plasmapy.formulary.relativity.relativistic_energy(particle: str | Integral | Particle | CustomParticle | Quantity, V: Quantity, *, mass_numb: Integral | None = None, Z: Integral | None = None, m=None, v=None) Quantity[source]

Calculate the sum of the mass energy and kinetic energy of a relativistic body.

The total energy of a relativistic body is:

\[E = γ m c^2,\]

where \(m\) is the rest mass of the body and \(γ\) is its Lorentz_factor.

  • particle (particle-like) – A representation of a particle from which to get the mass of the relativistic body. If it is a Quantity, then it must have units of mass and describe the body’s rest mass.

  • V (Quantity) – The velocity in units convertible to meters per second.

  • mass_numb (integer, keyword-only, optional) – The mass number of an isotope, if not provided to particle.

  • Z (integer, keyword-only, optional) – The charge number of an ion or neutral atom, if not provided to particle.

  • m (object) – Formerly the mass of the body. Will raise a TypeError if provided. Use particle instead.

  • v (object) – Formerly the velocity of the body. Will raise a TypeError if provided. Use V instead.


The total energy of the relativistic body.

Return type:



UnitsWarning – If units are not provided, SI units are assumed.


>>> import astropy.units as u
>>> velocity = 1.4e8 * u.m / u.s
>>> mass = 1 *
>>> relativistic_energy(mass, velocity)
<Quantity 1.01638929e+17 J>
>>> relativistic_energy(mass, 299792458 * u.m / u.s)
<Quantity inf J>
>>> relativistic_energy(1 *, 1.4e8 * u.m / u.s)
<Quantity 1.01638929e+11 J>