Cosmological Redshift Calculator

Doppler shift results from an object's velocity relative to the observer through space. Cosmological redshift results from the expansion of space itself stretching photon wavelengths during their journey. For small velocities (v much less than c) and small distances, they give similar numerical results, but for distant galaxies the cosmological interpretation is physically more appropriate.

The cosmic microwave background has a redshift of about z = 1100. This corresponds to the surface of last scattering — when the universe cooled enough for neutral hydrogen to form (~3,000 K) and photons could travel freely. The universe was about 1,101 times smaller than today. The CMB photons that were emitted at visible/near-infrared wavelengths are now microwave radiation due to this extreme redshift.

Yes. A negative redshift (blueshift, z < 0) means the object is moving toward us. Nearby galaxies can be blueshifted due to their peculiar velocity (local gravitational motions) overcoming the Hubble recession. The Andromeda Galaxy (M31) is blueshifted at z = -0.001 and is approaching the Milky Way at about 110 km/s. It will merge with our galaxy in about 4.5 billion years.

As of 2026, the James Webb Space Telescope has spectroscopically confirmed galaxies at redshifts above z = 13-16, seen less than 300-400 million years after the Big Bang. Photometric redshift candidates (less certain) suggest objects at even higher z. The Gunn-Peterson trough in quasar spectra allows indirect probing to higher redshifts through neutral hydrogen absorption.

Astronomers identify known emission or absorption lines in a galaxy's spectrum (hydrogen Lyman-alpha, Balmer series, calcium H and K lines, etc.) and measure how much their wavelengths have shifted from their known laboratory values. The ratio of shift to rest wavelength gives z directly, independent of any cosmological model.

Photometric redshift (photo-z) estimates the redshift from broad-band photometric measurements in multiple color filters without taking a full spectrum. By comparing the shape of the spectral energy distribution to template galaxy spectra at various redshifts, a statistical estimate of z can be made. It is less accurate than spectroscopic z but can be applied to vastly larger numbers of galaxies from survey data.

The epoch of reionization (roughly z = 6-12) is when the first stars and galaxies formed, producing enough ultraviolet radiation to ionize the neutral hydrogen that had filled the universe since recombination at z = 1100. This era is one of the major targets of JWST and future radio telescopes like the Square Kilometre Array, which will observe the 21 cm neutral hydrogen line from this period.

For z much less than 1, the Hubble approximation v = cz works well. For high redshifts, the actual recession velocity requires integration of the Friedmann equations over the full expansion history. The recession velocity can formally exceed c for the most distant objects, but this is physically meaningful — it represents the rate of increase of proper distance due to space expansion, not motion through space.

The Lyman-alpha forest is a series of absorption lines in quasar spectra, caused by neutral hydrogen clouds at different redshifts between the quasar and Earth. Each cloud absorbs at the Lyman-alpha rest wavelength (121.6 nm) redshifted to the cloud's distance. The density and distribution of these clouds is an important cosmological probe, tracing large-scale structure and the intergalactic medium.