At normal pressures gas acts as a continuous fluid. In near-vacuum, tiny channels or high altitude, molecules travel distances comparable to the system size between collisions and continuum fluid dynamics breaks down.
How to use the Knudsen Number Calculator
- Mean free path
- Mean free path λ
- Gas (kinetic diameter)
- Pressure
- Temperature
- Characteristic length L
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose whether you know the mean free path or want it computed, then enter the characteristic length.
Inputs explained
| Field | What to enter |
|---|---|
| Mean free path | Choose one: Known value, From gas, pressure and temperature |
| Mean free path λ | Units: nm, µm, mm, m |
| Gas (kinetic diameter) | Choose one: Air (N₂/O₂ average), Nitrogen, Oxygen, Argon … |
| Pressure | Units: kPa, Pa, mbar, Torr, atm |
| Temperature | Units: K, °C |
| Characteristic length L | Units: µm, mm, m, nm |
What each result means
- Mean free path = [lam]
- Knudsen number = [lam]÷[Characteristic length L]
Example values
How the main result changes when Mean free path λ changes and everything else stays at the example values above:
| Mean free path λ (nm) | Knudsen number |
|---|---|
| 34 | 0.0679 |
| 51 | 0.0679 |
| 68 | 0.0679 |
| 85 | 0.0679 |
| 102 | 0.0679 |
| 136 | 0.0679 |
Formula
Kn = λ/L, λ = k_B·T / (√2·π·d²·p)
Worked example
Inputs — Mean free path: From gas, pressure and temperature; Gas (kinetic diameter): Air (N₂/O₂ average); Pressure: 101.325 kPa; Temperature: 293.15 K; Characteristic length L: 1 µm.
Results — Mean free path = 67.85611 nm; Knudsen number = 0.06786; Flow regime = Slip flow.
Key terms
- Mean free path
- Average distance between molecular collisions.
Frequently asked questions
What is the mean free path of air at sea level?
About 68 nm.
When is the continuum assumption valid?
For Kn below about 0.01.
Where is high Kn important?
Vacuum systems, MEMS devices and spacecraft re-entry.
How does pressure affect λ?
λ is inversely proportional to pressure.