Comparing identifiable spectral features
For a reference wavelength λ₀ and observed wavelength λ, z=(λ−λ₀)/λ₀. Positive values indicate longer wavelengths and negative values blueshift; both wavelengths must use consistent units.
A reference feature at 500 nanometres observed at 600 nanometres gives z=0.2. This compares the same spectral feature, not the overall colour of a cooler, intrinsically redder star.
Motion and cosmic expansion
Relative line-of-sight motion shifts measured wavelengths. Repeated stellar spectra can track periodic motion and help investigate orbiting systems.
Cosmological redshift instead describes wavelength stretching during propagation through expanding space. It is distinct from local Doppler motion, so an unrestricted low-speed velocity formula cannot describe every distant galaxy.
Distances require interpretation
Redshift itself is a wavelength ratio. Inferring velocity, distance or emission age requires a mechanism, appropriate approximations and, for cosmological interpretation, model parameters.
Expansion makes light-travel time different from present distance. Local motions can also produce blueshift: an expanding universe does not require every individual observed object to be redshifted.