PHYSICS / RELATIVISTIC MOMENTUM
Calculate relativistic momentum from rest mass and speed, with a classical momentum comparison.
METHOD / WORKED EXAMPLE
Relativistic momentum preserves the conservation framework while correcting classical mv for motion that is no longer slow compared with light.
WORKED DEFAULT
For an electron at 0.8c, gamma is 1.6667, classical momentum is about 2.18e-22 kg m/s, and relativistic momentum is about 3.64e-22 kg m/s.
READ THE RESULT
The result is momentum magnitude along the entered motion. Direction and multi-particle conservation still require a signed vector model and a clearly defined inertial frame.
ASSUMPTIONS AND LIMITS
Rest mass is invariant, motion is represented along one direction, and beta must stay below one.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
COMMON QUESTIONS
As beta approaches one, gamma rises without bound while speed remains below c. Adding energy therefore produces progressively larger momentum and smaller speed increases for an object with rest mass. The equation does not permit the object to cross the light-speed boundary by entering beta equal to or above one.
This page returns a non-negative magnitude based on a non-negative speed fraction. Momentum is physically a vector, so collision or field problems need a chosen axis and signed components. Apply direction separately, or use a vector workflow before adding momenta from multiple particles in one conservation equation.
The ordinary calculator evaluates mv and is appropriate as a low-speed approximation. This tool evaluates gamma-mv and displays the classical value as a comparison. At small beta they nearly agree; at relativistic beta the gamma factor creates a material, physically required difference in momentum and energy accounting.
RELATED TOOLS
Use boundary
Multiply classical momentum by the Lorentz factor required for momentum conservation between inertial frames. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
p = gamma m v