Mean Free Path Calculator
Gas molecules dart about and collide constantly, and the mean free path is the average distance one travels between collisions. It shrinks as a gas is compressed and stretches as it is rarefied, which is why molecules in a vacuum chamber can cross it without hitting anything. This calculator uses the kinetic theory result to find the mean free path from the absolute temperature, the pressure and the molecular collision diameter. Enter SI units (kelvin, pascals, metres) and read the result in metres and nanometres.
Mean free path formula
lambda = k * T / (sqrt(2) * pi * d^2 * P)
k = 1.380649e-23 J/K (Boltzmann constant)
T = temperature (K), P = pressure (Pa)
d = molecular diameter (m)
The root-two factor accounts for the motion of all colliding molecules. Mean free path rises with temperature and falls with pressure and molecular size squared. The result is given in metres and nanometres.
Kinetic theory context
- The Boltzmann constant is exactly 1.380649 times ten to the minus twenty-third joules per kelvin.
- Air molecules have an effective diameter of roughly 3.7 times ten to the minus tenth metres.
- Air at room conditions has a mean free path of about 68 nanometres.
- In a high vacuum the mean free path can reach metres, enabling molecular beams.
- Mean free path sets the scale for gas viscosity, thermal conductivity and diffusion.
Mean free path: frequently asked questions
What is the mean free path?
The mean free path is the average distance a gas molecule travels between successive collisions with other molecules. It grows when the gas is less dense, so it is large at low pressure and high temperature, and small at high pressure. It governs how heat, momentum and matter diffuse through a gas.
What is the mean free path formula?
From kinetic theory, the mean free path is lambda = k * T / (sqrt(2) * pi * d^2 * P), where k is the Boltzmann constant, T the absolute temperature, d the molecular diameter and P the pressure. The factor of root two accounts for the relative motion of all the molecules, not just one.
What molecular diameter should I enter?
Use the effective collision diameter of the gas molecule in metres. Air molecules are roughly 3.7 times ten to the minus tenth metres across. The diameter is a measured kinetic property of the gas, so it ships here as a user-editable input so you can match your gas species.
Why must temperature be in kelvin and pressure in pascals?
The formula is built from SI quantities, so temperature must be the absolute temperature in kelvin and pressure in pascals. Convert from Celsius by adding 273.15, and from atmospheres by multiplying by 101,325 pascals, before entering the values.
What is the mean free path of air at room conditions?
For air at 25 degrees Celsius (about 298 kelvin) and standard atmospheric pressure, the mean free path is roughly 68 nanometres. In a high vacuum it can stretch to metres or more, which is why vacuum chambers let molecular beams travel in straight lines.
Official sources
- U.S. National Institute of Standards and Technology: Boltzmann constant.
- U.S. National Institute of Standards and Technology: Physical Measurement Laboratory.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.