What it does
In an expanding universe, “how far away” has several answers. A galaxy’s light set off long ago, the galaxy is much further away now, and the distance you need depends on whether you are turning a flux into a luminosity or an angle into a size. This calculator works them all out from one redshift: the age of the universe now and when the light left, the lookback time, the comoving, angular diameter and luminosity distances, the physical scale in kpc per arcsecond, the distance modulus, the comoving volume, the Hubble rate and the CMB temperature at that redshift. A chart shows how the distances grow with redshift.
How to use it
- Type the redshift z, for example 0.05 for a nearby galaxy cluster or 3 for a distant galaxy.
- Choose a cosmology. Planck 2018 is the default. WMAP 9-year and the round textbook values (H0 = 70, Ωm = 0.3) are there too, or type your own.
- Leave Flat universe ticked unless you need curvature. Then ΩΛ is set so everything adds up to 1. Untick it to type ΩΛ yourself; the curvature Ωk is then 1 − Ωm − ΩΛ − Ωr.
- Include radiation adds photons and neutrinos (CMB at 2.7255 K, Neff = 3.046). It matters at high redshift and makes the ages match those published by Planck.
- Download the results with the chart as PNG, PDF or Word.
What each number means
- Lookback time is how long the light has been travelling.
- Comoving distance is where the object is now, measured along the line of sight.
- Angular diameter distance turns an angle on the sky into a physical size. It reaches a maximum near z = 1.6 and then falls, so very distant galaxies look larger again.
- Luminosity distance turns the flux you measure into the luminosity the object gives out. The distance modulus is 5 log₁₀(D_L / 10 pc).
- kpc per arcsecond is the size of one arcsecond at that redshift.
- Recession velocity is shown as cz and as a special-relativity Doppler speed. At high redshift neither is a real velocity; use the distances instead.
Worked example
With Planck 2018 (H0 = 67.66 km/s/Mpc, Ωm = 0.3111, flat) the universe is 13.786 billion years old, matching Planck’s 13.787 ± 0.020. A galaxy at z = 3 sent out its light 11.643 billion years ago, when the universe was 2.143 billion years old. It is now 6,504 Mpc away (comoving). Its angular diameter distance is 1,626 Mpc, so one arcsecond spans 7.883 kpc. Its luminosity distance is 26,015 Mpc, a distance modulus of 47.076.
Frequently asked questions
How are the results worked out? By numerical integration of the Friedmann equation, following Hogg’s “Distance measures in cosmology” (1999). Checks against exact formulas (matter-only, empty and flat ΛCDM universes) agree to better than 1 part in a million.
Why do my numbers differ a little from another calculator? Different defaults: H0, Ωm, whether radiation is included, and whether massive neutrinos are counted. Set the same values and the results agree.
Is anything sent anywhere? No. Everything runs in your browser and works offline.
Where the numbers come from
- Distance formulas: Hogg (1999), Distance measures in cosmology.
- Preset parameters: Planck 2018 and WMAP 9-year published results (two numbers each), and round textbook values.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.