Kinetic Energy (Relativistic)

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Equation / Last modified by KurtHeckman on 2019/03/01 00:22
vCalc.Kinetic Energy (Relativistic)

The Relativistic Kinetic Energy calculator compute the kinetic energy of an object accounting for speeds where relativity has a measurable effect.

INSTRUCTIONS: Choose units and enter the following:

  • (M) This is the mass of the object
  • (V) This is the velocity of the object

Kinetic Energy (EK):  The calculator returns the kinetic energy in Joules.  However, this can be automatically converted to compatible units via the pull-down menu.

Energy Calculators:

The Math / Science

The formula for relativistic kinetic energy is:

         `E_K = (m•c²)/sqrt(1 - "v²/c²") - m•c²`


This equation computes the relativistic kinetic energy EK for a mass traveling at a relativistic velocity.  If the speed of the mass, m, is a significant portion of the speed of light, c, it is necessary to use the this equation to compute the Kinetic Energy.


Relativistic kinetic energy is energy possessed by any object due to motion when the effect of relativity is accounted for.  For most objects traveling at small fractions of the speed of light, relativistic effects are generally insignificant for practical application.  However, when the speed of a mass is a significant fraction of the speed of light, then it is necessary to account for relativistic effects to produce usable calculations of kinetic energy.

The equation for Kinetic Energy, EK bears resemblance to the famous Mass-Energy Equivalence equation, E = mc2 introduced by Einstein, which includes both kinetic energy and rest mass energy.  The equation for kinetic energy alone is the deduction of the rest mass energy component from this total.

The kinetic energy is equivalent to the work required to accelerate an object from rest to the speed, v.   Therefore, as can be seen from the equation, as v approaches the the speed of light, the resulting energy approaches infinity.  Thus, an infinite amount of work (an apparent impossibility) is required to accelerate a mass to the speed of light.

See also