Root Mean Square Speed Calculator: Ideal Gas Mol...

What is Root Mean Square Speed?

Root Mean Square (RMS) speed is the square root of the average squared speed of gas molecules. It is derived from the Kinetic Theory of Gases and relates to the temperature and molar mass of the gas. It represents the most statistically significant measure of molecular speed in a gas sample.

💨 RMS Speed Calculator

Use our free calculator for instant, accurate results.

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📐 Formula

v_rms = √(3RT/M)

R = 8.314 J/(mol·K) (gas constant), T = temperature (Kelvin), M = molar mass (kg/mol). Convert g/mol to kg/mol by dividing by 1000.

📝 Worked Example

RMS speed of N₂ (M=0.028 kg/mol) at 25°C (T=298K):
v_rms = √(3 × 8.314 × 298 / 0.028)
v_rms = √(265,248) = 515 m/s

📝 How to Use the Calculator

Select GasChoose from common gases (N₂, O₂, H₂, CO₂) or enter molar mass manually.

Enter TemperatureTemperature in Celsius or Kelvin.

CalculateView RMS speed, average speed, and most probable speed.

Compare GasesSee how lighter gases (H₂) move much faster than heavier ones (Xe) at the same temperature.

❓ FAQ

What is the difference between RMS speed, average speed, and most probable speed?

For a Maxwell-Boltzmann distribution: v_rms > v_avg > v_mp. v_rms = √(3RT/M), v_avg = √(8RT/πM), v_mp = √(2RT/M).

Why do lighter gases effuse faster?

Graham's Law of Effusion: rate ∝ 1/√M. H₂ (M=2) effuses 4× faster than O₂ (M=32) at the same temperature.