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Knudsen Number from Mean Free Path & Length
Calculate the dimensionless ratio of molecular mean free path to a chosen characteristic length, with inverse calculations.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
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Formula and method
A mean free path of 0.0000001 m divided by a characteristic length of 0.001 m gives Kn = 0.0001.
Knudsen number = mean free path ÷ characteristic length
Worked example
Enter these known values and leave the other values blank.
- Molecular mean free path
- .0000001 m
- Characteristic length
- .001 m
- Knudsen number
- 0.0001
Assumptions and limitations
- Mean free path and characteristic length are positive and refer to the same physical problem.
- The numerical ratio is independent of the selected length unit. Choosing a physically appropriate characteristic length remains part of the model.
- The retained message split at Kn = 1 is a coarse length comparison, not a complete continuum, slip, transition or free-molecular regime classification.
Common questions
Does Kn below one guarantee continuum behavior?
No. A ratio below one spans several regimes. The appropriate approximation depends on how small the ratio is and on the problem and boundary conditions.
Can I solve for a length?
Yes. Enter the ratio and either positive length to recover the other.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
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