Cosmological Redshift Calculator

Cosmological Redshift

Redshift quantifies how much the wavelength of light from a distant source stretches by the time it reaches us. The defining relation is z = (λ_obs - λ_em) / λ_em, where λ_em is the emitted wavelength and λ_obs the wavelength we observe. Equivalently, 1 + z = a(t₀) / a(t_em), where a(t) is the cosmic scale factor — the redshift directly measures how much the universe has expanded since the light was emitted.

Edwin Hubble's 1929 observations of galaxy redshifts versus distance gave the first evidence that the universe is expanding, leading to the Big Bang model. The cosmic microwave background, emitted at the surface of last scattering, has z ≈ 1100, meaning the universe has expanded by a factor of about 1100 since then.

Applications

Cosmological redshift is the workhorse of observational cosmology: it sets distances to galaxies and quasars, calibrates the Hubble constant H₀, and times the cosmic expansion history. LIGO has detected neutron-star mergers with z near 0.01, where electromagnetic counterparts (kilonovae) let us cross-check the gravitational-wave standard siren with the optical redshift.

FAQ

Is cosmological redshift a Doppler effect? Not exactly — it comes from the stretching of space itself between emission and detection, not from local relative motion through space.

Can z be negative? Yes — that would be a blueshift, common for nearby galaxies whose peculiar motion dominates over the cosmic expansion (Andromeda is approaching us).

What is the highest known redshift? As of the mid-2020s, JWST has confirmed galaxies up to z ≈ 13-14, seen as they were only about 300 million years after the Big Bang.