Redshift Calculator
Calculate cosmological redshift z from observed and rest wavelengths, the recession velocity (classical and relativistic), and a Hubble-law distance estimate.
Cómo usar esta calculadora
- 1Enter the observed wavelength of a spectral line from the object.
- 2Enter the line's known rest (laboratory) wavelength.
- 3Read the redshift z and whether it is a red- or blueshift.
- 4See the recession velocity and an approximate Hubble-law distance.
Cómo funciona
Redshift and recession velocity
z = (observed − rest wavelength) ÷ rest wavelength classical: v = c × z (small z only) relativistic: v = c × ((1+z)² − 1) ÷ ((1+z)² + 1) Hubble's law: distance = v ÷ H₀
Redshift is the stretching of light to longer (redder) wavelengths, and it is measured by comparing the observed wavelength of a known spectral line against its rest wavelength — the wavelength it has in a laboratory. The redshift z is the fractional change: the difference between observed and rest wavelengths divided by the rest wavelength. A positive z means the light has stretched (redshift), indicating the source is moving away, while a negative value means it has compressed (blueshift) toward an approaching source. For small redshifts, the recession velocity is simply the speed of light times z, but this breaks down at high z, where a relativistic formula is required because velocities approach the speed of light. Once the velocity is known, Hubble's law — that recession velocity is proportional to distance, with the Hubble constant as the proportionality — turns it into an estimate of how far away the object is. This chain from wavelength shift to distance is one of the primary ways astronomers measure the scale of the universe.
Ejemplo resuelto
The hydrogen-alpha line has a rest wavelength of 656.3 nm. Observed at 665 nm in a galaxy's spectrum, the redshift is (665 − 656.3) ÷ 656.3 ≈ 0.0133, implying a recession velocity of roughly 3,950 km/s and, by Hubble's law, a distance of about 56 megaparsecs — around 184 million light-years.
Redshift Calculator: la guía completa
Reading the universe in spectral lines
Redshift is measured not from the overall colour of a galaxy but from the precise positions of spectral lines — the sharp features in a spectrum where specific elements absorb or emit light at exact, known wavelengths. Hydrogen, calcium, and other elements produce these fingerprints at wavelengths measured precisely in the laboratory. When astronomers observe the same recognisable pattern of lines in a distant object but shifted uniformly toward longer wavelengths, they can measure the shift exactly, because they know where each line 'should' be. This is what makes redshift such a powerful and precise tool: it relies on identifiable markers, not fuzzy overall colour.
The fractional shift in these lines is the redshift z, and it directly encodes how much the light has been stretched on its journey to us. A galaxy's entire spectrum — every line — shifts by the same fraction, which is the signature of a genuine redshift rather than some other change in the light. By identifying even one known line and measuring its displacement, an astronomer extracts z, and from z everything else follows. This technique, spectroscopy, transformed astronomy from merely charting positions and brightnesses into measuring motions and distances across the cosmos.
From velocity to the expanding universe
In the early twentieth century, Edwin Hubble and others found that almost all galaxies are redshifted, and that the more distant a galaxy, the greater its redshift. This relationship — recession velocity proportional to distance — is Hubble's law, and it was the pivotal evidence that the universe is expanding. Galaxies are not flying apart through space so much as being carried apart by the expansion of space itself, which stretches the light travelling through it. The redshift of a distant galaxy is thus largely cosmological, a record of how much the universe has expanded during the light's journey.
This makes redshift a cosmic ruler and clock. Because greater distance means greater redshift, measuring z gives an estimate of distance through Hubble's law, and since light takes time to travel, it also tells us how far back in time we are looking. A galaxy at high redshift is seen as it was billions of years ago, its light emitted when the universe was younger and smaller. Redshift surveys of millions of galaxies have mapped the large-scale structure of the universe and traced its expansion history, making the humble wavelength shift one of the foundations of modern cosmology. The value of z has become the standard way astronomers describe the distance and epoch of remote objects.
The limits of the simple picture
The calculations here capture the essence of redshift but simplify a subtle reality, and it is worth knowing where the approximations hold. The relation v equals c times z is only valid for small redshifts, where velocities are far below the speed of light. As z grows toward and beyond 1, this simple formula would give velocities exceeding light speed, which is unphysical; the relativistic Doppler formula corrects this, and for cosmological distances even that is really a stand-in for a fuller treatment based on the expansion of space rather than motion through it. At the highest redshifts, distance and velocity depend on the detailed expansion history and the cosmological model.
The distance estimate carries its own uncertainties. Hubble's law uses the Hubble constant, whose precise value has been the subject of intense research and some tension between measurement methods, so any distance derived from it is approximate and depends on the constant assumed. For nearby galaxies, local motions can also contaminate the cosmological redshift, and blueshifts occur for a few galaxies, like Andromeda, that are approaching us because their local gravitational attraction outweighs the cosmic expansion. This calculator gives a clear, order-of-magnitude sense of how redshift translates into velocity and distance, which is exactly how astronomers first use it, while the precise cosmological interpretation at high redshift belongs to detailed modelling beyond a simple formula.
Preguntas frecuentes
How do I calculate redshift?
Redshift z = (observed wavelength − rest wavelength) ÷ rest wavelength. If a line with a rest wavelength of 656.3 nm is observed at 665 nm, z = (665 − 656.3) ÷ 656.3 ≈ 0.0133. It's the fractional stretch of the light's wavelength.
What does redshift tell us?
That an object is moving away (light stretched to longer wavelengths) and, for distant galaxies, how far away it is. Redshift arises because the universe's expansion stretches light in transit. By Hubble's law, greater redshift means greater distance and a view further back in time.
How does redshift give distance?
Convert redshift to recession velocity, then apply Hubble's law: distance = velocity ÷ the Hubble constant. A velocity of about 3,950 km/s gives roughly 56 megaparsecs. The estimate depends on the assumed Hubble constant and is approximate, especially at high redshift.
Why isn't v = cz always valid?
Because it would give velocities above the speed of light for large redshifts, which is impossible. The simple formula holds only for small z. At higher redshifts a relativistic formula is needed, and cosmological redshift is really about the expansion of space, requiring a fuller model.