Updated November 2026 by Elena Stone
To convert redshift to distance, you need a model of how the universe has expanded. With the Planck 2018 values (H₀ = 67.4 km/s/Mpc, Ωm = 0.315), an object at redshift z = 1 emitted its light 7.95 billion years ago and is now 11.1 billion light-years away. At small redshifts (below about z = 0.05) Hubble’s law works: distance ≈ cz ÷ H₀, or about 4,450 megaparsecs times z.
Enter a redshift below, or tap one of the example objects. The calculator returns the light-travel distance, the comoving distance, the luminosity distance and the angular diameter distance, plus the lookback time and the age of the universe when the light left. It also works in reverse: give it a distance and it returns the redshift.
Get z from a spectral line
Redshift = observed wavelength / rest wavelength − 1. The result fills the redshift box above.
Gly is billions of light-years, Mly millions of light-years, Mpc megaparsecs. The calculator finds the redshift that gives this distance, then shows the full results.
Planck 2018 cosmology: H0 67.4 km/s/Mpc, Ωm 0.315, flat
Light from z = 1 left its source 7.95 billion years ago. The source is now 11.1 billion light-years away.
- Light-travel distance
- 7.95 Gly
- How far the light has travelled to reach us: lookback time multiplied by the speed of light.
- Comoving distance
- 11.1 Gly
- Where the source is now, with the expansion since the light left included. Also called proper distance today.
- Luminosity distance
- 22.2 Gly
- The distance that makes the source's brightness obey the inverse-square law. It is always larger than the comoving distance.
- Angular diameter distance
- 5.55 Gly
- The distance that makes the source's apparent size on the sky come out right. It shrinks again at high redshift.
- Lookback time
- 7.95 Gyr
- How long ago the light left the source.
- Age of the universe then
- 5.84 Gyr
- How old the universe was when the light left.
- Age of the universe now
- 13.8 Gyr
- The age of the universe today in the chosen cosmology.
- Recession velocity today
- 0.765 × c
- Hubble constant times comoving distance, as a multiple of the speed of light. Space itself is stretching, so this can exceed 1.
- Scale on the sky
- 8.24 kpc/arcsec
- The physical size that one arcsecond covers at the source.
- Distance modulus
- 44.2 mag
- The gap in magnitudes between how bright the source looks and how bright it really is.
- Hubble's law estimate (cz/H0)
- 14.5 Gly
- The straight-line estimate, good only at small redshift. Here it is off by 30.8% (too high).
Distance by redshift
- Light-travel distance
- Comoving distance
- Angular diameter distance
- Luminosity distance (runs off the top)
Curves are recomputed for the cosmology you pick. The dashed vertical line is your redshift.
Method: flat or curved ΛCDM with radiation (photons and 3.046 massless neutrinos, CMB temperature 2.7255 K). Comoving distance is the Hubble distance c/H0 times the integral of 1/E(z) from 0 to z; lookback time and age use the same integrand with an extra factor 1/(1 + z), all integrated numerically. Light-travel distance is lookback time times c. Luminosity distance is (1 + z) times the transverse comoving distance and angular diameter distance is that distance divided by (1 + z). Planck 2018: H0 67.4 km/s/Mpc, Ωm 0.315 (Planck Collaboration 2020). Results agree with the astropy cosmology package to better than 0.05%.
How to use the redshift to distance calculator
- Enter the redshift (z). Type it in or pick an example, from the Virgo Cluster (z = 0.004) to the cosmic microwave background (z = 1090). If you only have a spectrum, open Get z from a spectral line, choose the line (H-alpha, Lyman-alpha and others) and enter the wavelength you measured.
- Choose the cosmology. The default is Planck 2018. Switch to H₀ = 73 to see the effect of the Hubble tension, or choose Custom to set H₀, Ωm and ΩΛ yourself, including universes that are not flat.
- Read the results. The first line answers the usual question: how long the light traveled and how far away the object is today. The rows below give every standard distance measure in billions of light-years, millions of light-years or megaparsecs.
- Go the other way if you need to. The Distance → redshift tab takes a light-travel, comoving or luminosity distance and finds the matching z.
Use Share link to send the exact calculation to someone, or Copy results to paste every value into notes or homework.
Which distance do you need?
In an expanding universe “how far away is it?” has more than one answer. The light left the source when it was much closer to us, the space it crossed kept stretching on the way, and the source has kept moving away since. Each distance measure answers a different question.
| Distance | What it answers | z = 1 (Planck 2018) |
|---|---|---|
| Light-travel distance | How long has the light been traveling? Lookback time multiplied by the speed of light. This is the figure news stories quote as “X billion light-years away”. | 7.95 billion light-years |
| Comoving distance | How far away is the object right now? Also called the proper distance today. Use it for “where is it now” questions and for maps of the universe. | 11.1 billion light-years |
| Luminosity distance | How far away does it look based on its brightness? Use it with the inverse-square law, supernova distances and the distance modulus. | 22.2 billion light-years |
| Angular diameter distance | How far away does it look based on its apparent size? Use it to turn an angle on the sky into a physical size in kiloparsecs. | 5.55 billion light-years |
The four agree at small redshifts and split apart quickly beyond z ≈ 0.1. The angular diameter distance has a strange feature: it peaks at 5.85 billion light-years near z = 1.6 and then shrinks. Galaxies more distant than that look larger on the sky, because the light we see left them when the universe was small and they were close to us.
