Enter the mass and temperature of any gas into the calculator to determine the average velocity of the particles contained in that gas.

Particles Velocity Formula

The following equation is used to calculate the average particle velocity of a gas at a certain temperature.

v = (8*k*T/(π*m))^{1/2}
  • Where v is the average velocity (m/s)
  • k is the Boltzman Consant = 1.3806*10^-23 J/K
  • T is the temperature (Kelvin)
  • m is the mass in atomic mass units

To calculate the particle velocity, divide the product of 8 times the temperature times the Boltzmann constant by pi times the mass, then raise the result to the one-half power.

Particle Velocity Definition

This is also known as the Maxwell-Boltzmann Equation or distribution. This represents the average velocity of gas as a whole. Since temperature if the average kinetic energy of a gas, then calculating the velocity of any single particle using temperature would be impossible. Instead, we can calculate the average velocity since the temperature is also an average.

The larger the mass, the less the velocity, and vice versa with regard to temperature. Which makes logical sense. As temperature increases, kinetic energy increases.

How to calculate particle velocity?

How to calculate a particle velocity?

  1. First, determine the temperature of the gas.

    Measure the temperature in Kelvin of the gas being analyzed.

  2. Next, determine the mass of the gas.

    Measure the total mass of the gas in AMUs.

  3. Finally, calculate the particle velocity.

    Using the formula above, along with the Boltzman constant, calculate the particle velocity.


What is a particle velocity?

Particle velocity is often defined as the average speed of movement of particles within an ideal gas.

Particles Velocity Calculator