Relativistic Kinetic Energy Calculator
Calculate kinetic energy with relativistic corrections for high velocities.
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Enter the rest mass and velocity. The calculator shows both relativistic and classical kinetic energy so you can see the difference.
- Enter rest mass. The mass of the object when stationary.
- Enter velocity. Must be less than the speed of light.
- Read the result. See the relativistic KE with the percentage difference from classical mechanics.
About the Relativistic Kinetic Energy Calculator
At speeds approaching the speed of light, the classical kinetic energy formula (KE = 0.5mv2) significantly underestimates the true kinetic energy. The relativistic formula KE = (gamma - 1)mc2, where gamma is the Lorentz factor, correctly accounts for the increasing effective mass at high velocities. As velocity approaches c, kinetic energy approaches infinity, which is why no massive object can reach the speed of light. Particle accelerators like the LHC routinely deal with relativistic kinetic energies.
Frequently Asked Questions
When does the relativistic correction matter?
The correction becomes significant above about 10% of the speed of light. At 90% of c, relativistic KE is about 1.3 times the classical value.
Why can't anything reach the speed of light?
As velocity approaches c, the Lorentz factor approaches infinity, meaning it would take infinite energy to accelerate a massive object to the speed of light.
What is the Lorentz factor?
The Lorentz factor (gamma) equals 1/sqrt(1 - v2/c2). It quantifies relativistic effects. At low speeds it is nearly 1. At 99% of c it is about 7.09.