# Mean Free Path Calculator

URL: https://speedycalculator.com/calculators/physics/mean-free-path/
Last updated: 2026-10-30

> The mean free path calculator finds the average distance a gas molecule travels between collisions from its kinetic diameter, the pressure and the temperature.

## Inputs

- Gas
- Kinetic diameter (nm, Å, pm)
- Pressure (kPa, Pa, mbar, Torr, atm)
- Temperature (K, °C, °F)

## Results

- Mean free path λ
- Number density

## Formula

```
λ = k_B·T / (√2·π·d²·p)
```

## Explanation

In air at sea level a molecule travels only about 68 nm between collisions – but in a vacuum chamber it can be metres. The mean free path decides whether gases behave as continuous fluids.

### How to use the Mean Free Path Calculator

- **Gas**
- **Kinetic diameter**
- **Pressure**
- **Temperature**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the gas (or enter its kinetic diameter), the pressure and temperature.

### Tips

- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.

### Common mistakes to avoid

- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).

### Inputs explained

FieldWhat to enterGasChoose one: Air, Nitrogen, Oxygen, Argon …Kinetic diameterUnits: nm, Å, pmPressureUnits: kPa, Pa, mbar, Torr, atmTemperatureUnits: K, °C, °F

### Example values

How the main result changes when **Kinetic diameter** changes and everything else stays at the example values above:

Kinetic diameter (nm)Mean free path λ (nm)0.18267.85610.27367.85610.36467.85610.45567.85610.54667.85610.72867.8561

## Worked example

Inputs — Gas: Air; Pressure: 101.325 kPa; Temperature: 293.15 K.

Results — **Mean free path λ = 67.85611 nm**; Number density = 2.5035e25 m⁻³.

## Key terms

- **Mean free path**: Average distance between collisions.

## FAQ

**What is the mean free path in air?**
About 68 nm at sea level and 20 °C.

**How does it depend on pressure?**
Inversely – halving the pressure doubles it.

**What is the kinetic diameter?**
An effective size of a molecule for collisions.

**Why does it matter for vacuum systems?**
Above about 1 cm, gas behaves as free molecules.

**What formula does the Mean Free Path Calculator use?**
λ = k_B·T / (√2·π·d²·p).


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)