Enter the mass (kg) and the velocity (m/s) into the calculator to determine the Relativistic Energy. 

Relativistic Energy Formula

The following equation is used to calculate the Relativistic Energy. 

KE = m*c^2 * (SQRT(1-V^2/C^2)-1)

Variables:

  • Where KE is the Relativistic Energy (Joules)
  • m is the mass (kg) 
  • V is the velocity (m/s) 
  • c is the speed of light (299,792,458 m/s)

How to Calculate Relativistic Energy?

The following two example problems outline the steps and information needed in order to calculate Relativistic Energy.

Example Problem #1:

  1. First, determine the mass (kg). In this example, the mass (kg) is measured to be 95.
  2. Next, determine the velocity (m/s). For this problem, the velocity (m/s) is calculated to be 4.
  3. Finally, calculate the Relativistic Energy using the formula above: 

KE = m*c^2 * (SQRT(1-V^2/C^2)-1) = (Joules)

Inserting the values from above and solving the equation with the imputed values gives: 

KE = 95*299792458^2 * (SQRT(1-4^2/299792458^2)-1)

FAQ

What is Relativistic Energy?

Relativistic Energy refers to the total energy of an object moving at significant fractions of the speed of light. It incorporates both the kinetic energy due to the object’s motion and its rest mass energy, according to the principles of Einstein’s theory of relativity.

Why is the speed of light (c) significant in the formula for Relativistic Energy?

The speed of light (c) is a fundamental constant in physics, representing the maximum speed at which all energy, matter, and information in the universe can travel. In the formula for Relativistic Energy, it sets the scale for how velocities compare to the speed of light, affecting the relativistic effects on mass and energy.

How does Relativistic Energy differ from Classical Kinetic Energy?

Classical Kinetic Energy, given by the formula 1/2 mv^2, assumes that mass remains constant regardless of an object’s speed. However, Relativistic Energy accounts for the fact that an object’s mass increases as its velocity approaches the speed of light, leading to significantly higher energy values at high velocities. This difference becomes especially noticeable at speeds close to the speed of light, where classical mechanics no longer accurately describes physical phenomena.