Redshift Calculator

Calculate cosmological redshift, recession velocity, and comoving distance of a distant astronomical object using Hubble's Law and special relativity.

REDSHIFT (z)
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Recession Velocity
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v / c ratio
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Approx Distance (Mpc)
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Light Travel Time (Gyr)
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What Is Redshift?

Redshift is the phenomenon where electromagnetic radiation from an object is shifted toward longer wavelengths (toward the red end of the spectrum). In cosmology, redshift occurs because the expansion of the universe stretches the wavelength of light as it travels across vast distances. The redshift value (z) directly indicates how much the universe has expanded since the light was emitted.

Edwin Hubble's 1929 discovery that galaxies exhibit redshifts proportional to their distances was the first observational evidence for the expanding universe. Today, redshift is the primary tool for measuring cosmic distances and mapping the large-scale structure of the universe.

Redshift Formulas

z = (λobserved - λrest) / λrest
v = c × ((z+1)² - 1) / ((z+1)² + 1) (relativistic)
d = v / H0 (Hubble's Law, for small z)

Notable Redshift Values

ObjectRedshift (z)Distance (Gly)Lookback Time
Andromeda Galaxy-0.001 (blueshift)2.5 Mly2.5 Myr
Virgo Cluster0.00454 Mly54 Myr
Distant Quasar2.0~10 Gly~10 Gyr
Early Galaxy (JWST)13.2~13.4 Gly~13.4 Gyr
CMB Radiation1089~13.8 Gly~13.8 Gyr

Types of Redshift

  • Cosmological redshift: Caused by the expansion of space itself stretching light wavelengths. Dominates for distant galaxies.
  • Doppler redshift: Caused by relative motion of source and observer. Applies to nearby objects and peculiar velocities.
  • Gravitational redshift: Caused by light climbing out of a gravitational well (predicted by general relativity). Observed near massive objects like neutron stars and black holes.

Frequently Asked Questions

Can redshift be greater than 1? Does that mean faster than light?

Yes, redshift can be much greater than 1 (the most distant observed galaxies have z > 10). This does not violate relativity because the recession velocity is due to the expansion of space itself, not motion through space. The relativistic Doppler formula correctly handles this: even at z = infinity, the velocity asymptotically approaches c but never exceeds it in the special relativity formula. In general relativistic cosmology, superluminal recession velocities are allowed because they represent the rate of space expansion.

What is the Hubble constant?

The Hubble constant (H0) describes the current rate of expansion of the universe, typically measured in km/s/Mpc. Current measurements give values around 67-73 km/s/Mpc, with a notable tension between different measurement methods. It means that for every megaparsec (3.26 million light-years) of distance, galaxies recede approximately 70 km/s faster.

How is redshift measured?

Astronomers compare spectral lines (absorption or emission features at specific wavelengths) from distant objects to known laboratory wavelengths. The fractional shift in these lines gives the redshift z directly. Common lines used include hydrogen alpha (656.3 nm), calcium H and K lines, and the Lyman alpha line (121.6 nm).