Free 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
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.
Example Calculation
1 kg at 0.9c.
- 01gamma = 2.294
- 02KE = (2.294 - 1) * 1 * (2.998e8)^2
- 03KE = 1.294 * 8.988e16
- 04KE = 1.163e17 J
- 05Classical: 0.5 * 1 * (2.698e8)^2 = 3.640e16 J
- 06Relativistic is 3.2x larger
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