Relativistic Energy Calculator (E=γmc²)

From mass and speed (or velocity ratio β), compute the special-relativity total energy E=γmc², rest energy, kinetic energy, relativistic momentum, and the Lorentz factor γ.

Input

Enter a mass and a speed (or velocity ratio β) to compute the special-relativity total energy E=γmc² and related quantities.

Mass m

Enter the rest mass in kilograms (for example, an electron is about 9.109×10⁻³¹ kg).

Speed input method

Choose whether to enter the velocity ratio β or the velocity v in meters per second.

Velocity ratio β

× c

Enter a value from 0 up to but below 1 (β=v/c). Closer to 1 means stronger relativistic effects.

Result

Total energy E=γmc²

934.931434MeV

In joules: 1.4979e-10 J

Rest energy mc²

560.95886 MeV

Kinetic energy (γ−1)mc²

373.972574 MeV

Relativistic momentum γmv

3.9972e-19 kg·m/s

Lorentz factor γ

1.666667

E=γmc², E0=mc², K=(γ−1)mc², p=γmv, γ=1/√(1−β²). The speed of light c is 299792458 m/s.

How it works

Total energy is computed as E=γmc², where γ is the Lorentz factor, m is the mass, and c is the speed of light (299792458 m/s).
The Lorentz factor is γ=1/√(1−β²), where β is the velocity ratio v/c. As β approaches 1, γ grows rapidly.
Rest energy is E0=mc², kinetic energy is K=(γ−1)mc², and relativistic momentum is p=γmv.
Energies are shown in both J (joules) and MeV (mega-electronvolts), converted using 1 MeV ≒ 1.602176634×10⁻¹³ J.
Inputs that reach or exceed the speed of light (β of 1 or more) are not allowed.

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