OrbitLab

Redshift Calculator

How fast is this object moving away from us?

Observed wavelength (nm)

Rest wavelength (nm)

Redshift (z)

0.006

Recession velocity: 1,685.366 km/s

What you entered

Observed wavelength (nm): 660Rest wavelength (nm): 656.3

1
z = (λ_observed − λ_rest) ÷ λ_rest
(660 − 656.3) ÷ 656.3= 0.0056
2
v ÷ c = ((1+z)² − 1) ÷ ((1+z)² + 1)
(1.0113 − 1) ÷ (1.0113 + 1)= 0.0056 c
3
Recession velocity
0.0056 × 299792.458 km/s= 1685.3655 km/s

Result

Redshift (z): 0.006

A redshift of z = 0.006 implies this object is receding at roughly 1,685 km/s.

Redshift and recession velocity

Redshift z is the fractional change in wavelength. Velocity uses the relativistic Doppler relation, which keeps the result below the speed of light at any z. Rows use the hydrogen-alpha line at 656.3 nm.

Observed wavelength	Redshift z	Velocity	As a fraction of c
656.3 nm	0.0000	0.0 km/s	0.0000 c
660 nm	0.0056	1,685.4 km/s	0.0056 c
700 nm	0.0666	19,298.6 km/s	0.0644 c
800 nm	0.2190	58,593.4 km/s	0.1954 c
1,000 nm	0.5237	119,283.8 km/s	0.3979 c
1,312.6 nm	1.0000	179,875.5 km/s	0.6000 c
5,250.4 nm	7.0000	290,568.1 km/s	0.9692 c

At small z the velocity is almost exactly z times c, which is why the simple approximation is taught first. It breaks down badly further out: at z = 1 it would predict exactly light speed, where the correct answer is 0.6 c. Cosmological redshift is expansion of space rather than motion through it, so these velocities are a convenient interpretation rather than a literal speed.

Stretched light reveals motion

When a light source moves away, its wavelength stretches toward the red end of the spectrum — measuring exactly how much a known spectral line has shifted gives the redshift z, directly convertible to a recession velocity for modest speeds.

The evidence behind the expanding universe

Edwin Hubble's discovery that distant galaxies show systematically higher redshift the farther away they are (more distant = faster receding) was the original evidence for the universe's expansion.

Frequently asked questions

A hydrogen spectral line normally at 656.3 nm is observed at 662.0 nm — what is the redshift?

z = (observed - rest)/rest = (662.0 - 656.3)/656.3 = 5.7/656.3 = 0.0087. The recession velocity is about 0.0087 × c ≈ 2,600 km/s.

How is the redshift calculator different from the Hubble expansion calculator?

The redshift calculator converts observed vs rest wavelength into z and recession velocity. The Hubble expansion calculator converts distance directly into recession velocity using v = H₀d. Both measure the same expansion but start from different observational inputs.

Can redshift tell us how far away a galaxy is?

For small z (below about 0.1), distance ≈ z × c / H₀. For a z of 0.0087: distance ≈ 0.0087 × 3×10⁵ / 70 ≈ 37.3 Mpc (about 122 million light-years). At higher z, the relationship requires cosmological corrections.