Speed as a Fraction of c Calculator

About this calculator

In special relativity, speeds are naturally expressed relative to the speed of light, c ≈ 299,792,458 m/s, using the dimensionless ratio β = v/c. This calculator takes any speed and reports β, its equivalent percentage of c, and the Lorentz factor γ = 1/√(1 − β²), the multiplier that governs how much time dilation, length contraction, and relativistic mass increase occur at that speed.

Physicists and astronomers use β and γ constantly: particle accelerators quote beam energies in terms of γ, astrophysicists describe jets from black holes or gamma-ray bursts as “relativistic” when β approaches 1, and GPS satellite clock corrections rely on the same γ factor at far smaller speeds. Because γ grows without bound as v approaches c, this tool makes it easy to see just how close to light speed a given value actually is — for everyday speeds β is vanishingly small and γ is indistinguishable from 1, while for particle-accelerator speeds γ can reach into the thousands.