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# Kinetic Energy (Relativistic)

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 (E _{K}):** The calculator returns the kinetic energy in Joules. However, this can be automatically converted to compatible units via the pull-down menu.

#### Energy Calculators:

- Kinetic Energy (change of velocity) : K = ½⋅m⋅(V
_{1}-V_{2})² - Kinetic Energy: KE= ½⋅m⋅v²
- Relativistic Kinetic Energy
- Mass Energy Equivalent (E = m⋅c²)
- Potential Energy
- Potential Energy of Gravity (two bodies)
- Force of Gravity
- Nuclear Binding Energy (BE)
- Kinetic Molecular Theory is the kinetic energy in gases.
- Plank's Equation

#### The Math / Science

The formula for relativistic kinetic energy is:

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

where:

- E
_{K}is the relativistic kinetic energy - m is the mass
- v is the velocity
- c is the speed of light

This equation computes the relativistic kinetic energy *E _{K}* 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.

#### Definition

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, *E _{K}* bears resemblance to the famous Mass-Energy Equivalence equation, E = mc

^{2}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

**Kinetic Energy (Relativistic)**, references 1 equation/constant.

**Equations and Constants **

**Kinetic Energy (Relativistic)**, is used in 1 calculator.

**Calculators**