Relativistic Momentum Calculator
Calculate the relativistic momentum, kinetic energy, and total energy of a particle moving at a significant fraction of the speed of light.
At speeds approaching the speed of light, classical momentum p = mv breaks down. The correct relativistic formula is:
p = γmv = mv / √(1 − v²/c²)
Total energy: E = γmc² Rest energy: E₀ = mc² Kinetic energy: KE = (γ − 1)mc² Energy-momentum relation: E² = (pc)² + (mc²)²
Where:
- p = Relativistic momentum (kg·m/s)
- γ = Lorentz factor = 1/√(1 − v²/c²)
- m = Rest mass (kg)
- v = Velocity
- c = Speed of light = 2.998 × 10⁸ m/s
Particle rest masses:
- Electron: m_e = 9.109 × 10⁻³¹ kg = 0.511 MeV/c²
- Proton: m_p = 1.673 × 10⁻²⁷ kg = 938.3 MeV/c²
- Neutron: m_n = 1.675 × 10⁻²⁷ kg = 939.6 MeV/c²
Why does momentum diverge as v → c? As γ → ∞, the momentum and energy diverge. This is why you can never accelerate a massive particle to the speed of light — it would require infinite energy.
Photons (massless particles): Photons have m = 0 but carry momentum p = E/c = h/λ (de Broglie). They always travel at exactly c.