Universe Expansion Calculator
Enter a galaxy redshift and adjust the Hubble constant and density parameters to compute how fast that galaxy is receding, how far away it is today (proper distance), its comoving distance, and how long ago the light you see left it (lookback time). The calculator uses the Friedmann equation for a flat Lambda-CDM universe, the same model used by Planck and the standard cosmological community. All outputs update instantly as you type.
What is the universe expansion calculator?
This tool uses the Friedmann equation for a spatially flat Lambda-CDM (LCDM) universe to convert a galaxy redshift into the physical quantities cosmologists care about: recession velocity, proper distance, comoving distance, lookback time, and the age of the universe at the moment the observed light was emitted. Unlike the simplest version of Hubble's law (v = H0 x d), this calculator integrates over the full expansion history, so it remains accurate at high redshifts where the linear approximation breaks down.
Key concepts: redshift, distance, and lookback time
Redshift (z) measures how much the wavelength of light has stretched during its journey to us. A galaxy at z = 1 emitted its light when the universe was half its current size (scale factor a = 0.5). Proper distance is the physical separation between us and the galaxy right now, if you could freeze the expansion and measure it. Comoving distance strips out expansion and stays constant for objects at rest in the Hubble flow. Lookback time tells you how old the universe was when the light left, which sets a natural limit on what we can observe: we cannot see light from before the universe became transparent (z ~ 1100).
Why recession velocities can exceed the speed of light
General relativity allows regions of space to recede from each other faster than light without violating special relativity, because it is the fabric of space itself expanding rather than an object moving through space. The most distant observable galaxies recede at several times the speed of light. Light from objects beyond the Hubble sphere (where v = c) can still reach us because the expansion is decelerating locally, so photons emitted toward us eventually find themselves in regions that recede more slowly. The cosmological event horizon is slightly larger than the Hubble sphere but still finite, meaning some galaxies are already receding so fast that no future light from them will ever reach us.
The Hubble tension: Planck vs. SH0ES
The Hubble constant sets the scale of all cosmological distances and ages. Two independent measurement methods give values that disagree by about 9%, which is highly statistically significant and is known as the Hubble tension. The Planck collaboration measures H0 = 67.4 km/s/Mpc from the cosmic microwave background anisotropies combined with the standard LCDM model. The SH0ES collaboration measures H0 = 73.0 km/s/Mpc using the cosmic distance ladder anchored by Cepheid variable stars and Type Ia supernovae. This calculator lets you switch between these presets to see how the choice affects every calculated output, which at z = 0.5 amounts to roughly a 1.5 billion light-year difference in proper distance and about 0.7 billion years difference in age.
Cosmological benchmarks by redshift
| Object / epoch | Redshift (z) | Proper distance (Gly) | Lookback time (Gyr) |
|---|---|---|---|
| Andromeda Galaxy (M31) | ~0.001 | ~2.5 | ~2.5 Myr |
| Virgo Cluster | ~0.004 | ~54 | ~54 Myr |
| Nearby survey galaxies (SDSS) | 0.01-0.3 | 130-3,800 | 0.1-3.3 |
| Peak of star formation | ~2 | ~16,000 | ~10.4 |
| Most distant confirmed galaxy (GS-z14-0) | ~14.2 | ~32,000 | ~13.1 |
| Cosmic microwave background | ~1100 | ~45,700 | ~13.8 |
Values for the Planck 2020 flat LCDM cosmology (H0=67.4, Om=0.315). CMB = cosmic microwave background.
Frequently asked questions
What is redshift and how is it measured?
Redshift is the fractional stretching of a photon's wavelength as the universe expands during the light's journey to us. It is measured by identifying spectral lines (absorption or emission features at known rest wavelengths) in a galaxy's spectrum and comparing them to the same lines in a laboratory reference. If a hydrogen line emitted at 121.6 nm arrives at 182.4 nm, the redshift is z = (182.4 - 121.6) / 121.6 = 0.5. The deeper a galaxy, the more the universe has expanded while its light traveled, and the higher its redshift.
How can recession velocity exceed the speed of light?
Special relativity forbids objects from moving faster than light through space, but it places no limit on the rate at which space itself expands. When two points in space are separated by a large enough distance, the cumulative effect of expansion along that path can cause them to recede from each other faster than c. Galaxies currently beyond about 4,200 Mpc (roughly 14 billion light-years) recede from us superluminally. Critically, light from those galaxies can still reach us today because much of the journey occurred when the universe was expanding more slowly.
What is the difference between proper distance and comoving distance?
Proper distance is the physical distance between two points at a single instant of cosmic time, as if you could snap a tape measure across the universe right now. It grows over time as the universe expands. Comoving distance factors out that expansion by scaling coordinates so that the distance between two objects at rest in the Hubble flow stays constant. For a flat universe the two are related simply: proper distance = comoving distance x scale factor, or at z = 0 they are equal. Comoving distance is the natural coordinate for computing volumes and number densities of sources.
What are the cosmological parameters Omega_m and Omega_Lambda?
These are energy density fractions relative to the critical density that would make the universe geometrically flat. Omega_m covers all matter (ordinary baryonic matter plus dark matter) and Omega_Lambda represents dark energy, modeled as a cosmological constant. In the Planck 2020 best fit, Omega_m = 0.315 and Omega_Lambda = 0.685, summing to 1.0 confirming flatness to high precision. Dark energy drives the acceleration of expansion: at early times matter dominated and the expansion decelerated; the transition to dark-energy domination and accelerating expansion occurred at around z = 0.4.
What is lookback time and how does it differ from light travel time?
Lookback time and light travel time are the same thing: the time elapsed between the emission of the observed photons and now. If a galaxy has a lookback time of 10 billion years, the light you detect left that galaxy 10 billion years ago when the universe was about 3.8 billion years old. This is different from proper distance: light does not travel in a straight line through an expanding universe, so a photon that takes 10 billion years to arrive does not come from 10 billion light-years away. For z = 2 in Planck cosmology, the light travel time is about 10.4 billion years but the proper distance today is about 17 billion light-years.
Why does this calculator show a current universe age that depends on H0?
The age of the universe is the lookback time integrated all the way back to z approaching infinity (the Big Bang). It depends on H0 because the Hubble constant sets the overall timescale: a higher H0 means faster expansion throughout history and therefore a younger universe. At H0 = 67.4 (Planck) the age is about 13.8 billion years; at H0 = 73.0 (SH0ES) it drops to about 12.6 billion years. This is one reason the Hubble tension matters: a significantly higher H0 would make the universe younger than some of the oldest known globular clusters, creating a logical inconsistency.