Relativistic Kinetic Energy Calculator

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The rest mass of the object. For an electron, use 9.109e-31 kg or 0.511 MeV/c2. For a proton, use 1.673e-27 kg or 938.3 MeV/c2.
The velocity of the object. In units of c (fraction of the speed of light), values must be between 0 and 1.
Show the classical (Newtonian) kinetic energy alongside the relativistic result so you can see how much they diverge at high speeds.
Relativistic Kinetic EnergyHighly relativistic
106.0 fJ

KE = (gamma - 1) x m0 x c2

Lorentz Factor (gamma)2.294157
Total Relativistic Energy187.8 fJ
Rest Energy (E0)81.87 fJ
Relativistic Momentum5.639e-22 kg m/s
Classical KE (for comparison)33.16 fJ
Classical KE Error68.71%
Kinetic Energy in MeV0.6613MeV
Velocity (fraction of c)0.9c
0.9 c
Non-relativistic<0.1Mildly relativistic0.1-0.5Relativistic0.5-0.9Highly relativistic0.9-0.99Ultra-relativistic0.99+

At 90.00% of c: KE = 106.0 fJ, total energy = 187.8 fJ

  • At 90.00% of c the Lorentz factor is 2.2942, meaning the moving mass is effectively 2.2942x heavier than at rest.
  • The classical formula underestimates the true kinetic energy by 68.7%, which grows rapidly as velocity approaches c.
  • Total relativistic energy includes rest energy (E0 = m0c2) plus kinetic energy: even a stationary object stores enormous energy in its mass.

Next stepTry increasing velocity toward 0.99c or above to see how rapidly the Lorentz factor and energy diverge from classical predictions.

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