Redshift Calculator

Redshift measures how much a known spectral feature is observed at a longer wavelength than its laboratory value. It is defined as z = (observed wavelength - rest wavelength) / rest wavelength, equivalently observed divided by rest minus one. A positive value is redshift, while a negative value is blueshift. Because the ratio is dimensionless, both wavelengths may use nanometres, angstroms, or another unit as long as they match. For motion along the line of sight, this calculator converts redshift to radial velocity with the special-relativistic Doppler relation. The exact expression uses beta = ((1 + z) squared - 1) / ((1 + z) squared + 1), then velocity = beta times the speed of light. At very small redshift this approaches the familiar approximation velocity = cz. The relativistic form prevents inferred speed from exceeding light speed as redshift grows. A distance estimate is then produced with Hubble's law, distance = velocity / H0. The default Hubble constant is 70 kilometres per second per megaparsec, a convenient rounded value for educational estimates. This means a galaxy one megaparsec away participates in cosmic expansion at roughly 70 kilometres per second in the local linear model. Different observational methods and cosmological analyses yield somewhat different H0 values, so the field is editable. Doppler velocity and Hubble-law distance are useful approximations, especially for nearby galaxies moving mainly with cosmic expansion. They are not a complete cosmological distance calculation. At moderate and high redshift, the relationship among redshift, lookback time, comoving distance, luminosity distance, and angular-diameter distance depends on matter density, dark energy, curvature, and the expansion history. Peculiar velocities caused by local gravity can also dominate the Hubble flow for nearby objects. Spectral identification is essential. Astronomers compare recognizable absorption or emission lines such as hydrogen alpha with calibrated rest wavelengths. Measurement uncertainty, line blending, instrument calibration, air versus vacuum wavelength conventions, and incorrect line identification all affect z. Using several lines provides a stronger result than relying on a single feature. Use this calculator for classroom work, quick checks of spectra, and intuition about redshift and recession. Do not use its linear Hubble distance as a precision result for high-redshift cosmology. Professional analysis normally fits a cosmological model and reports the reference frame, wavelength convention, uncertainty, and adopted parameters so another researcher can reproduce the calculation.