Mean Free Path and Knudsen Number Calculator
Estimate hard-sphere gas mean free path, collision time and dimensionless Knudsen number.
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Result
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Calculation steps
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How to calculate
Use the dilute hard-sphere ideal-gas collision model and the same physical length basis for λ and device scale.
λ=kBT/(√2 π d² P); Kn=λ/L; mean molecular speed=√(8RT/(πM))
Worked example
At fixed gas and temperature, halving pressure doubles mean free path and Knudsen number.
Assumptions and input details
Collision diameter is an effective entered parameter, not inferred from molecular identity. Dilute ideal hard spheres and characteristic geometry; no real-gas transport correction or universal continuum-validity certification. Mean collision time uses mean speed as an approximate kinetic measure.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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