Relativistic Total Energy

E = \gamma mc^2 = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}

The total energy of a moving particle, including rest energy and kinetic energy.

Variables

Total energy

Lorentz factor

Allowed values: 1 or more

unitless

Rest mass

Allowed values: greater than 0

Speed of the particle

m/s

Speed of light

Allowed values: greater than 0

m/s

Your notes

0/5000

Constants in this formula

Speed of Light in Vacuum

299,792,458. Exact by definition.

m/s

Other modern physics formulas with the same quantities

Relativistic Momentum (Special Relativity) shares Lorentz factor, Rest mass, Speed of light
Energy-Momentum Relation (Special Relativity) shares Total energy, Rest mass, Speed of light
Lorentz Factor (Special Relativity) shares Lorentz factor, Speed of light
Time Dilation (Special Relativity) shares Lorentz factor, Speed of light
Length Contraction (Special Relativity) shares Lorentz factor, Speed of light
Proper Time (Special Relativity) shares Lorentz factor, Speed of light

Where this formula is listed

Modern Physics formulas, under Special Relativity, alongside Relativistic Velocity Addition, Relativistic Doppler Effect and Relativity of Simultaneity.
In the modern physics list it comes after Mass-Energy Equivalence and before Relativistic Kinetic Energy.
Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Relativistic Total Energy formula?

Relativistic Total Energy is written E = γmc² = mc²/√(1 − v²/c²). The total energy of a moving particle, including rest energy and kinetic energy. It belongs to Modern Physics, under Special Relativity.

What are the units in E = γmc² = mc²/√(1 − v²/c²)?

In SI units, E is total energy, measured in J; γ is lorentz factor (dimensionless); m is rest mass, measured in kg; v is speed of the particle, measured in m/s; c is speed of light, measured in m/s.