Cosmological Redshift Calculator
Computes cosmological redshift, recession velocity, comoving distance, or the Hubble time from redshift z and the Hubble constant. Ideal for astronomy students and researchers analyzing galaxy observations.
About this calculator
Cosmological redshift z describes how much the universe has expanded since light left a distant source: z = (λ_obs − λ_emit) / λ_emit, equivalently the scale factor ratio a_obs/a_emit = 1 + z. For small redshifts (z ≪ 1), Hubble's law gives the recession velocity v ≈ H₀ × d, where H₀ is the Hubble constant (≈ 70 km/s/Mpc today). Inverting this, the comoving distance is d = c × z / H₀ in Mpc. The recession velocity is v = c × z (in km/s when c = 299,792.458 km/s). The Hubble time — an estimate of the age of the universe — is t_H = 9.78 × 10⁹ / H₀ years. These are all first-order approximations; a full cosmological model requires integrating over the expansion history, but these formulas are accurate for z ≲ 0.3.
How to use
A galaxy has measured redshift z = 0.05 and you use H₀ = 70 km/s/Mpc. To find distance: d = 299,792.458 × 0.05 / 70 ≈ 214.1 Mpc. To find recession velocity: v = 299,792.458 × 0.05 ≈ 14,990 km/s. To find the Hubble time: t_H = 9.78 × 10⁹ / 70 ≈ 13.97 billion years. Enter redshift = 0.05 and Hubble constant = 70, then switch between calculation types to reproduce each result. For the scale factor, the calculator returns 1 + z = 1.05.
Frequently asked questions
What does cosmological redshift tell us about the distance of a galaxy?
Cosmological redshift arises because the universe is expanding: photons traveling through space are stretched along with the fabric of spacetime, increasing their wavelength. A higher redshift z means the light was emitted when the universe was more compressed, implying both greater distance and look-back time. For z ≪ 1, Hubble's law d = cz/H₀ gives a straightforward distance estimate. For larger redshifts, a full cosmological model (specifying matter, dark energy, and curvature densities) is needed to convert z to a proper comoving distance accurately.
How is the Hubble constant used in calculating cosmological distances?
The Hubble constant H₀ (measured in km/s/Mpc) describes the current rate at which the universe expands: every megaparsec of distance corresponds to an additional H₀ km/s of recession velocity. Dividing a galaxy's recession velocity by H₀ gives its approximate distance. Its inverse, the Hubble time t_H = 1/H₀ ≈ 9.78 × 10⁹/H₀ years, sets a rough upper bound on the age of the universe. There is currently a 'Hubble tension' — different measurement methods give slightly different values of H₀, around 67–73 km/s/Mpc — which is one of the biggest open questions in cosmology.
Why is cosmological redshift different from the Doppler redshift?
The Doppler redshift results from relative motion through space between source and observer and is described by the relativistic Doppler formula. Cosmological redshift, by contrast, arises from the expansion of space itself: the photon's wavelength is stretched as it travels through an expanding universe, regardless of any local peculiar velocity. Galaxies beyond the Hubble radius can have recession velocities greater than c without violating special relativity, because it is space itself expanding rather than objects moving through space. At low redshifts the two effects are mathematically similar, but their physical interpretations and the corrections needed at high z differ fundamentally.