The redshift to distance formula
Redshift itself is measured from a spectrum. If a line with a rest wavelength λrest is observed at λobs:
z = λobs ÷ λrest − 1
Hydrogen’s H-alpha line sits at 656.28 nm in the lab. Observed at 984.42 nm, it gives z = 984.42 ÷ 656.28 − 1 = 0.5.
Small redshifts: Hubble’s law
For nearby galaxies, distance is proportional to redshift:
d = cz ÷ H₀
Here c is the speed of light (299,792 km/s) and H₀ is the Hubble constant. With H₀ = 67.4, a galaxy at z = 0.01 is 299,792 × 0.01 ÷ 67.4 = 44.5 megaparsecs away, or 145 million light-years. The shortcut breaks down as z grows, because it ignores how the expansion rate has changed over time:
| Redshift | Hubble’s law (cz/H₀) | Comoving distance | Hubble’s law error |
|---|---|---|---|
| 0.01 | 44.5 Mpc | 44.4 Mpc | +0.2% |
| 0.05 | 222 Mpc | 220 Mpc | +1.2% |
| 0.1 | 445 Mpc | 434 Mpc | +2.5% |
| 0.5 | 2,224 Mpc | 1,951 Mpc | +14% |
| 1 | 4,448 Mpc | 3,401 Mpc | +31% |
| 3 | 13,344 Mpc | 6,505 Mpc | +105% |
Any redshift: the cosmological integral
The exact comoving distance adds up the distance light covers in each small step of its trip, with the expansion rate at that time:
DC = (c ÷ H₀) ∫0z dz′ ÷ E(z′), where E(z) = √(Ωr(1+z)⁴ + Ωm(1+z)³ + Ωk(1+z)² + ΩΛ)
Ωm is the matter density (normal and dark matter), ΩΛ is dark energy, Ωr is radiation and Ωk is curvature, which is zero in a flat universe. The other distances follow from DC in a flat universe:
- Luminosity distance: DL = (1 + z) × DC
- Angular diameter distance: DA = DC ÷ (1 + z)
- Lookback time: tL = (1 ÷ H₀) ∫0z dz′ ÷ ((1 + z′) E(z′)), and the light-travel distance is tL × c
The integral has no simple closed form, so the calculator solves it numerically. Its results match the astropy cosmology library to better than 0.05%.
Distances of well-known objects from their redshift
All values use Planck 2018 parameters. Tap an object to load it into the calculator.
| Object | Redshift (z) | Light-travel time (Gyr) | Comoving distance (Gly) | Luminosity distance (Gly) | Age of the universe then |
|---|---|---|---|---|---|
| Virgo Cluster (M87) | 0.00428 | 0.0619 | 0.0620 | 0.0623 | 13.7 Gyr |
| Coma Cluster | 0.0231 | 0.329 | 0.333 | 0.341 | 13.5 Gyr |
| Quasar 3C 273 | 0.158 | 2.05 | 2.20 | 2.55 | 11.7 Gyr |
| Galaxy at z = 1 | 1 | 7.95 | 11.1 | 22.2 | 5.84 Gyr |
| Quasar TON 618 | 2.219 | 10.8 | 18.3 | 59.0 | 2.95 Gyr |
| GN-z11 | 10.6 | 13.4 | 31.8 | 369 | 434 Myr |
| MoM-z14 | 14.44 | 13.5 | 33.8 | 522 | 282 Myr |
| Cosmic microwave background | 1090 | 13.8 | 45.2 | 49,300 | 371 thousand years |
Gly is billions of light-years. Click an object to load its redshift into the calculator. Change the cosmology there to see how much the numbers depend on it.
The light from the quasar TON 618 has traveled 10.8 billion years, yet the quasar is now 18.3 billion light-years away. For the most distant galaxies the gap is larger still. MoM-z14, at z = 14.44, emitted the light we see 282 million years after the Big Bang. That light has traveled 13.5 billion years and the galaxy is now 33.8 billion light-years from us. The edge of the observable universe is 46 billion light-years away for the same reason. See the most distant black holes ever discovered for more objects in this range, or the list of galaxies by distance for nearby ones.
