RMS Speed (v_rms)Chemistry
Root-Mean-Square (RMS) Molecular Speed Calculator (v_rms)
Calculate root-mean-square speed (v_rms), mean velocity (v_avg), and most probable speed (v_mp) in m/s using Maxwell-Boltzmann kinetic molecular theory.
Calculated Result
Root-Mean-Square Speed (v_rms)
1km/h
Calculator Inputs
g/mol
Quick select:
Quick select:
Root-Mean-Square Speed (v_rms)
1km/h
Mean Velocity (v_avg)
1 km/h
Most Probable Speed (v_mp)
1 km/h
Speed in km/h
3.6 km/h
Exact Kinetic Correspondence: The three velocities map the dynamic kinetic spread of the Maxwell-Boltzmann distribution.
Maxwell-Boltzmann Characteristic Velocities
Most Probable v_mp
1 m/s(33%)
Mean Speed v_avg
1 m/s(33%)
RMS Speed v_rms
1 m/s(33%)
Standard physical chemistry and kinetic molecular theory (KMT) velocity calculator.
Calculation Methodology
Root-Mean-Square Speed: v_rms = sqrt( 3 * R * T / M ). Mean Speed: v_avg = sqrt( 8 * R * T / (π * M) ). Most Probable Speed: v_mp = sqrt( 2 * R * T / M ). R = 8.314 J/(mol K); M in kg/mol.
Frequently Asked Questions
Because average molecular kinetic energy directly depends on velocity squared (1/2 m v^2); thus v_rms directly embodies the thermal kinetic temperature of the ensemble.
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