RMS Speed Calculator Formula

Understand the math behind the rms speed calculator. Each variable explained with a worked example.

Use the RMS Speed Calculator

Formulas Used

RMS Speed

v_rms = sqrt(3 * 8.314 * temp / molar_mass_kg)

Variables

VariableDescriptionDefault
tempTemperature (T)(K)298
molar_mass_kgMolar Mass(kg/mol)0.028

How It Works

Root-Mean-Square Speed

Formula

v_rms = √(3RT / M)

Where:

  • v_rms = root-mean-square speed (m/s)
  • R = 8.314 J/(mol·K)
  • T = temperature (K)
  • M = molar mass (kg/mol)

    • RMS speed is slightly higher than the average molecular speed due to the squaring in the averaging.

    Worked Example

    Calculate the RMS speed of N₂ molecules (M = 0.028 kg/mol) at 298 K.

    temp = 298molar_mass_kg = 0.028
    1. 01v_rms = √(3RT/M)
    2. 02v_rms = √(3 × 8.314 × 298 / 0.028)
    3. 03v_rms = √(7434.6 / 0.028)
    4. 04v_rms = √(265521)
    5. 05v_rms = 515.3 m/s

    Ready to run the numbers?

    Open RMS Speed Calculator