Cosmological Redshift Calculator
Enter a spectral line's rest and observed wavelengths, or a redshift z directly, to find the redshift, recession velocity and Hubble distance of a galaxy.
How to use the redshift calculator
- Enter the rest and observed wavelengths in nanometres, or switch to entering z directly.
- Optionally set the Hubble constant, which defaults to 70 km/s/Mpc.
- Read the redshift, recession velocity and Hubble distance.
Examples
Hydrogen-alpha line, slightly shifted
rest = 656.3 nm, observed = 660 nm
z = 0.00564, v = 1690 km/s, distance = 24.1 Mpc
A redshift of one
z = 1
v = 299,792 km/s (Doppler approximation)
Frequently asked questions
What is redshift?
Redshift is the stretching of light to longer wavelengths as a source moves away. For galaxies it grows with distance as the universe expands.
What is the redshift formula?
z = (observed wavelength minus rest wavelength) divided by the rest wavelength. A z of 0.01 means the wavelength was stretched by one percent.
How is recession velocity found from redshift?
This tool uses the simple Doppler approximation v = c times z. It is accurate at small z but overstates speed at large z, where relativistic formulas are needed.
What is the Hubble distance?
It is the recession velocity divided by the Hubble constant, v / H0. With H0 near 70 km/s/Mpc it gives a rough distance in megaparsecs.
Why does z = 1 not mean the speed of light?
The Doppler approximation gives v = c at z = 1, but the correct relativistic treatment keeps velocity below c. Use this estimate only for low redshifts.
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