Relativistic Energy Calculator — E = mc²
Calculate rest energy, relativistic kinetic energy, and total energy at high speeds. Covers E = mc², Lorentz factor, and why mass increases with velocity.
E = mc² is probably the most famous equation in physics, but most people only know half the story. It describes rest energy — the energy locked up in mass at zero velocity. The full relativistic picture includes kinetic energy and shows that objects get heavier as they approach the speed of light, requiring infinite energy to actually reach c. That's why nothing with mass can hit light speed.
The CalcHub relativistic energy calculator computes rest energy, total relativistic energy, and the Lorentz factor for any mass and velocity.
The Key Equations
Rest energy: E₀ = mc² Total relativistic energy: E = γmc² Relativistic kinetic energy: KE = (γ − 1)mc² Lorentz factor: γ = 1 / √(1 − v²/c²)Where c = 2.998 × 10⁸ m/s
How the Lorentz Factor Grows
| v/c | γ | KE increase over classical |
|---|---|---|
| 0.1 (10% of c) | 1.005 | 0.5% |
| 0.5 | 1.155 | 15.5% |
| 0.9 | 2.294 | 129.4% |
| 0.99 | 7.089 | Massive |
| 0.999 | 22.37 | Enormous |
| 0.9999 | 70.7 | Extraordinary |
How Much Energy Is in Mass?
E₀ = mc²For 1 kg of anything: E = 1 × (3 × 10⁸)² = 9 × 10¹⁶ J = 90 petajoules
For comparison: the bomb dropped on Hiroshima released about 6.3 × 10¹³ J — from converting just 0.7 g of mass to energy.
Can we ever convert all mass to energy?
In matter-antimatter annihilation, yes — a particle and its antiparticle annihilate completely into photons. In fission and fusion, only a tiny fraction (0.1–0.7%) of mass converts to energy. Even so, that fraction produces enormous energy because c² is so large.
Why does relativistic mass increase near the speed of light?
In modern physics, the preferred view is that mass stays constant (rest mass) and what increases is the difficulty of accelerating — represented by the Lorentz factor γ. Applying F = ma to relativistic particles requires using relativistic momentum p = γmv, which grows without bound as v → c.
Does E = mc² apply to photons?
Photons have zero rest mass, so E₀ = 0 for them. But they still have energy: E = hf (Planck's equation), and momentum p = E/c. The full energy-momentum relation E² = (mc²)² + (pc)² unifies both massive and massless particles.