Redshift Calculator
Find redshift and recession velocity from wavelengths.
Results update as you type.
How it works
Redshift is how astronomers measure the motion of stars and galaxies and the expansion of the universe, and this calculator computes it. You enter the observed wavelength of a spectral line and its rest wavelength, the wavelength it has in a laboratory, and it returns the redshift z and an approximate recessional velocity. Redshift is the fractional stretching of light: the observed wavelength minus the rest wavelength, divided by the rest wavelength. When a light source moves away, its waves are stretched to longer, redder wavelengths, giving a positive redshift; a source moving toward us produces a blueshift, a negative value. By comparing the shifted wavelength of a known spectral line to its laboratory value, astronomers determine how fast an object is receding. For small redshifts, the recessional velocity is approximately the speed of light times z, the formula this calculator uses. Redshift is one of the most powerful tools in astronomy: it revealed that distant galaxies are receding, leading to the discovery of the expanding universe, and it lets astronomers measure distances, map the cosmos, and study objects billions of light-years away. For very large redshifts, the simple velocity approximation breaks down and relativistic or cosmological formulas are needed. Both wavelengths must be positive. Enter the observed and rest wavelengths to find the redshift and velocity.
z = (λ_observed − λ_rest) / λ_rest ; v ≈ c·z
Redshift z is the fractional increase in wavelength: the observed wavelength minus the rest wavelength, divided by the rest wavelength. For small redshifts, the recessional velocity is approximately the speed of light times z. Larger wavelengths than emitted mean the source is moving away, stretching the light toward the red end of the spectrum.
Source:Astrophysics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter observed wavelength and rest wavelength.
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Adjust the options
Fine-tune any options to match your situation.
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Read your result
Redshift (z) updates instantly as you type — no button to press.
Frequently asked questions
What is redshift?
Redshift is the stretching of light to longer, redder wavelengths when its source moves away from the observer. It is measured as z, the fractional change in wavelength. Astronomers use redshift to determine how fast stars and galaxies are receding and, through Hubble's law, how far away distant galaxies are.
How is redshift calculated?
Subtract the rest wavelength, the wavelength the light has at its source, from the observed wavelength, then divide by the rest wavelength. The result is the redshift z. A positive value means the source is moving away and the light is stretched; a negative value, a blueshift, means it is approaching and the light is compressed.
How does redshift give velocity?
For small redshifts, the recessional velocity is approximately the speed of light multiplied by z. So a redshift of 0.01 corresponds to a velocity of about one percent of light speed. This calculator uses that linear approximation, which is accurate for nearby objects with modest redshifts but not for very distant, high-redshift sources.
What is the difference between redshift and blueshift?
Redshift occurs when a source moves away, stretching its light to longer wavelengths, giving a positive z. Blueshift occurs when a source approaches, compressing its light to shorter wavelengths, giving a negative z. Most distant galaxies are redshifted due to cosmic expansion, while some nearby objects, like the Andromeda galaxy, are blueshifted.
When does the simple velocity formula fail?
The approximation velocity equals the speed of light times z works only for small redshifts, roughly below 0.1. For larger redshifts, the recessional velocity would exceed light speed under the naive formula, which is unphysical. High-redshift objects require relativistic Doppler or cosmological expansion formulas that properly account for the geometry of an expanding universe.