Relativistic Kinetic Energy Calculator

Calculate relativistic kinetic energy: KE = (gamma - 1) * m0 * c^2, which reduces to 0.5mv^2 at low speeds.

kg
m/s

Relativistic KE

116,253,787,752,619,490.0000 J

Classical KE (comparison)36,396,020,000,000,000.0000 J
Relativistic / Classical3.1941

Relativistic KE vs Rest Mass

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Formule

## Relativistic Kinetic Energy At high speeds, the classical KE formula (0.5mv^2) underestimates the true kinetic energy. ### Formula **KE = (gamma - 1) * m0 * c^2** This approaches 0.5 m0 v^2 for v much less than c, and grows without bound as v approaches c.

Exemple Résolu

1 kg at 0.9c.

  1. 01gamma = 2.294
  2. 02KE = (2.294 - 1) * 1 * (2.998e8)^2
  3. 03KE = 1.294 * 8.988e16
  4. 04KE = 1.163e17 J
  5. 05Classical: 0.5 * 1 * (2.698e8)^2 = 3.640e16 J
  6. 06Relativistic is 3.2x larger