What cosmological parameters does this calculator use?

By default it uses Planck 2018 values: H₀ = 67.4 km/s/Mpc, Ω_M = 0.315, Ω_Λ = 0.685, with a flat universe (Ω_k = 0). You can override these in the advanced settings panel.

What is the difference between comoving and luminosity distance?

Comoving distance is the distance measured in coordinates that expand with the universe — it represents the distance between two points as measured today. Luminosity distance is larger by a factor of (1+z) and is the distance you would infer from comparing a source's apparent and intrinsic brightness.

What is lookback time?

Lookback time is the time elapsed between when the light was emitted and when it was received (now). For a galaxy at z = 1, the lookback time is about 7.7 billion years, meaning we see it as it was 7.7 Gyr ago.

Can I enter negative redshifts?

Negative redshifts (blueshifts) occur for nearby gravitationally bound systems like the Andromeda galaxy (z ≈ −0.001), where local peculiar velocity toward us exceeds the Hubble flow. However, cosmological distance integrals assume universal FLRW expansion and require non-negative redshifts (z ≥ 0). Local blueshifts decoupled from Hubble expansion cannot be converted to cosmological distance or lookback time.

Redshift to Distance Calculator

Enter a cosmological redshift value (z) to get the comoving distance, luminosity distance, and lookback time.

Redshift Input

Redshift (z)

Range: 0 to 1100 (CMB surface of last scattering)

Quick presets

Advanced: Cosmological Parameters

H₀ — Hubble constant (km/s/Mpc)

Ω_M — Matter density

Ω_Λ — Dark energy density

Distance Results

Enter a redshift value above to see results.

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Summary

Cosmological redshift measures how much a galaxy's light has been stretched by the expansion of the universe. This calculator converts a redshift value (z) into three key distances: comoving distance (the coordinate distance in today's expanding universe), luminosity distance (used to compute the apparent brightness of standard candles), and lookback time (how long ago the light was emitted). The computation uses numerical integration of the ΛCDM Friedmann equation with standard Planck 2018 cosmological parameters.

How it works

Enter the redshift value (z) of a galaxy or quasar. Common values: Virgo Cluster z ≈ 0.0036, Coma Cluster z ≈ 0.023, most distant quasars z > 6.
Optionally adjust H₀, Ω_M, or Ω_Λ to use custom cosmological parameters.
The calculator numerically integrates the ΛCDM comoving distance integral: D_C = (c/H₀) ∫ dz′ / E(z′).
Luminosity distance is derived as D_L = (1+z) × D_C.
Lookback time is computed by integrating 1/[(1+z)H(z)] and converting to gigayears.
Results update instantly as you type.

Use cases

Estimate the distance to a galaxy from its spectroscopic redshift.
Compute lookback time to understand how far back in cosmic history a source was observed.
Convert between redshift and luminosity distance for supernova cosmology.
Explore how distance scales change with different cosmological parameters.
Verify cosmological distance calculations in research or coursework.
Understand the scale of the observable universe at a given redshift.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu