Calculate the root-mean-square (RMS) velocity of gas particles based on temperature and molar mass.
Last updated: March 2026 | By ForgeCalc Engineering
Root-mean-square (RMS) velocity is a measure of the speed of particles in a gas. Because gas particles move in random directions with a distribution of speeds, the average velocity is zero. RMS velocity provides a useful average speed that directly relates to the kinetic energy and temperature of the gas.
According to the kinetic molecular theory, the average kinetic energy of gas molecules is proportional to the absolute temperature (in Kelvin). This means that at a given temperature, lighter molecules move faster on average than heavier ones.
Where:
• v_rms is the RMS velocity (m/s)
• R is the ideal gas constant (8.314 J/(mol·K))
• T is the absolute temperature (K)
• M is the molar mass of the gas (kg/mol)
RMS velocity is used because it is directly related to the average kinetic energy (KE = 1/2 m v²). The average speed is slightly lower than the RMS speed in a Maxwell-Boltzmann distribution.
At 25°C, the RMS velocity of air molecules (mostly N₂ and O₂) is approximately 500 m/s (over 1,100 mph), which is faster than the speed of sound.
Hydrogen is the lightest gas. At atmospheric temperatures, its RMS velocity is high enough that some molecules reach escape velocity (11.2 km/s), allowing them to leak into space over time.
It's a probability distribution that describes the speeds of particles in an ideal gas at a given temperature. It shows that while most particles move near the average speed, some move very slowly and some move very fast.
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