Relativistic Energy Particle Calculator

Summary

Enter a particle rest mass and speed (as a fraction of c) to get total relativistic energy, rest energy, kinetic energy, and Lorentz factor.

How it works

1. Enter the particle's rest mass in kg, or select a preset (electron, proton, neutron, muon).
2. Set the velocity β = v/c as a decimal between 0 and 1 (exclusive), or use the slider.
3. The calculator computes the Lorentz factor γ = 1/√(1−β²).
4. Rest energy E₀ = mc² is derived from the mass alone.
5. Total energy E = γmc² and kinetic energy KE = (γ−1)mc² are calculated.
6. Results appear instantly in joules, MeV, and GeV for easy cross-reference.

Use cases

• Estimate the kinetic energy of a cosmic ray proton at near-light speed.
• Compare rest energy and total energy for electrons in a particle accelerator.
• Verify textbook special relativity problems.
• Explore how the Lorentz factor grows as β approaches 1.
• Convert particle energies between joules and electron-volts.
• Understand why rockets cannot reach c — energy diverges as β → 1.

Frequently Asked Questions