperature increases the mean free path proportionally.
Formula
How this is calculated
Kinetic theory models gas molecules as rigid spheres moving randomly. When two identical spheres of diameter d approach each other, their centres must come within d to collide, giving an effective collision cross-section of π d². A given molecule sweeps out a cylinder of cross-section √2 π d² per unit time (the √2 factor arises from averaging over the Maxwell–Boltzmann speed distribution of the target molecules). The mean free path is therefore λ = 1 / (√2 π d² n), where n = P / (k_B T) is the number density from the ideal-gas law. Substituting gives the displayed formula.
Molecular diameters used here are kinetic (collision) diameters from experimental viscosity data — they differ slightly from covalent radii. The formula assumes the ideal-gas limit (dilute gas, elastic collisions, no intermolecular attractions), which holds well at pressures below a few hundred atmospheres and well above the critical temperature.
At standard conditions (20 °C, 101 kPa) the mean free path of air molecules is approximately 68 nm — about 200 times the molecular diameter. Reducing pressure by a factor of 1 000 (to ~100 Pa, a rough vacuum) raises λ to ~68 µm. This is why vacuum systems require pressures below ~1 Pa to stop gas-phase heat conduction.
Frequently asked questions
It decreases proportionally: λ ∝ 1/P. Doubling the pressure halves the mean free path because there are twice as many molecules per unit volume, so collisions happen sooner.
At constant pressure, higher temperature means lower number density (n = P / k_B T), so molecules are farther apart on average. λ ∝ T at constant P.
It comes from averaging the relative speed between colliding molecules over the Maxwell–Boltzmann distribution. The relative speed is √2 times the average speed, so the collision rate is √2 times higher than if all other molecules were stationary.
TG we-Calculate Editorial Team. (2026). Mean Free Path Calculator — Gas Molecules [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/mean-free-path-calculator
TG we-Calculate Editorial Team. "Mean Free Path Calculator — Gas Molecules." TG we-Calculate. 2026. https://we-calculate.com/calculator/mean-free-path-calculator.
TG we-Calculate Editorial Team, "Mean Free Path Calculator — Gas Molecules," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/mean-free-path-calculator
@misc{wecalculate_mean_free_path_calculator, title = {Mean Free Path Calculator — Gas Molecules}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/mean-free-path-calculator}}, year = {2026}, note = {TG we-Calculate} }
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