Redshift and Recession Velocity Calculator

Redshift occurs when light from a distant object is stretched to longer (redder) wavelengths by the object’s motion away from the observer or by the expansion of spacetime itself. The redshift value (z) can be converted to a recession velocity.

The Formulas:

Redshift: z = (λ_observed − λ_rest) / λ_rest

For low velocities (z « 1), the classical Doppler formula applies:

v ≈ z × c

Where c = speed of light = 299,792 km/s

For high redshifts (relativistic, z approaching or exceeding 1):

v = c × [(z+1)² − 1] / [(z+1)² + 1]

Worked Example:

A galaxy is observed with the Hydrogen-alpha line at 780 nm instead of its rest wavelength of 656.3 nm.

z = (780 − 656.3) / 656.3 = 123.7 / 656.3 = 0.1884

Since z < 0.5, classical approximation is fine:

v ≈ 0.1884 × 299,792 = 56,483 km/s

That’s about 18.8% the speed of light.

Cosmological Distance Estimate:

Using Hubble’s Law: v = H_0 × d

Where H_0 ≈ 70 km/s/Mpc (Hubble constant)

Distance = 56,483 / 70 = 807 Megaparsecs ≈ 2.6 billion light-years

Famous Redshift Reference Values:

Practical Tips:

• Negative z (blueshift) means the object is approaching — rare, and only for nearby galaxies
• Cosmological redshift is not Doppler shift — it’s caused by space itself expanding