Redshift Calculator

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Cosmological Redshift

As light travels through expanding space, its wavelength stretches. The redshift z measures this stretching as the fractional change in wavelength:

A redshift of z = 1 means the observed wavelength is twice the emitted wavelength. Higher redshift means the object is farther away and the light was emitted longer ago.

Recessional Velocity

For low redshifts (z < 0.1), the classical Doppler approximation works well:

For higher redshifts, the special-relativistic Doppler formula is more accurate:

Hubble's Law

Hubble's law relates recessional velocity to distance via the Hubble constant:

Where H₀ ≈ 70 km/s/Mpc is the Hubble constant and d is the comoving distance. This provides a good distance estimate for z < 1. For very high redshifts, the relationship between distance and redshift depends on the full cosmological model.

Lookback Time

The lookback time approximates how long ago the light was emitted. For a matter-dominated universe:

where t₀ ≈ 13.8 billion years is the age of the universe. This is a simplified estimate; exact values require full cosmological integration.

Important Notes

• Distances at high redshift are model-dependent and should be treated as approximations.
• The Hubble constant is taken as 70 km/s/Mpc (a commonly used value; actual measurements range from ~67 to ~73).
• For z > ~1, Hubble's law overestimates distance. This calculator uses a simplified comoving distance integral for better accuracy at moderate redshifts.
• Peculiar velocities of nearby galaxies can dominate over the cosmological redshift at very low z.