Speed of Light Calculator

No massive object or information can travel faster than c. However, some phenomena can appear to exceed c: phase velocity in certain media, the 'scissors effect' of crossing laser beams, and the recession velocity of distant galaxies in an expanding universe (which can exceed c for galaxies beyond the Hubble radius). None of these transmit information faster than c.

Light interacts with electrons in the glass medium: photons are absorbed and re-emitted by atoms, creating a slight delay. The macroscopic effect is that the phase of the electromagnetic wave propagates more slowly. The photons themselves always travel at c between interactions; the refractive index describes the net slowing of the wave phase.

A light-year is the distance light travels in one Julian year (365.25 days exactly). = 299,792,458 m/s × 365.25 × 86,400 s = 9,460,730,472,580,800 metres (exact). This is about 9.461 × 10¹⁵ m or 63,241 AU.

The question is surprisingly subtle. If c had changed, it would change the fine structure constant α = e²/(4πε₀ℏc). Astronomical spectroscopy of quasar absorption lines spanning billions of years of cosmic history show no variation in α to one part per million, suggesting c has not changed measurably over cosmic time.

Ole Rømer made the first quantitative measurement in 1676 by observing that the timing of Jupiter's moon Io's eclipses was systematically early or late depending on Earth's distance from Jupiter. Fizeau made the first terrestrial measurement in 1849 using a rotating toothed wheel and a mirror 8 km away, obtaining c ≈ 313,000 km/s. Michelson achieved 299,796 km/s in 1926 using a rotating octagonal mirror.

Maxwell showed in 1865 that the speed of electromagnetic waves is c = 1/√(ε₀μ₀), where ε₀ is the electric permittivity and μ₀ is the magnetic permeability of free space. This not only revealed that light is an electromagnetic wave but also that c is determined by the fundamental electromagnetic constants, suggesting a deep unity in physics.

Special relativity shows that for a massive particle, the relativistic energy is E = γmc² where γ = 1/√(1-v²/c²). As v → c, γ → ∞, so infinite energy would be required to reach c. For massless particles like photons, the only consistent velocity in special relativity is exactly c — they cannot slow down without gaining mass, which they don't have.

GPS satellites orbit at 20,200 km altitude where time runs slightly faster due to weaker gravity (gravitational time dilation: +45 μs/day) but also slightly slower due to orbital velocity (kinematic time dilation: -7 μs/day), net +38 μs/day. Without relativistic corrections, GPS position errors would accumulate at about 10 km per day. The entire GPS system is a real-world test of special and general relativity.

When a charged particle travels through a medium faster than the phase velocity of light in that medium (c/n), it emits Cherenkov radiation — a blue glow analogous to a sonic boom. In water (n=1.333), light travels at 225,000 km/s. Relativistic electrons from beta decay or accelerators can exceed this speed, producing the characteristic blue glow seen in nuclear reactor pools. This is a particle detection principle used in Cherenkov detectors and neutrino telescopes.