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Ideal Gas Molecular Root Mean Square Speed

Find molecular RMS speed from absolute temperature and molar mass, with retained gas presets, custom mass and reviewed hydrogen and water values.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. 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 and a molar mass of 28 g/mol, molecular RMS speed is about 516.963 m/s in the ideal-gas model.

RMS speed = √(3RT / molar mass in kg/mol)

Worked example

Enter these known values and leave the other values blank.

Gas
Enter custom molar mass
Molar mass (selected mass unit per mol)
28 g /mol
Temperature of gas
300 K
RMS speed
517 m/s

Assumptions and limitations

  • RMS speed is the square root of mean squared molecular speed. It differs from mean speed, most probable speed, bulk flow velocity and sound speed.
  • The default molar gas constant is 8.31446261815324 J/(mol·K). A custom positive value must be consistent with these internal units.
  • The molar-mass selector displays mass per mole; for example 28 in grams means 28 g/mol, or 0.028 kg/mol internally.
  • The seven gas presets retain approximate molar masses, with hydrogen corrected to 2.01588 g/mol and water vapor to 18.0153 g/mol. Use custom mode for a reviewed mixture or isotopic composition.
  • Zero kelvin returns the formal zero-speed limit of this classical equation. Real gases cease to behave as ideal gases near condensation and very low temperatures.
  • The source retains a hidden sound-speed relation using an approximate heat-capacity ratio. The visible RMS result does not require that ratio.

Common questions

Why does a lighter molecule move faster at the same temperature?

In this model RMS speed varies inversely with the square root of molar mass. Reducing molar mass to one quarter doubles RMS speed.

References

Bookify requires a positive molar gas constant for the RMS-speed relation. Bookify corrects the hydrogen and water-vapor molar-mass presets to the NIST WebBook values of 2.01588 and 18.0153 g/mol.

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