Redshift Calculator
Enter the observed and rest wavelengths of a spectral line to get the redshift z — plus the low-redshift recession velocity of the source in km/s.
Redshift and velocity at once
Enter the observed and rest wavelengths and the calculator returns the redshift z and the approximate recession velocity (v ≈ c·z) together.
Use the same unit
Both wavelengths must use the same unit — nanometres, ångströms, whatever you like — because z is a ratio and the unit cancels out.
What is redshift?
A stretch in wavelength
The redshift calculator turns two wavelengths — the observed wavelength of a spectral line and its known rest wavelength in the lab — into the redshift z, the fractional amount by which the light has been stretched toward longer (redder) wavelengths. When a source moves away from us, its light is shifted to longer wavelengths, and the bigger the shift, the faster it is receding. Redshift is one of the cornerstones of modern astronomy: it is how we measure the recession of distant galaxies, map the expansion of the universe, and estimate cosmic distances. A positive z means the object is moving away; a negative value (a blueshift) means it is approaching.
Enter the observed and rest wavelengths in the same unit to get the redshift z and the approximate recession velocity instantly.
The redshift is the change in wavelength divided by the rest wavelength, and the recession velocity follows from multiplying it by the speed of light.
z = (λ_observed − λ_rest) / λ_restBecause z is a ratio of two wavelengths, it is dimensionless — the unit cancels, so it does not matter whether you measure in nanometres or ångströms as long as both values share the same unit. For small redshifts the recession velocity is simply v ≈ c × z, where c is the speed of light (299,792,458 m/s); the calculator reports it in km/s.
Suppose the hydrogen-alpha line, which sits at 656.3 nm in the lab, is observed at 660 nm.
Find the wavelength shift
660 − 656.3 = 3.7 nm — how far the line has moved.
Divide by the rest wavelength
3.7 / 656.3 ≈ 0.005637 — the redshift z, a dimensionless ratio.
Convert to a velocity
c × 0.005637 ≈ 1690 km/s — the approximate recession velocity at this low z.
The redshift z tells you how much the light has been stretched: z = 0.005637 means the wavelength is about 0.56% longer than at rest. Small redshifts like this come from nearby objects with modest recession speeds, while quasars and the most distant galaxies reach z values of several or more, where the light has been stretched many times over. The recession velocity (about 1690 km/s here) is what that shift implies for how fast the source is moving away from us — at low z it is close to c × z, but at large z the simple proportion breaks down and a relativistic treatment is needed. Keep both numbers in view: z is the raw, unit-free measurement straight from the spectrum, and the velocity is the physical interpretation that follows from it.
The redshift itself is exact, but the velocity is an approximation worth understanding.
The v ≈ cz approximation only holds for small z
The recession velocity v ≈ c × z is a low-redshift approximation. It is accurate when z is small (well under about 0.1), but for large redshifts the relativistic Doppler formula is required and v ≈ cz overstates the true speed — velocity can never exceed the speed of light. Make sure both wavelengths use the same unit, and remember that cosmological redshift reflects the expansion of space itself, not motion through it.