Enter the absolute temperature and the mass of the particle into the calculator to determine the thermal velocity.

Thermal Velocity Formula

The following equation is used to calculate the Thermal Velocity.

Vth = SQRT ( k * T / m)
  • Where Vth is the thermal velocity (m/s)
  • k is the boltzmann constant (1.380649*10^-23 J/K)
  • T is the absolute temperature (K)
  • m is the mass (kg)

To calculate the thermal velocity, take the square root of the Boltzmann constant times the absolute temperature divided by the mass.

What is a Thermal Velocity?


Thermal velocity describes the speed of a particle based on it’s temperature and mass.

How to Calculate Thermal Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Thermal Velocity.

First, determine the absolute temperature. In this example, the absolute temperature is found to be 300K.

Next, determine the mass. For this problem, the mass is found to be .005 kg.

Finally, calculate the Thermal Velocity using the formula above:

Vth = SQRT ( k * T / m)

Vth = SQRT ( 1.380649*10^-23*300 * / .005)

Vth = 9.10159e-10 m/s