About this tool
The Redshift & Recession Velocity Calculator converts a galaxy's redshift into how fast it is receding and roughly how far away it lies. Enter the redshift z directly, or give the observed and rest (laboratory) wavelengths of a spectral line and z is worked out for you.
Redshift z = (λ_observed − λ_rest) ÷ λ_rest. The low-redshift recession velocity is v = c × z, while the relativistic Doppler form v = c × ((1+z)² − 1) ÷ ((1+z)² + 1) keeps the speed below the speed of light for large z. Hubble distance = v ÷ H₀, where the Hubble constant H₀ defaults to 70 km/s/Mpc and can be adjusted to any value you prefer.
The speed of light is taken as 299,792.458 km/s, and the distance is reported in both megaparsecs and millions of light-years. These are simple cosmological estimates rather than a full ΛCDM model, but they capture the core Hubble-law relationship between redshift, velocity and distance. Everything is computed in your browser.
Frequently asked questions
What is redshift z?
It measures how much a spectral line is stretched toward longer wavelengths: z = (observed − rest) ÷ rest. A positive z means the source is moving away (redshift); a negative z means it is approaching (blueshift).
When should I use the relativistic velocity?
For small z (below about 0.1) v = cz is accurate. As z grows, cz eventually exceeds the speed of light, so the relativistic Doppler formula is used to keep the recession velocity physically below c.
How is Hubble distance estimated?
By Hubble's law, distance = recession velocity ÷ H₀. With H₀ = 70 km/s/Mpc the result is in megaparsecs, also shown in millions of light-years. Changing H₀ scales the distance inversely.
Can I use this for cosmological (high-z) galaxies?
It gives a useful first estimate, but very distant galaxies need a full cosmological model that accounts for the expansion history and dark energy. Treat high-z distances here as approximate Hubble-law values.
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