Particles Velocity Calculator

Background.

The air in a quiet room is anything but still. At room temperature its nitrogen molecules travel at roughly 500 metres per second — faster than a cruising airliner and faster than sound — and they collide with one another billions of times a second, so no molecule keeps one speed or direction for long. What stays fixed, for a gas held at a steady temperature, is the spread of speeds across the whole population: the Maxwell–Boltzmann distribution.

That distribution has no single speed, so it is summarised three ways. The most probable speed is the peak of the curve, the speed more molecules have than any other. The mean speed is the ordinary average. The root-mean-square speed is the square root of the average squared speed, and it is the one tied directly to kinetic energy and therefore to temperature and pressure. Because the curve has a long tail of fast molecules, the three always come in the same order and ratio: the mean is about 1.128 times the most probable speed, and the rms about 1.225 times.

All three depend on just two things, absolute temperature and molar mass. Speed grows with the square root of temperature, so doubling the kelvin temperature makes molecules about 41% faster. It falls with the square root of molar mass, which is why light gases are so quick: helium at 300 K has an rms speed of about 1,367 m/s, more than two and a half times nitrogen's. That difference is one reason a helium balloon goes soft sooner than one blown up with air.

The figures describe an ideal gas in equilibrium — a vast population of molecules, not any single one of them, and not a directed beam or a plasma out of balance.

What is particles velocity calculator?

Molecular speed here means three statistical measures of how fast the molecules of an ideal gas move at a given temperature: the most probable speed, √(2RT/M); the mean speed, √(8RT/πM); and the root-mean-square speed, √(3RT/M). Each is in metres per second and summarises the whole population of molecules in a gas at equilibrium, whose individual speeds range widely above and below these values.

How to use this calculator.

1. 01Enter Absolute temperature in kelvin. Add 273.15 to a Celsius reading: 0 °C is 273.15 K and 27 °C is 300.15 K.
2. 02Enter Molar mass in grams per mole. Nitrogen (N₂) is 28.0134, oxygen (O₂) about 32.00, helium 4.0026 and carbon dioxide about 44.01.
3. 03For air, entering its average molar mass of about 28.97 g/mol gives a representative figure, but each gas in a mixture has its own distribution, and oxygen molecules run slightly slower than nitrogen ones.
4. 04Use the rms speed for anything involving energy or pressure, the mean speed for collision and effusion rates, and the most probable speed to locate the peak of the distribution.

The formula.

All three speeds share the form √(c × R × T ÷ M), with c = 2 for the most probable speed, 8/π for the mean and 3 for the root-mean-square. R is the molar gas constant, 8.31446261815324 J/(mol·K), exact since the 2019 redefinition of the SI; T is the temperature in kelvin; M is the molar mass in kilograms per mole, which is why the g/mol figure you enter is divided by 1,000. The rms form comes from setting the average kinetic energy per mole, ½Mv²rms, equal to (3/2)RT. Because each c is fixed, the ratios between the three never change: 1 : 1.128 : 1.225. Temperature and molar mass enter only as the ratio T/M, so quadrupling the temperature has the same effect as switching to a gas one quarter as heavy: both double every speed.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Chemistry 2e, 2019. Chapters 4, 9, and 12. Retrieved 2026-08-06.
2. [2]NIST. CODATA 2022. Molar gas constant. Retrieved 2026-08-06.
3. [3]OpenStax, Rice University. University Physics, 2016. Volume 1 mechanics and Volume 2 thermodynamics. Retrieved 2026-08-06.