Universe Expansion Calculator

Redshift (z) measures how much the wavelength of light from a distant galaxy has been stretched by the universe's expansion. A redshift of z=1 means the universe was half its current size when that light was emitted. Higher redshift values correspond to objects farther away and further back in time, making it one of the most fundamental observables in cosmology. See also our Luminosity Calculator.

The Hubble Constant (H₀) describes the current rate at which the universe is expanding, in units of km/s/Mpc. The Planck satellite measurement gives 67.4 km/s/Mpc, while local distance ladder measurements suggest ~73 km/s/Mpc — a discrepancy known as the 'Hubble tension.' For most cosmological calculations, the default value of 67.4 is appropriate.

Proper distance is the physical separation between two points in the universe at a specific moment in time (today). Comoving distance factors out the universe's expansion and remains constant for objects moving only with the cosmic flow. At z=0 (today), proper and comoving distances are equal; at earlier times, proper distance = comoving distance × scale factor a = 1/(1+z).

Lookback time is how long ago the light you're observing was emitted. For example, a galaxy at redshift z=1 has a lookback time of roughly 7.7 billion years, meaning we see it as it was 7.7 billion years ago. This is calculated by integrating the inverse of the Hubble parameter over the expansion history of the universe.

Yes — and this is not a violation of special relativity. Galaxies beyond the Hubble radius (~4,200 Mpc) recede faster than light due to the expansion of space itself, not motion through space. We can still observe some of these galaxies because the light they emitted long ago, when they were closer, has been traveling toward us ever since.

Ωm is the matter density parameter representing the fraction of the universe's critical density contributed by all matter (normal baryonic matter plus dark matter). ΩΛ is the dark energy density parameter associated with the cosmological constant (Λ). In a flat universe, Ωm + ΩΛ ≈ 1. The standard Planck 2018 values are Ωm = 0.315 and ΩΛ = 0.685.

The scale factor a = 1/(1+z) describes the relative size of the universe compared to today. At z=0, a=1 (the universe is its present size). At z=1, a=0.5 (the universe was half its current linear size). The scale factor is central to Friedmann equations which govern cosmic expansion.

The current age of the universe (~13.8 billion years) is obtained by integrating the inverse Hubble parameter from z=∞ to z=0 using the Friedmann equations. This integral depends on H₀, Ωm, and ΩΛ. The calculator estimates lookback time for a given redshift z by numerically integrating from 0 to z, which represents the time elapsed since that epoch.