Redshift Calculator

Redshift z is a dimensionless ratio describing how far a spectral feature has been stretched between emission and detection. Because it is defined as the fractional change in wavelength, z = (lambda_obs - lambda_emit) / lambda_emit, it requires no distance or brightness information - only two wavelengths, one from the laboratory and one from the source spectrum. Identified lines act as rest-frame anchors: hydrogen-alpha at 656.28 nm, Lyman-alpha at 121.57 nm, and the calcium H and K doublet near 396.8 and 393.4 nm. Turning z into a velocity uses the relativistic Doppler relation v = c times ((1+z)^2 - 1) / ((1+z)^2 + 1), which keeps v below c for every finite z. Turning z into a distance instead demands a cosmological model, so this tool integrates the Friedmann equation for a flat Lambda-CDM universe using the Planck 2018 values H0 = 67.4 km/s/Mpc, Omega_M = 0.315 and Omega_Lambda = 0.685. Values span an enormous range. Virgo Cluster galaxies sit near z = 0.004, typical Sloan Digital Sky Survey galaxies fall between 0.05 and 0.7, quasars peak around z = 2 to 3, the JWST record holder JADES-GS-z14-0 is at z = 14.32, and the cosmic microwave background is at z = 1089. Two caveats matter most. Below roughly z = 0.01, peculiar velocities of a few hundred km/s badly contaminate the cosmological signal - Andromeda is blueshifted at -300 km/s and yields no meaningful Hubble distance. Every distance here also inherits the Hubble tension: adopting 73 km/s/Mpc instead of 67.4 shrinks all results by about 8 percent.

Systematic measurement of galaxy redshifts began with Vesto Slipher at Lowell Observatory, who obtained a spectrum of the Andromeda nebula in 1912 showing a blueshift near 300 km/s. By 1917 he had radial velocities for about 25 spiral nebulae, and the great majority were shifted toward the red - a lopsidedness nobody could then explain. Carl Wirtz noted a correlation with apparent faintness in 1924, and Georges Lemaitre derived an expanding solution and a linear velocity-distance relation in 1927. Edwin Hubble, using Cepheid distances and velocities largely gathered by Milton Humason at Mount Wilson, published the observational relation in 1929 with a slope near 500 km/s/Mpc, far too steep because the Cepheid calibration was wrong. Walter Baade corrected that calibration in 1952 by separating stellar populations, roughly halving the constant, and Allan Sandage spent decades pushing it downward again. Interpretation shifted too: the shift is now understood as the stretching of wavelengths by expanding space rather than motion through it. Maarten Schmidt identified the quasar 3C 273 at z = 0.158 in 1963, Penzias and Wilson detected the microwave background in 1965, and large redshift surveys from the CfA survey of the 1980s through 2dF and the Sloan Digital Sky Survey turned redshift into the primary coordinate for mapping cosmic structure.