Calculate redshift

Compare classical and relativistic recession speed, Hubble-law distance, and a simplified light-travel time from redshift.

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ToolRedshift Calculator
Input
Output
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Preview

How it works

Classical speed is cz, relativistic Doppler speed uses c((1+z)²−1)/((1+z)²+1), and Hubble-law distance divides cz by H₀. Lookback time divides that distance by c instead of integrating a full cosmological expansion model.

  • H₀ begins at 70 km/s/Mpc.
  • The simplified distance and time deliberately use the classical Hubble-law value.

Worked example

A galaxy at z = 0.1
Hubble constant left at the default 70 km/s/Mpc
Input
											0.1
Output
												Redshift: 0.1
Classical velocity km s: 29979.2458
Relativistic velocity km s: 28487.0661
Hubble distance mpc: 428.2749
Hubble distance mly: 1396.8562
Lookback time gyr: 1.3969

When to use this

Astronomy lessons convert spectral shifts, cosmology exercises compare Hubble distances, and outreach examples estimate simplified light-travel time.

Edge cases

  • Near z = 1, cz can exceed c while the relativistic expression remains below c.
  • Full lookback time needs cosmological density parameters and integration.
  • Nearby peculiar velocities and local flows are absent.

References