Free · Physics models
Ideal Gas Molecular Speed Statistics
Compare RMS, mean and most-probable molecular speeds for a Maxwell gas.
- 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
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
At 300 K with M = 0.032 kg/mol and the rounded R = 8.314 J/(mol·K), RMS speed is about 483.561 m/s.
vrms = √(3RT/M); vmean = √(8RT/(πM)); vmost probable = √(2RT/M).
Worked example
Enter these known values and leave the other values blank.
- Temperature (T)
- 300 K
- Molar gas constant (R)
- 8.314 J/(mol·K)
- Molar mass (M)
- .032 kg/mol
- Root mean square velocity (υᵣₘₛ)
- 483.56 m/s
- Average velocity (υₐᵥₑ)
- 445.51 m/s
- Most probable molecular speed
- 394.826 m/s
Assumptions and limitations
- Maxwell–Boltzmann distribution for an equilibrium ideal gas. Molar mass is in kg/mol and temperature is absolute.
- The third speed is the most probable speed, rather than the median; its label is corrected accordingly.
- The adjustable default gas constant is rounded to 8.314 J/(mol·K). Preset molar masses are approximate.
- 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.