Cosmic Distance Calculator - Redshift to Distance
Calculate comoving distance, luminosity distance, angular diameter distance and lookback time from cosmological redshift in a flat FLRW universe.
Cosmological Parameters (Flat ΛCDM)
Current physical distance factoring in the continuous metric expansion of space since photon emission.
Cosmological Distance Measures vs. Redshift (z)
Comparison of Comoving (D_C), Luminosity (D_L), and Angular Diameter (D_A) distances. Notice how D_A turns over at z ≈ 1.5!
Hand-Verified Relativistic Cosmological Example
• Hubble Distance: D_H = c / H₀ = 299,792.5 / 70 = 4,282.75 Mpc
• Comoving Integral: ∫₀^0.1 dz' / E(z') ≈ 0.09772
• Comoving Distance: D_C = 4,282.75 × 0.09772 = 418.5 Mpc (1.365 Billion Light-Years)
• Luminosity Distance: D_L = (1 + 0.1) × 418.5 = 460.3 Mpc (1.501 Billion Light-Years)
• Angular Diameter: D_A = 418.5 / (1 + 0.1) = 380.4 Mpc (1.241 Billion Light-Years)
• Lookback Time: t_L ≈ 1.30 Billion Years (Light Travel Distance = 1.30 Gly)
Standard Empirical Cosmological Parameter Sets
| Observational Dataset | Hubble Constant (H₀) | Matter Density (Ωₘ) | Dark Energy (Ω_Λ) | Observational Source & Technique |
|---|---|---|---|---|
| Planck 2018 (Baseline CMB) | 67.4 km/s/Mpc | 0.315 | 0.685 | High-precision cosmic microwave background anisotropy measurements from the ESA Planck satellite mission. |
| Standard Textbook (Flat ΛCDM) | 70 km/s/Mpc | 0.3 | 0.7 | Standard pedagogical benchmark widely used across academic astrophysics textbooks and literature. |
| SH0ES / HST Cepheids & SNe Ia | 73 km/s/Mpc | 0.3 | 0.7 | Local Universe distance ladder calibration based on Hubble Space Telescope Cepheid variable stars and Type Ia supernovae. |
| WMAP 9-Year Final Results | 69.3 km/s/Mpc | 0.286 | 0.714 | Wilkinson Microwave Anisotropy Probe 9-year full sky cosmological parameter synthesis. |
Frequently Asked Questions About Cosmic Distances
Astrophysics & Cosmology Authority Citations
Planck Collaboration: Planck 2018 Cosmological Parameters
Definitive European Space Agency mission results providing the most precise baseline measurements of H0, Ωm, and dark energy density.
Ned Wright's Cosmology Tutorial and Calculator
Classic UCLA astrophysics reference for relativistic integration of cosmological distance measures in Friedmann universes.
Astropy Cosmology Module Documentation
Standard peer-reviewed astronomical Python software library implementing FLRW metric distance integrals.
Related Calculators
Quick Tips
- 1Use consistent units throughout calculations
- 2Consider significant figures in results
- 3Document experimental conditions
- 4Verify results with control calculations