Redshift Distance Calculator (ΛCDM)

Compute DL, DA, and DC from redshift in a flat ΛCDM universe. Private by design—everything runs locally in your browser.

Inputs & Parameters

Presets:

Results

Comoving Distance :—
Angular Diameter :—
Luminosity Distance :—
Hubble Distance :—
Uses flat ΛCDM: E(z)=√(ΩM(1+z)3 + ΩΛ), DH=c/H0, DC=DH∫0zdz/E(z), DA=DC/(1+z), DL=DC(1+z). c = 299,792.458 km/s.

How it works

This calculator assumes a spatially flat ΛCDM cosmology. It computes the comoving distance via numerical integration of 1/E(z). Angular diameter and luminosity distances follow from standard relations. All computation is client-side for privacy.

Understanding Redshift & Cosmological Distances

This redshift distance calculator converts a measured redshift z into several standard cosmological distances used by astronomers and cosmologists. In a flat ΛCDM model (Lambda Cold Dark Matter), we specify the Hubble constant H0 (km/s/Mpc) and the matter density parameter ΩM. Flatness implies ΩΛ = 1 − ΩM, where ΩΛ accounts for dark energy (Λ). With these, the expansion history enters through E(z) = √(ΩM(1+z)3 + ΩΛ).

What each distance means

  • Comoving distance (DC) – the “map distance” in today’s Universe, integrating expansion effects from now back to redshift z. It is computed as DC = DH ∫0z dz/E(z), where DH = c/H0 is the Hubble distance.
  • Angular diameter distance (DA) – links a source’s physical size to its observed angular size via θ = size / DA. In ΛCDM, DA = DC / (1+z). Notably, at high redshift, DA can decrease with increasing z, so very distant objects can appear larger than somewhat nearer ones.
  • Luminosity distance (DL) – relates a source’s intrinsic luminosity to its observed flux: F = L / (4π DL2). In ΛCDM, DL = DC(1+z).

Choosing cosmological parameters

The default preset uses Planck 2018 values (e.g., H0 ≈ 67.4, ΩM ≈ 0.315), which fit the cosmic microwave background under ΛCDM. Many local-distance ladder analyses (e.g., SH0ES) report a higher H0 (≈ 73 km/s/Mpc). Because DH = c/H0, a higher H0 yields smaller distances at the same redshift. For transparent reporting, cite the H0 and ΩM you use.

Practical notes for observers

  • Low redshift (z ≪ 1): Hubble’s law v ≈ H0 D is a good first approximation, but peculiar velocities can be a significant fraction of the signal.
  • Photometry & SEDs: If you derive luminosities from fluxes, consider K-corrections and bandpass effects; DL alone isn’t the whole story.
  • Angles to sizes: Convert arcseconds to radians before applying size = θ · DA. One arcsecond is approximately 4.848 × 10−6 radians.
  • Units: This tool reports Gpc for readability; internally the integration is performed in Mpc via DH.

Method overview

The calculator performs a fast numerical integration of 1/E(z) from 0 to your chosen redshift, using the speed of light c = 299,792.458 km/s. All computation runs entirely in your browser for privacy and responsiveness. Whether you are estimating a galaxy’s physical size from imaging, converting observed fluxes to luminosities, or teaching the difference between DL, DA, and DC, this redshift calculator provides a clear, ΛCDM-consistent foundation for distance determinations.

FAQs

Which cosmology does this use?

Flat ΛCDM with adjustable H0 and ΩM (so ΩΛ=1−ΩM).

Which distances are reported?

Comoving (DC), angular diameter (DA), and luminosity (DL), plus the Hubble distance DH.

Are computations private?

Yes—everything runs locally in your browser; nothing is uploaded.

What units are used?

Outputs are shown in Gpc (with Mpc basis internally for integration).

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