How to Use Mean Free Path Calculator
- Pick input mode — diameter & n, or diameter, P, T.
- Enter diameter — pm, nm, or Å.
- Enter remaining values — n in m⁻³ or P & T in lab units.
- Read λ in metres alongside the derived number density.
Formula & Theory - Mean Free Path Calculator
λ = 1 / (√2 · π · d² · n)
Ideal-gas density (used when P,T are provided):
n = P / (kB · T)
kB = 1.380649 × 10⁻²³ J/K| Symbol | Meaning |
|---|---|
| λ | Mean free path (m) |
| d | Molecular diameter (m) |
| n | Number density (m⁻³) |
| P | Pressure (Pa) |
| T | Absolute temperature (K) |
Assumptions and Limits
- Hard-sphere kinetic theory; real gases have softer potentials.
- Single-species gas; mixtures need a weighted sum.
Use Cases for Mean Free Path Calculator
- Vacuum science — Confirm molecular vs. viscous flow regimes.
- Sputter coating — Estimate λ to choose chamber pressure.
- Atmospheric physics — Compare λ across altitudes.
- Education — Visualise kinetic theory predictions.
The Mean Free Path Calculator quickly bridges molecular diameter and macroscopic state.