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Angular size
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Linear size
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Distance
redshift z
Cosmological angular-diameter calculator
Computes DA, DL, DC, DLT, lookback time and the kpc-per-arcsec scale for an arbitrary ΛCDM model. All math runs in your browser — no server, no tracking, no waiting on archives.
Cosmological distances at this redshift
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About
KosmoCal converts between an object's angular size on the sky and its physical linear size at a given redshift, using a full ΛCDM cosmology. It's the in-browser equivalent of a Ned Wright cosmology calculator — but with bidirectional live binding, paper-quality presets (Planck 2018, WMAP9, DES Y3, SH0ES, custom), and instant scale-per-arcsec readout.
For redshift z, the angular diameter distance is DA = DM / (1+z), where the transverse comoving distance DM is the standard sinh/sin transformation of the line-of-sight comoving distance DC = (c/H₀) ∫₀z dz'/E(z'). E(z) = √(Ωm(1+z)³ + Ωk(1+z)² + ΩΛ). The linear size is θ × DA (with θ in radians).
Hogg 1999 · astro-ph/9905116 — canonical reference for cosmological distance measures.
Pen 1999 · ApJS 120, 49 — analytical fit for flat ΛCDM.
Planck Collab. 2020 · A&A 641, A6 — Planck 2018 parameters.
Hinshaw et al. 2013 · ApJS 208, 19 — WMAP9.
Riess et al. 2022 · ApJ 934, L7 — SH0ES H₀.
If you use KosmoCal in a publication, please cite the underlying cosmology reference (Hogg 1999) and the cosmology preset you chose. KosmoCal itself is part of the EuKosmos research-tool family by M. Rahaman.