RMS Speed of Gas Molecules Calculator
Gas molecules move at a spread of speeds described by the Maxwell-Boltzmann distribution, and three statistics summarise that spread: the most probable speed, the mean speed and the root-mean-square speed. They depend only on the gas temperature and molar mass. This calculator takes the absolute temperature and the molar mass and returns all three speeds in metres per second. It is a core tool for kinetic theory, diffusion, effusion and understanding why lighter gases move faster and escape atmospheres more easily.
Molecular speed formulas
RMS speed: v_rms = sqrt(3 * R * T / M)
Mean speed: v_mean = sqrt(8 * R * T / (pi * M))
Most probable: v_p = sqrt(2 * R * T / M)
R = 8.314462618 J / (mol * K)
All three speeds scale with the square root of temperature divided by molar mass. The RMS speed is always the largest, then the mean, then the most probable speed, in fixed ratios.
Kinetic theory context
- The molar gas constant R is exactly 8.314462618 joules per mole per kelvin.
- Nitrogen has a molar mass of about 0.028 kilograms per mole.
- Nitrogen at room temperature has an RMS speed near 515 metres per second.
- Lighter gases move faster, which is why hydrogen and helium escape atmospheres readily.
- Convert molar mass from grams per mole to kilograms per mole by dividing by 1,000.
RMS speed of gas: frequently asked questions
What is the root-mean-square speed of a gas?
The root-mean-square (RMS) speed is the square root of the average of the squared molecular speeds in a gas. From kinetic theory it is v_rms = sqrt(3 * R * T / M), where R is the gas constant, T the absolute temperature and M the molar mass. It is the speed associated with the average kinetic energy of the molecules.
How do RMS, mean and most probable speed differ?
All three describe the Maxwell-Boltzmann distribution but weight it differently. The most probable speed is the peak of the distribution, the mean speed is the simple average, and the RMS speed is the largest of the three. Their ratio is fixed: most probable to mean to RMS is sqrt(2) to sqrt(8/pi) to sqrt(3).
What molar mass should I enter?
Enter the molar mass of the gas in kilograms per mole. Nitrogen is 0.028, oxygen 0.032 and hydrogen 0.002 kilograms per mole. Note many tables list grams per mole, so divide by 1,000. Molar mass is a fixed property of the gas, so it is supplied as a user-editable input.
Why does temperature have to be in kelvin?
The kinetic theory formula uses the absolute temperature, which must be in kelvin and starts at absolute zero. Convert from Celsius by adding 273.15. Using Celsius or Fahrenheit directly would give the wrong speed, since the molecular kinetic energy is proportional to absolute temperature.
How fast do air molecules move at room temperature?
Nitrogen molecules in air at about 298 kelvin have an RMS speed near 515 metres per second, faster than the speed of sound. Lighter molecules move faster: hydrogen at the same temperature exceeds 1,900 metres per second, which is why light gases escape planetary atmospheres more readily.
Official sources
- U.S. National Institute of Standards and Technology: Molar gas constant.
- NASA Glenn Research Center: Kinetic theory of gases.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.