Cosmological Redshift Calculator
Compute the cosmological redshift (z), recession velocity, or distance of a galaxy from its observed vs. rest wavelength. Essential for astronomers and physics students analyzing spectral data from distant objects.
About this calculator
Cosmological redshift occurs when light from a distant galaxy is stretched to longer wavelengths as the universe expands. The redshift parameter z is defined as z = (λ_obs − λ_rest) / λ_rest, where λ_obs is the observed wavelength and λ_rest is the rest (emitted) wavelength. A positive z means the galaxy is moving away. For small redshifts, the recession velocity is approximated as v = c × z, where c ≈ 299,792.458 km/s. Using Hubble's Law, the distance to the galaxy is estimated as d = v / H₀, where H₀ is the Hubble constant (typically ~70 km/s/Mpc). Together these three relations connect a simple spectral measurement to fundamental cosmological quantities.
How to use
Suppose a hydrogen emission line with a rest wavelength of 656.3 nm is observed at 700.0 nm. Step 1 — Enter 700.0 nm as the observed wavelength and 656.3 nm as the rest wavelength. Step 2 — Select 'Redshift': z = (700.0 − 656.3) / 656.3 = 43.7 / 656.3 ≈ 0.0666. Step 3 — Select 'Velocity': v = 299,792.458 × 0.0666 ≈ 19,966 km/s. Step 4 — With H₀ = 70 km/s/Mpc, select 'Distance': d = 19,966 / 70 ≈ 285 Mpc. The galaxy lies roughly 285 megaparsecs away.
Frequently asked questions
What does a cosmological redshift value of z = 1 actually mean for a galaxy?
A redshift of z = 1 means the observed wavelength is exactly twice the emitted wavelength — the light has been stretched by 100%. This does not mean the galaxy was moving at the speed of light when it emitted the light; rather, the fabric of space itself expanded by a factor of 2 between emission and observation. At z = 1, the galaxy is roughly 6.7 billion light-years away in comoving distance. Recession velocities derived from Hubble's Law become unreliable at such large redshifts, requiring full cosmological models.
How is redshift different from the Doppler effect used for nearby objects?
The classical Doppler effect describes frequency shifts caused by the relative motion of a source through space and works well for stars and galaxies in our cosmic neighbourhood (z ≪ 1). Cosmological redshift, however, is caused by the expansion of space itself stretching photon wavelengths during their journey. For z greater than about 0.1, the simple Doppler formula overestimates recession velocity and a relativistic or full cosmological treatment is needed. The calculator's velocity output uses the linear Hubble approximation, best suited for modest redshifts.
Why do astronomers use the Hubble constant to convert recession velocity to distance?
Hubble's Law (v = H₀ × d) is an empirical relationship showing that, on large scales, galaxies recede faster the farther they are — a direct consequence of uniform cosmic expansion. Dividing a galaxy's recession velocity by H₀ (in km/s/Mpc) yields its distance in megaparsecs. The value of H₀ is currently measured at roughly 67–73 km/s/Mpc, and the uncertainty (the 'Hubble tension') is an active research topic. Choosing the right H₀ matters: a 5 km/s/Mpc difference shifts a calculated distance by several percent.