Boneyard Tools

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

  1. Enter the rest and observed wavelengths in nanometres, or switch to entering z directly.
  2. Optionally set the Hubble constant, which defaults to 70 km/s/Mpc.
  3. 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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