Redshift Distance Converter
Convert redshift values to various cosmological distances including luminosity distance, angular diameter distance, and lookback time. Based on standard ΛCDM cosmology.
Redshift & Distance Conversion
Cosmological Parameters
Understanding Cosmological Distances
What is Redshift?
Redshift (z) is the fractional change in wavelength of light due to the expansion of the universe:
z = (λ_observed - λ_rest) / λ_rest
Types of Cosmological Distances
- Comoving Distance: Distance in today's coordinates, accounting for expansion
- Luminosity Distance: Distance inferred from apparent brightness
- Angular Diameter Distance: Distance inferred from angular size
- Light Travel Distance: Distance light has actually traveled
Hubble's Law (Low Redshift)
For nearby objects (z < 0.1):
v = H₀ × d
z ≈ v/c = H₀ × d / c
ΛCDM Cosmological Model
Standard model parameters (Planck 2018):
- H₀ = 67.4 km/s/Mpc (Hubble constant)
- Ω_m = 0.315 (matter density parameter)
- Ω_Λ = 0.685 (dark energy density parameter)
- Ω_k = 0 (curvature parameter, flat universe)
Redshift Examples
| Object | Redshift (z) | Distance | Lookback Time |
|---|---|---|---|
| Local Group galaxies | 0.001 - 0.01 | 1 - 40 Mpc | 3 - 130 Myr |
| Virgo Cluster | ~0.004 | ~16 Mpc | ~50 Myr |
| Coma Cluster | ~0.023 | ~100 Mpc | ~300 Myr |
| Distant galaxies | 1 - 2 | 3 - 6 Gpc | 8 - 10 Gyr |
| CMB (recombination) | ~1100 | ~46 Gpc | ~13.7 Gyr |
Distance-Redshift Relationship
In an expanding universe, the relationship between distance and redshift depends on cosmological parameters and is calculated through integration of the Friedmann equation.