iCosmos — Cosmology Calculator
iCosmos is a free online cosmology calculator created by Oxford cosmologist Mihran Vardanyan. Compute comoving, angular diameter and luminosity distances, comoving volume, lookback time, the age of the universe and the growth factor for any ΛCDM or w0waCDM universe, with live plots, model comparison and PNG, PDF, SVG and CSV exports. Originally developed at the University of Oxford; OxTALENT Award 2012.
What iCosmos calculates
- Comoving, transverse comoving, angular diameter and luminosity distances
- Whole-sky comoving volume, lookback time, age of the universe today and at any redshift
- Linear growth factor and growth rate
- Hubble parameter H(z), deceleration parameter, density parameters and dark-energy equation of state
- ΛCDM, curved and w0–wa (CPL) dark-energy models, with Planck 2018 and DESI DR2 presets
- Live plots, comparison of up to six universes, and PNG, PDF, SVG and CSV exports for papers and lectures
About the author
Mihran Vardanyan is a cosmologist who earned his DPhil in cosmology at the University of Oxford, supervised by Joseph Silk and Roberto Trotta. He developed iCosmos during his research years at Oxford Astrophysics, where his work applied Bayesian model selection to the curvature and size of the Universe. Mihran Vardanyan on LinkedIn · Mihran Vardanyan on Google Scholar
- M. Vardanyan, R. Trotta & J. Silk (2009), How flat can you get? A model comparison perspective on the curvature of the Universe, MNRAS 397, 431.
- M. Vardanyan, R. Trotta & J. Silk (2011), Applications of Bayesian model averaging to the curvature and size of the Universe, MNRAS Letters 413, L91.
Referenced in research and teaching
Research that used iCosmos
- Taylor et al. (2014) — The Core Collapse Supernova Rate from the SDSS-II Supernova Survey. The Astrophysical Journal 792, 135. Used the iCosmos calculator to examine how cosmological parameters affect comoving volume; cites Vardanyan in the references.
- Diemer (2018) — COLOSSUS: A Python Toolkit for Cosmology, Large-scale Structure, and Dark Matter Halos. The Astrophysical Journal Supplement Series 239, 35. Tested the growth factor of the widely used COLOSSUS code against the iCosmos calculator.
- Jo et al. (2021) — Star formation rate density across the cosmic time. Astrophysics and Space Science 366, 18. References the iCosmos calculator (icosmos.co.uk).
- Martocchia & Polcaro (2010) — GRB 080319b and SN1054. Memorie della Società Astronomica Italiana Supplementi 14, 242–245. Credits Mihran Vardanyan’s iCosmos calculator in a footnote for its cosmological distance estimate.
- Bilton (2016) — Tracing Star Formation around Quasars with Polycyclic Aromatic Hydrocarbons. MPhil thesis, The Open University. Computed the angular diameter distances of its quasar sample with the iCosmos calculator.
Teaching and reference resources
- NASA/IPAC Extragalactic Database (NED) — Extragalactic Articles. Caltech / IPAC. Lists iCosmos among its cosmology calculators, alongside Ned Wright’s calculator.
- Hubble Frontier Fields — Strong Gravitational Lensing Primer (Coe, 2013). Space Telescope Science Institute. Recommends iCosmos for computing angular diameter distances.
- Wikipedia — Distance measure. External links. Links iCosmos as a calculator of cosmological distance measures, with graph generation.
- Case Western Reserve University — Cosmology and the Structure of the Universe (Fall 2020). Stacy McGaugh, ASTR/PHYS 328/428. Links iCosmos among the course’s cosmology calculators.
- University of Sydney — Senior Astrophysics, Lecture 5 (2011). Scott Croom, Distances and the CMB. Lists iCosmos as a useful calculator with a graphing facility.
- Centro de Astrobiología (CSIC-INTA) — Astrofísica Extragaláctica y Cosmología. Tema 11: Cosmología relativista. Links iCosmos in its distances-versus-redshift teaching material.
- Spectroscopic Determination of Cosmological Distances and Parameters (Walker, 2022). Monograph, v2.0. Cites “M. Vardanyan, iCosmos” among its cosmology calculators.
- Cosmology Resource Materials. Curated list on GitHub. Lists iCosmos with the ICRAR and Ned Wright calculators.
Frequently asked questions
What is iCosmos?
iCosmos is a free online cosmology calculator. For any universe you choose (matter, dark energy, radiation, curvature, w0–wa dark energy and the Hubble constant) it computes the comoving, angular diameter and luminosity distances, comoving volume, lookback time, the age of the universe and the linear growth factor at any redshift, and plots how they change.
Who created iCosmos?
iCosmos was created by Mihran Vardanyan, who developed it during his DPhil research in cosmology at Oxford Astrophysics, University of Oxford, supervised by Joseph Silk and Roberto Trotta. It first went online in 2008 and was recognised in the University of Oxford’s OxTALENT awards in 2012.
How accurate is iCosmos?
Every number is checked automatically against independent calculations. On the published benchmark of 21 universes, distances and ages agree with SciPy and mpmath reference values to about 1 part in 10¹⁴ and the growth factor to about 2 × 10⁻⁹; in stress tests over 400 random universes across the full parameter range, the growth factor agrees with the exact Heath integral to better than 10⁻⁹. Where a quantity cannot be computed reliably, the calculator says so instead of showing a number. The validation tables are on the Reference page.
Who uses iCosmos?
iCosmos has been used in published research (for example in The Astrophysical Journal), in theses, and in university cosmology courses, and is listed by the NASA/IPAC Extragalactic Database and Wikipedia among cosmology calculators.
How do I cite iCosmos?
Vardanyan, Mihran. iCosmos V4: Cosmology Calculator. https://icosmos.co.uk/. Include your access date, model parameters and exported data when reporting calculations.
Calculators for each quantity
- Angular diameter distance calculator: How far away an object is, judged by how big it looks: DA = physical size ÷ angular size.
- Luminosity distance calculator: The distance that converts an observed flux into a luminosity: F = L / (4π DL2).
- Comoving distance calculator: The distance to an object today, in coordinates that expand with the universe.
- Lookback time calculator: How long ago the light we see from redshift z set off: tL = t0 − t(z).
- Age of the universe calculator: The cosmic time since the Big Bang, today and when the light from redshift z was emitted.
- Comoving volume calculator: The volume of space, measured today, within redshift z over the whole sky.
- Linear growth factor calculator: How much small density fluctuations have grown, from the early universe to redshift z.
- Hubble parameter H(z) calculator: The expansion rate of the universe when the light from redshift z was emitted.
- Distance modulus calculator: The difference between apparent and absolute magnitude at redshift z: μ = m − M.
- Redshift to distance calculator: Redshift does not give a single distance: here are all of them, and which one to use.
- Curvature of the universe calculator: The shape of space follows from what the universe contains: Ωk = 1 − Ωm − ΩΛ − Ωr.
How to cite iCosmos
Vardanyan, Mihran. iCosmos V4: Cosmology Calculator. https://icosmos.co.uk/. Include your access date, model parameters and exported data when reporting calculations.