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. Developed at the University of Oxford; OxTALENT Award 2012.
What iCosmos computes
iCosmos computes, for any redshift and any model of the universe, the comoving distance, the angular diameter distance, the luminosity distance and the distance modulus, the lookback time and the age of the universe, the comoving volume, the Hubble parameter, the growth factor and the curvature of space. It also gives what surveys measure: BAO distances, the CMB acoustic scale, the matter power spectrum and σ₈, and it sets your model beside published values of the Hubble constant. To start from a redshift alone, use redshift to distance. Plots show how each quantity changes with redshift, and a reference model can be overlaid for comparison. Lecturers and tutors can link to any plot with the parameters already set. iCosmos was developed at the University of Oxford and won First Prize in the Student IT Innovation category of Oxford’s OxTALENT awards in 2012.
Used in teaching and research
- Space Telescope Science Institute (Hubble Frontier Fields lensing primer)
- NASA/IPAC Extragalactic Database, Caltech (list of cosmology calculators)
- Case Western Reserve University (cosmology course)
- University of Sydney (senior astrophysics lectures)
- The Open University (MPhil thesis)
- Centro de Astrobiología (CSIC-INTA) (cosmology teaching notes)
- Full list of references
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
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.
- BAO distance calculator: Baryon acoustic oscillations measure distances in units of the sound horizon rd, a standard ruler set in the early universe.
- The Hubble tension: Two ways of measuring today’s expansion rate H0 disagree. Compare the published values and see what each one implies for the age and size of the universe.
- CMB acoustic scale calculator: The acoustic angle θ* is the angle the sound horizon at last scattering subtends on the sky, the best-measured of the cosmological parameters (Planck: 0.03 %).
- Matter power spectrum calculator: The power spectrum P(k) tells how strongly matter is clumped on each scale; σ8 sums it up in one number.
- σ₈, fσ₈ and S₈ calculator: σ8 measures how clumpy matter is on scales of 8 h⁻¹ Mpc; fσ8 and S8 are the combinations galaxy surveys measure.
Explore
- Compare: Plot up to six universes on the same axes: Planck 2018, DESI DR2, Einstein–de Sitter or your own parameters, with ratio plots and a table of values.
- Cosmic history: How the expansion rate, scale factor, lookback time, density parameters and deceleration change over cosmic time, for any cosmological model.
- Learn: Six animated lessons on cosmic distances, short explanations and eight guided experiments, all calculated live from the cosmological model you choose.
- Reference: The equations iCosmos solves, its constants and numerical methods, measured accuracy against independent codes, data sources and how to cite.
- About: iCosmos was developed at the University of Oxford by Mihran Vardanyan. Its history, the OxTALENT award, and the research and courses that use it.
About the author
Mihran Vardanyan: 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.
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 won First Prize in the Student IT Innovation category of 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 matter + Λ + curvature universes (H₀ = 70, Ωm 0.005–3, ΩΛ −1 to 3.5, including near-loitering and very low-density open models), the growth factor agrees with the exact Heath integral to better than 10⁻⁹. A further 200 random evolving-dark-energy universes are checked for finite or explained results, not for accuracy. 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 was one of the calculators used to test the cosmology code of Astropy, the standard Python package for astronomy, and the growth factor of the COLOSSUS toolkit. It has been used in research published 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.
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.
iCosmos 4.12.0 · updated