How this calculator works
Redshift compares a spectral feature observed at the telescope with the same feature at rest. Wavelength grows by 1+z while frequency shrinks by the same factor. Negative z is blueshift. The displayed velocity is the special-relativistic Doppler equivalent for purely radial motion; cosmological recession velocity requires an expansion model instead. The scale factor output assumes the shift is cosmological and normalizes the present scale factor to one.
Formula
1+z = lambda_observed/lambda_emitted = nu_emitted/nu_observed. beta = [(1+z)^2-1]/[(1+z)^2+1]; v = beta c; a_emission = 1/(1+z).
Worked example
An emitted 500 nm line observed at 1000 nm has z = 1. Its Doppler-equivalent radial speed is 0.6c, while a cosmological interpretation gives a = 0.5.
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Frequently asked questions
Can redshift be negative?
Yes. A blueshift has -1 < z < 0; the wavelength stays positive.
Is velocity equal to cz?
Only approximately at small Doppler shifts. The relativistic expression stays below c.
Does cosmological redshift imply this local velocity?
No. The Doppler-equivalent velocity is a comparison, not the general cosmological recession speed.