Relativistic Energy Momentum Calculator

Explore particle behavior near light speed precisely. Compare total energy, kinetic energy, and momentum easily. See graphs, exports, formulas, and reference values for decisions.

Calculator Inputs

Example Data Table

These sample rows are generated from the same equations used by the calculator, using MeV as the display unit.

Scenario Rest Mass (MeV/c²) β γ Total Energy (MeV) Kinetic Energy (MeV) pc (MeV)

Formula Used

Core Definitions

Let β = v/c, where v is particle speed and c is the speed of light.

γ = 1 / √(1 - β²) E₀ = m₀c²

Momentum and Energy

p = γm₀v E = γm₀c² K = E - E₀ = (γ - 1)m₀c² E² = (pc)² + (m₀c²)²

Derived Outputs

β = pc / E λ = h / p η = 0.5 × ln[(1 + β)/(1 - β)]

Mode Logic

The calculator can solve from velocity, direct momentum, total energy, or kinetic energy.

  • Velocity mode starts with β or v.
  • Momentum mode uses the invariant relation to solve energy.
  • Total energy mode derives γ from E/E₀.
  • Kinetic energy mode first adds rest energy, then solves normally.

How to Use This Calculator

  1. Select the input mode that matches your known quantity.
  2. Enter the particle rest mass and choose the mass unit.
  3. Provide velocity, momentum, total energy, or kinetic energy.
  4. Choose your preferred display unit for energy outputs.
  5. Set graph limits for β if you want a wider comparison curve.
  6. Press the calculate button to show results above the form.
  7. Use CSV or PDF export buttons to save the output summary.

Frequently Asked Questions

1) What does β represent?

β is the particle speed divided by the speed of light. It is dimensionless and must stay below 1 for particles with nonzero rest mass.

2) What does γ tell me?

γ is the Lorentz factor. It shows how strongly relativistic effects grow as speed approaches light speed, affecting total energy, momentum, and time dilation relationships.

3) Why is total energy larger than kinetic energy?

Total energy includes rest energy plus kinetic energy. Kinetic energy measures only motion-related energy above the particle’s rest-energy baseline.

4) Why does the calculator show pc separately?

pc has energy units, making it convenient for the invariant relation E² = (pc)² + (m₀c²)². It helps compare energy and momentum on the same scale.

5) Can I use this for electrons or protons?

Yes. Enter their rest masses in kg, atomic mass units, or energy-based mass units such as MeV/c² or GeV/c².

6) Why is the invariant check useful?

It verifies that the computed values satisfy the relativistic energy-momentum relation. A ratio near 1 indicates the calculations are internally consistent.

7) What is de Broglie wavelength here?

It is λ = h/p. The wavelength becomes smaller as momentum increases, which is important in quantum and particle physics applications.

8) Can this calculator handle photons?

Not directly in this interface. Photons have zero rest mass, so a separate massless-particle setup is better for pure photon energy and momentum work.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.