How the Hubble constant changes the answer
Every distance from redshift scales roughly with 1 ÷ H₀. Planck’s measurement of the cosmic microwave background gives H₀ = 67.4 km/s/Mpc. Measurements based on Cepheid variables and supernovae (the SH0ES team) give about 73. This disagreement is the Hubble tension, and it is unresolved.
| Redshift | Comoving distance, H₀ = 67.4 | Comoving distance, H₀ = 73 | Lookback time, 67.4 / 73 |
|---|---|---|---|
| 0.5 | 6.36 billion ly | 5.88 billion ly | 5.21 / 4.81 billion years |
| 1 | 11.1 billion ly | 10.2 billion ly | 7.95 / 7.34 billion years |
| 3 | 21.2 billion ly | 19.6 billion ly | 11.65 / 10.76 billion years |
The two values give distances about 8% apart. When you quote a distance from redshift, state the H₀ you used. Papers often write distances in units of h⁻¹ Mpc for this reason, where h = H₀ ÷ 100.
Can galaxies move away faster than light?
Yes. The recession velocity today is H₀ multiplied by the comoving distance. With Planck values it reaches the speed of light at z ≈ 1.48, and the calculator shows it as a multiple of c. A galaxy at z = 3 recedes at about 1.5 times the speed of light. This breaks no law of physics: nothing moves through space faster than light, but space between us and the galaxy is growing. For the same reason, the special relativity Doppler formula gives the wrong velocity for distant galaxies. Cosmological redshift is a stretch of the light’s wavelength by the expansion, by a factor of exactly 1 + z. Read more in our evidence that the universe is expanding.
Frequently asked questions
How do you convert redshift to distance?
For redshifts below about 0.05, use Hubble's law: distance = cz ÷ H₀, where c is 299,792 km/s and H₀ is about 67.4 to 73 km/s/Mpc. That gives roughly 4,450 megaparsecs times z. For larger redshifts you have to integrate the expansion history of the universe, which depends on H₀, the matter density and dark energy. A redshift calculator does that integral for you.
How far away is redshift 1?
With Planck 2018 parameters, light from an object at z = 1 left it 7.95 billion years ago, so its light-travel distance is 7.95 billion light-years. Because the universe kept expanding, the object is now 11.1 billion light-years away (comoving distance). Its luminosity distance is 22.2 billion light-years.
What is the difference between light-travel distance and comoving distance?
Light-travel distance is how long the light has been traveling multiplied by the speed of light. Comoving distance is how far away the object is today. They are nearly equal for nearby galaxies, but for an object at z = 3 the light traveled 11.7 billion years while the object is now 21.2 billion light-years away.
How do you calculate redshift from wavelength?
Divide the observed wavelength of a spectral line by its rest (laboratory) wavelength and subtract 1: z = λobs ÷ λrest − 1. For example, the hydrogen H-alpha line has a rest wavelength of 656.28 nm. If you observe it at 984.42 nm, the redshift is 0.5.
Why are there several different distances for the same redshift?
In an expanding universe the distance between us and a galaxy changes while its light is in transit. Comoving distance is the distance now, light-travel distance follows the light's travel time, luminosity distance is the distance implied by the object's brightness and angular diameter distance is the distance implied by its apparent size. They are equal only for nearby objects.
What Hubble constant should I use?
Use H₀ = 67.4 km/s/Mpc from Planck 2018 for consistency with most cosmology papers, or about 73 km/s/Mpc to match the Cepheid and supernova measurements of the SH0ES team. Distances from redshift scale with 1 ÷ H₀, so the choice changes results by about 8%. State which value you used.
What is the redshift of the most distant galaxy?
Among spectroscopically confirmed galaxies, MoM-z14 holds the record at z = 14.44, ahead of JADES-GS-z14-0 at about z = 14.2. At z = 14.44 the light left the galaxy about 282 million years after the Big Bang and the galaxy is now about 33.8 billion light-years away.
What does a negative redshift mean?
A negative redshift is a blueshift: the object is moving toward us. It happens only for nearby objects such as the Andromeda galaxy (z ≈ −0.001), where gravity within the Local Group outweighs cosmic expansion. A blueshift does not give a distance; Andromeda's distance of 2.5 million light-years comes from Cepheid variable stars.
Is a redshift above 1 faster than light?
A redshift above 1 does not mean the object moves through space faster than light. Cosmological redshift is a stretch of the light by the expansion of space. The recession velocity today, H₀ times the comoving distance, does exceed the speed of light beyond z ≈ 1.5 with Planck values, which relativity allows because space itself is expanding.
Sources
- Planck Collaboration (2020). Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6.
- Hogg, D. W. (1999). Distance measures in cosmology. The standard reference for the formulas above.
- Riess, A. G. et al. (2022). A comprehensive measurement of the local value of the Hubble constant. The Astrophysical Journal Letters 934, L7.
- Wright, E. L. (2006). A cosmology calculator for the World Wide Web. Publications of the Astronomical Society of the Pacific 118, 1711.
- The Astropy Collaboration. astropy.cosmology, used to check this calculator.
Related: how to calculate distances in space, how to measure star distances and how quasars form.
