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Maxwell–Boltzmann Mean Particle Speed

Calculate maxwell–boltzmann mean particle speed with compatible units, known-value inputs and clearly stated model assumptions.

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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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked inputs, Mean molecular speed is approximately 1027.0045 ms.

vmean = √(8kBT/(πm))

Worked example

Enter these known values and leave the other values blank.

Mass: 6.02214 u
Temperature: 300 K

Mean molecular speed: 1027 m/s

Assumptions and limitations

This is the arithmetic mean molecular speed of a classical Maxwell–Boltzmann gas. It differs from root-mean-square and most probable speeds.
Mass and absolute temperature are positive. The model assumes classical thermal equilibrium and nonrelativistic motion.
Use particle mass, not the molar mass of one mole.
Numerical arithmetic uses 64 significant digits; displayed values are rounded separately. Captured particle-mass and astronomical unit conversions retain their stated approximations.

Common questions

Which inputs and assumptions does this result use?

This is the arithmetic mean molecular speed of a classical Maxwell–Boltzmann gas. It differs from root-mean-square and most probable speeds.

References

Bookify retains the captured physical relationship and inverse controls, while replacing older or rounded constants with the 2022 CODATA values and full-precision π where applicable. Measured constants retain their physical uncertainty.

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