Relativistic Momentum Calculator

About this calculator

This calculator finds relativistic momentum using p = γ·m·v, where the classical formula p = m·v is scaled by the Lorentz factor γ = 1/√(1−v²/c²). At everyday speeds γ is essentially 1 and the result matches Newtonian mechanics, but as an object's velocity v approaches the speed of light c, γ grows sharply — momentum increases far faster than velocity does, which is part of why no massive object can actually reach light speed: it would take infinite momentum (and energy) to do so.

Particle physicists use this when designing accelerators and analyzing high-energy collisions, where particles routinely travel at a significant fraction of c; astrophysicists use it to model relativistic jets from black holes and the behavior of high-energy cosmic rays; and physics students use it as a core worked example when first studying special relativity. Enter an object's rest mass and velocity (as a fraction of light speed) to get its relativistic momentum.