What is cosmological redshift?

Cosmological redshift occurs because the universe is expanding. As light travels from a distant galaxy, the space it crosses stretches, lengthening the wavelength. The redshift parameter z = (λ_obs − λ_emit) / λ_emit quantifies this stretching. A galaxy with z = 1 had its light stretched to twice its original wavelength by the time it reached us.

Can a galaxy recede faster than light?

Yes. Galaxies beyond the Hubble radius (about 14 billion light-years today) are receding faster than c due to spacetime expansion, not motion through space, so special relativity is not violated. This calculator uses the relativistic Doppler formula for v, which asymptotes toward c but never exceeds it in the special-relativistic sense. The comoving distance calculation correctly handles superluminal recession.

What cosmological model does this calculator use?

Standard flat ΛCDM with H₀ = 67.4 km/s/Mpc, matter density Ω_m = 0.315, and dark energy density Ω_Λ = 0.685 (Planck 2018 best-fit values). Radiation density is neglected, which introduces less than 1% error for z < 1000.

What is the difference between redshift and recession velocity?

Redshift z is a dimensionless ratio of wavelength change. Recession velocity v is derived from z using the relativistic Doppler formula. For small z (nearby galaxies) v ≈ c × z. For large z the full formula must be used, and at z = 1 the recession velocity is about 0.6c.

What wavelength units should I use?

Any consistent unit works — Angstroms, nanometers, or micrometers — as long as both the observed and emitted wavelengths use the same unit. The ratio (λ_obs − λ_emit) / λ_emit is dimensionless.

How accurate is the lookback time?

The lookback time is computed by numerically integrating the comoving distance integral using 1000 steps of Gaussian-style summation. Results agree with published cosmological tables to better than 0.1% for z 100) the neglected radiation term introduces a small systematic error.

Redshift Calculator

Name: Redshift Calculator
Availability: InStock
Author: Nham Vu

Enter a redshift value z (or observed vs emitted wavelengths) to compute recession velocity, lookback time, and comoving distance for a distant galaxy.

Input Parameters

Input Mode

Known Object Preset

Redshift Parameter (z)

Negative z = blueshift (approaching object)

Model: Flat ΛCDM — H₀ = 67.4 km/s/Mpc, Ω_m = 0.315, Ω_Λ = 0.685 (Planck 2018)

Select a preset or enter a redshift value, then click Calculate.

Redshift z

Recession Velocity

Lookback Time

billion years

Comoving Distance

Mpc

Scale Factor

a = 1/(1+z)

Light Travel Dist.

billion ly

Universe Scale at Emission

Big Bang (a=0) Today (a=1)

Redshift Reference Scale

Object	z	Lookback (Gyr)	Scale

Summary

Enter a redshift value z (or observed vs emitted wavelengths) to compute recession velocity, lookback time, and comoving distance for a distant galaxy.

How it works

Choose input mode: enter the redshift parameter z directly, or supply an observed wavelength and the rest-frame (emitted) wavelength.
If using wavelengths, z is derived as (λ_observed − λ_emitted) / λ_emitted.
Recession velocity is computed with the relativistic formula: v = c × [(1+z)² − 1] / [(1+z)² + 1].
Lookback time and comoving distance are estimated using standard ΛCDM cosmology (H₀ = 67.4 km/s/Mpc, Ω_m = 0.315, Ω_Λ = 0.685) via numerical integration.
The scale factor at emission is a = 1 / (1 + z), showing how much smaller the universe was when the light departed.
Results update instantly when you click Calculate or press Enter.

Use cases

Determine how fast a distant galaxy is receding based on its spectral redshift.
Convert a measured spectral line shift into a cosmological distance.
Explore how lookback time grows with increasing z for astronomy courses.
Calculate the scale factor of the universe at the time of emission.
Verify redshift values from observational data against known galaxy catalogs.
Illustrate Hubble flow and the expansion of the universe for presentations.
Estimate the comoving distance to quasars and high-z objects.
Compare recession velocities at different redshifts for cosmology homework.

Frequently Asked Questions

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Last updated: 2026-05-29 · Reviewed by Nham Vu