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.

Is the Hubble law approximation accurate for high redshifts?

The simple linear Hubble law (d = cz/H₀) is only accurate for z ≪ 1. This calculator uses a full numerical integration of the ΛCDM Friedmann equation, which is accurate for any redshift where the standard cosmological model applies.

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?

A small negative redshift (blueshift) is physical — the Andromeda galaxy at z ≈ −0.001 is approaching us. This calculator handles small negative z values. Very large negative values are unphysical and will return an error.

Redshift to Distance Calculator

Name: Redshift to Distance Calculator
Availability: InStock
Author: Nham Vu

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

Redshift Input

Redshift (z)

Range: −0.1 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

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

How it works

Enter the redshift value (z) of a galaxy or quasar. Common values: Andromeda galaxy z ≈ −0.001, 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