PHYSICS / RELATIVISTIC ENERGY
Calculate kinetic energy from rest mass and speed using the special-relativistic energy relation.
METHOD / WORKED EXAMPLE
Relativistic kinetic energy measures the motion-dependent energy above mc squared and approaches the classical result only when speed is far below c.
WORKED DEFAULT
For an electron rest mass of 9.10938e-31 kg at 0.8c, gamma is 1.6667 and kinetic energy is about 5.46e-14 J; the classical half-mv-squared value is lower.
READ THE RESULT
Use joules as the primary SI result and compare the classical metric only to judge approximation error. Near light speed, the classical equation increasingly understates the required energy.
ASSUMPTIONS AND LIMITS
Rest mass is invariant, the object moves in an inertial frame, and gravity or interactions do not change the modeled energy.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
COMMON QUESTIONS
The classical expression is the low-speed approximation to relativistic kinetic energy. As beta grows, gamma introduces increasingly important higher-order terms, so one-half mv squared understates the energy. The page shows a classical comparison to expose that divergence, not to offer two interchangeable answers for precision work.
No. This calculator uses invariant rest mass and places all speed dependence in gamma, matching modern relativistic notation. Older sources sometimes describe relativistic mass as gamma times rest mass, but mixing that convention with this equation can double-count gamma and produce an incorrect kinetic energy.
Not by itself. It gives the kinetic energy of one modeled particle or object at one speed. Accelerator power also depends on particle rate, efficiency, field configuration, losses, duty cycle, and beam dynamics. Convert and aggregate only after defining those engineering quantities and their units.
RELATED TOOLS
Use boundary
Subtract rest energy from total relativistic energy after calculating gamma from the entered speed fraction. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
K = (gamma - 1)mc^2