Mean Free Path Calculator: Gas Molecules and Par...
Calculate the mean free path of molecules in a gas. Understand how pressure, temperature, and molecular size affect how far a molecule travels before colliding.
What is Mean Free Path?
Mean free path (λ) is the average distance a gas molecule travels between consecutive collisions. It determines thermal conductivity, viscosity, and diffusion in gases. In vacuum technology, it determines whether gas flow is viscous (λ << pipe diameter) or molecular (λ >> pipe diameter).
💨 Mean Free Path Calculator
Free calculator for instant results.
📐 Formula
λ = kT / (√2 × π × d² × P)
k = Boltzmann constant (1.38×10⁻²³ J/K), T = temperature (K), d = molecular diameter (m), P = pressure (Pa).
📝 Worked Example
Air at room temperature (T=293K, P=101325 Pa), d_N₂ ≈ 3.7×10⁻¹⁰ m:
λ = (1.38×10⁻²³ × 293) / (√2 × π × (3.7×10⁻¹⁰)² × 101325)
λ ≈ 68 nm = 0.068 μm
📝 How to Use
❓ FAQ
How does pressure affect mean free path?
Mean free path is inversely proportional to pressure. At vacuum (low P), λ becomes very long. In high vacuum (10⁻⁶ Pa), λ can exceed 100 km!
What is the Knudsen number?
Kn = λ/L (L = characteristic length). Kn << 1: continuum flow. Kn >> 1: molecular flow (each molecule acts independently). Critical for microfluidics and vacuum design.
Veer Kumavat
Founder & AuthorVeer is a 14-year-old student from Nashik, Maharashtra, who built SciFi Calculators to help students worldwide master STEM subjects. He is passionate about making complex science and math problems accessible through intuitive digital tools.