Hubble’s law calculator: velocity, distance and the Hubble constant
Hubble’s law says that, on average, a galaxy recedes from us at a speed proportional to its distance: v = H₀ × d. This Hubble’s law calculator solves that equation whichever way round you need it — the recession velocity of a galaxy at a known distance, the distance of a galaxy from its velocity or redshift, or the Hubble constant from a measured velocity and distance.
Alongside the answer it gives the quantities that follow from H₀ itself: the Hubble time 1/H₀, the Hubble distance c/H₀, the matter-only age ⅔ × 1/H₀ and the age of the universe in a flat ΛCDM model. A small table shows how much the answer moves between the Planck and SH0ES values of H₀ — the “Hubble tension”. Everything runs in your browser.
How to use the Hubble’s Law Calculator
- Pick Find velocity, Find distance or Find H₀.
- Enter the known values. Distances can be in megaparsecs or millions or billions of light-years; velocities in km/s or as a redshift z (converted with v = cz).
- Set the Hubble constant, or press one of the presets: 67.36 (Planck 2018), 70, or 73.04 (SH0ES 2022).
- Read the answer, the redshift z ≈ v/c and the Hubble time and age cards; change Ωm to see how the ΛCDM age responds.
Hubble’s Law Calculator features
Three ways to solve
Velocity from distance, distance from velocity or redshift, and H₀ from a velocity–distance pair.
Unit-aware
Mpc, million or billion light-years, km/s or redshift; switching unit converts the number you typed.
Hubble time and age
1/H₀ in billions of years, the Einstein–de Sitter age ⅔/H₀ and the flat ΛCDM age from numerical integration.
Hubble tension at a glance
The same distance and velocity under H₀ = 67.36, 70 and 73.04 km/s/Mpc.
The formula and a worked example
With H₀ in km/s per megaparsec and d in megaparsecs, v = H₀ d gives km/s. A galaxy 100 Mpc away (326 million light-years) with H₀ = 70 recedes at 70 × 100 = 7,000 km/s, a redshift of z ≈ 7,000/299,792 = 0.0233. Turned around, d = v / H₀, and H₀ = v / d: a galaxy at 100 Mpc moving away at 7,304 km/s implies H₀ = 73.04 km/s/Mpc.
Because H₀ has units of speed per distance, its inverse is a time. 1/H₀ = 977.8 / H₀ billion years, so H₀ = 70 gives a Hubble time of 13.97 billion years. That would be the age of the universe if it had always expanded at today’s rate. Gravity of matter slows expansion (a matter-only universe is ⅔ × 1/H₀ = 9.3 Gyr old); dark energy speeds it up. With Planck’s Ωm = 0.3153 the two nearly cancel and the age is 13.8 billion years.
Hubble constants in use
The two precise measurements disagree by about five standard deviations. Whether this “Hubble tension” points to new physics or to an unrecognised error is one of the open questions in cosmology. For a classroom answer, 70 km/s/Mpc is within 5% of either.
| Source | H₀ (km/s/Mpc) | Method |
|---|---|---|
| Planck 2018 (A&A 641, A6) | 67.36 ± 0.54 | Cosmic microwave background, ΛCDM fit |
| SH0ES, Riess et al. 2022 (ApJL 934, L7) | 73.04 ± 1.04 | Cepheid-calibrated type Ia supernovae |
| Textbook round value | 70 | Convenient for estimates |
When Hubble’s law stops being enough
The linear law is exact for the present-day expansion rate and proper distance, but velocities and distances measured by astronomers are only proportional for nearby galaxies, up to about z ≈ 0.1 (roughly 400 Mpc). Further out, the expansion history matters: there are several different distances (luminosity, angular-diameter, comoving), and redshift is no longer cz. For those, use the redshift calculator, which integrates the full ΛCDM model.
Very close galaxies have the opposite problem: their own motions of a few hundred km/s swamp the expansion. The Andromeda galaxy, 0.77 Mpc away, is approaching us at about 300 km/s. Hubble’s law describes the average flow, not individual galaxies in the Local Group. To convert distances between parsecs and light-years, see the light-year converter.
Hubble’s Law Calculator FAQ
What is Hubble’s law?
The observation that galaxies recede at speeds proportional to their distance, v = H₀d. Georges Lemaître derived it in 1927 and Edwin Hubble published his measurements in 1929; in 2018 the International Astronomical Union recommended calling it the Hubble–Lemaître law.
How do I calculate the Hubble constant?
Divide a galaxy’s recession velocity by its distance: H₀ = v/d, with v in km/s and d in Mpc. Choose Find H₀ in the Hubble’s law calculator and enter both values. Real measurements average many galaxies to beat down their individual motions.
How do I get the age of the universe from H₀?
The Hubble time 1/H₀ is a first estimate (977.8/H₀ billion years). A real age needs the matter and dark-energy content; with Planck values it is 13.8 billion years, which this page computes from Ωm.
Why is H₀ in km/s/Mpc?
It is a speed per unit distance: each megaparsec (3.26 million light-years) of distance adds about 70 km/s of recession velocity.
Can the recession velocity exceed the speed of light?
Yes, beyond the Hubble distance c/H₀ (about 4,300 Mpc) the proper distance grows faster than c. This is expansion of space, not motion through it, and relativity allows it.