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Calcimator

Cosmological Distance Calculator

Calculate luminosity distance, comoving distance, angular diameter distance, and lookback time using cosmological models.

Inputs

km/s/Mpc

Results

Luminosity Distance

458.25 Mpc

Comoving Distance

416.59 Mpc

Lookback Time

13.8 billion years

Angular Diameter Distance378.72 Mpc
Age at Emission0 billion years
Recessional Velocity32,077.79 km/s
How to Use This Calculator
  1. Enter the Redshift (z) of the object — from spectroscopic observations; nearby galaxies z ≈ 0.01–0.1, high-z quasars z > 2.
  2. Set the Hubble Constant (km/s/Mpc): Planck value is 67.4; SH0ES measurement is 73.0.
  3. Adjust Matter Density (Ω_m) and Dark Energy Density (Ω_Λ): standard ΛCDM uses 0.3 and 0.7 respectively.
  4. Read Luminosity Distance (Mpc) for flux-based calculations and Comoving Distance (Mpc) for volume statistics.
  5. Use Lookback Time (billion years) to determine the cosmic epoch you are observing and Age at Emission for context.

How the result changes with Redshift (z)

Redshift (z)Luminosity DistanceComoving DistanceLookback Time
17,280.67 Mpc3,640.34 Mpc138 billion years
3.551,714.2 Mpc11,492.04 Mpc483 billion years
6.5154,500.18 Mpc20,600.02 Mpc897 billion years
9281,376.64 Mpc28,137.66 Mpc1,242 billion years

What each input means

Redshift (z)
Cosmological redshift
Hubble Constant
Hubble constant
Matter Density (Ω_m)
Matter density parameter
Dark Energy Density (Ω_Λ)
Dark energy density parameter

How this is calculated

Formula

d_L ≈ (c/H_0) × z × [1 + 0.5(1 - Ω_m + Ω_Λ)z]

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Redshift (z) = 0.1, Hubble Constant = 70, Matter Density (Ω_m) = 0.3, Dark Energy Density (Ω_Λ) = 0.7 = 4 input(s) provided
  2. Calculate Luminosity Distance
    Luminosity Distance
    458.25 = 458.25
  3. Calculate Comoving Distance
    Comoving Distance
    416.59 = 416.59
  4. Calculate Lookback Time
    Lookback Time
    13.8 = 13.8
  5. Calculate Angular Diameter Distance
    Angular Diameter Distance
    378.72 = 378.72
  6. Calculate Age at Emission
    Age at Emission
    0 = 0

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