Free · Physics models
Ideal Gas Mean Free Path
Estimate the typical molecular travel distance between collisions from temperature, pressure and collision diameter.
- 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.
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Formula and method
At 300 K and 1 atm, a 100 pm collision diameter gives about 920.074 nm with the retained coefficient.
λ = kB T/(√2 π d² p).
Worked example
Enter these known values and leave the other values blank.
- Molecule kinetic diameter
- 100 pm
- Pressure
- 1 atm
- Temperature
- 300 K
- Mean free path
- 920 nm
Assumptions and limitations
- Dilute ideal gas with hard-sphere collisions; diameter is an effective collision diameter.
- The captured coefficient 1.38064852 × 10⁻²³ J/K is retained as a historical approximation. The modern exact SI value is 1.380649 × 10⁻²³ J/K, a relative difference of about 0.000035%.
- Temperature is absolute and pressure and diameter must be positive.
- Enter known quantities and clear the unknown to use available inverse branches. Locks retain supplied values. Consistency messages cover fully visible equations; identities with hidden dependencies may require a manual consistency check. Preset values are illustrative approximations, and unit selectors preserve the underlying quantity.
Common questions
How do I solve for a different quantity?
Clear that quantity and supply enough independent known values. Some outputs are one-way or tied to a selected preset, so they cannot determine every input.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.