Enter the molar mass and the temperature of the gas into the calculator to determine the root mean square molecular speed.

Molecular Speed Formula

The following formula is used to calculate molecular speed. 

V = SQRT ( 3*R*T / M)
  • Where V is the root mean square molecular speed (m/s)
  • R is the gas constant (8.3145 J/mol/K)
  • T is the temperature (k)
  • M is the molar mass kg/mol

To calculate a molecular speed, multiply 3 times the gas constant times the temperature, divide by the molar mass, then take the square root of this result.

What is molecular speed?

Molecular speed is a measure of the average velocity of a group of particles within a gas.

According to Kinetic Molecular Theory, all gas particles are at a random motion and velocity when their temperature is above 0, so it’s impossible to know any particle’s exact velocity, but the average velocity of all particles can be calculated.

How to calculate molecular speed?

Example Problem:

The following example problem outlines the steps and information required to calculate molecular speed.

First, determine the temperature of the gas. In this example, the gas has a temperature of 500 degrees Kelvin.

Next, determine the molar mass of the gas. In this example, the molar mass is equal to .0023 kg /mol.

Finally, using the formula above, along with the gas constant, calculate the molecular speed.

V = SQRT ( 3*R*T / M)

V = SQRT ( 3*8.3145*500 / .0023)

V = 2328.62 m/s