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Relativistic Kinetic Energy — result sheet
Calculate kinetic energy from mass and speed as a fraction of the speed of light using the Lorentz factor.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Relativistic kinetic energy KE = (gamma - 1) m c^2, where gamma = 1 / sqrt(1 - beta^2), beta is speed divided by c, and c = 299792458 m/s.
This calculator uses the special-relativistic Lorentz factor to calculate kinetic energy from invariant rest mass and a subluminal speed fraction. It returns joules and exajoules and does not model acceleration, radiation, collisions, or propulsion.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mass — kg; Finite nonnegative invariant rest mass in kilograms.; minimum 0; maximum 1000000000
- Speed as a fraction of c — c; Finite speed fraction from zero up to, but not including, c.; minimum 0; maximum 0.999999
Worked example
| Input | Value |
|---|---|
| Mass | 1 |
| Speed as a fraction of c | 0.6 |
A 1 kg mass at 0.6c has relativistic kinetic energy of about 2.2468879468e16 J.
Assumptions and limits
- Mass is a finite nonnegative invariant rest mass in kilograms, and speedFraction is a finite nonnegative ratio below one.
- The motion is represented by one speed magnitude in an inertial special-relativity model; beta is speed divided by the exact vacuum speed of light.
- The result is kinetic energy only. Acceleration history, radiation, collisions, fields, energy recovery, and equipment or mission advice are outside the calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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