RMS Molecular Speed Calculator — v = √(3kT/m)

Temperature is molecular motion: hotter gas means faster molecules. The Boltzmann constant k = 1.380649×10⁻²³ J/K is built in.

RMS Molecular Speed Calculator — v = √(3kT/m)

vrms=3kTmv_{rms} = \sqrt{\frac{3kT}{m}}

How to interpret the result

Nitrogen molecules in room-temperature air zip around at ~511 m/s — faster than a passenger jet — but collide billions of times per second, so they go nowhere fast.

Assumptions

  • Ideal gas (point particles, elastic collisions)
  • Temperature in kelvin
  • m is the mass of one molecule