RMS Speed Calculator — Gas Molecule Velocity
Find how fast gas molecules move at a given temperature. Enter the temperature (°C) and the molar mass of the gas to get the RMS speed, mean speed, most-probable speed, and mean translational kinetic energy per mole.
°C
g/mol
Root-mean-square speed of gas molecules at this temperature
- 1
Temperature in Kelvin
25 + 273.15 = 298.15 - 2
Molar mass in kg/mol
29 ÷ 1000 = 0.029 - 3
3 × R × T
3 × 8.3145 × 298.15 = 7,436.87 - 4
Divide by M (kg/mol)
7,436.87 ÷ 0.029 = 256,443.83 - 5
v_rms = √(3RT/M)
√(256,443.83) = 506.40
How does this calculator work?
Gas molecules at temperature T (K) with molar mass M (kg/mol) have RMS speed v_rms = √(3RT/M), mean speed v_avg = √(8RT/πM), and most-probable speed v_mp = √(2RT/M), where R = 8.314 J/(mol·K). Higher temperature and lower molar mass both give faster molecules.
Formula
How this is calculated
The kinetic theory of gases models molecules as point particles in constant random motion. Their speeds follow the Maxwell–Boltzmann distribution, from which three characteristic speeds are derived. The root-mean-square speed v_rms = √(3RT/M) is the speed of a molecule with the average kinetic energy, and is the most useful for energy calculations. The mean speed v_avg = √(8RT/(πM)) is the straightforward arithmetic average of all molecular speeds. The most-probable speed v_mp = √(2RT/M) is the speed at the peak of the Maxwell–Boltzmann distribution. All three increase with temperature and decrease with molar mass.
In these formulas, R = 8.314 J/(mol·K) is the universal gas constant, T is temperature in kelvin, and M is molar mass in kg/mol. The mean translational kinetic energy per mole is (3/2)RT, independent of the identity of the gas. Temperature is converted from °C to K by adding 273.15.
The model assumes an ideal gas: molecules are non-interacting point masses in thermal equilibrium. Real gases deviate at high pressures or near their boiling points. At very low temperatures or for light gases (H₂, He) quantum corrections may become relevant.
Frequently asked questions
The RMS speed squares and then roots the individual speeds, giving extra weight to the fastest molecules. The mean speed simply averages them. Because the Maxwell–Boltzmann distribution has a long high-speed tail, v_rms > v_avg > v_mp always.
Dry air is roughly 78% N₂ (M = 28), 21% O₂ (M = 32) and 1% Ar (M = 40), giving a weighted average molar mass of about 29 g/mol. Use the exact molar mass for pure gases: H₂ = 2, He = 4, N₂ = 28, CO₂ = 44, Cl₂ = 71.
For an ideal gas, RMS speed depends only on temperature and molar mass, not on pressure. At constant temperature, doubling the pressure doubles the number density but leaves each molecule's speed unchanged.
Also known as
TG we-Calculate Editorial Team. (2026). RMS Speed Calculator — Gas Molecule Velocity [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rms-speed-calculator
TG we-Calculate Editorial Team. "RMS Speed Calculator — Gas Molecule Velocity." TG we-Calculate. 2026. https://we-calculate.com/calculator/rms-speed-calculator.
TG we-Calculate Editorial Team, "RMS Speed Calculator — Gas Molecule Velocity," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rms-speed-calculator
@misc{wecalculate_rms_speed_calculator, title = {RMS Speed Calculator — Gas Molecule Velocity}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rms-speed-calculator}}, year = {2026}, note = {TG we-Calculate} }
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