Hubble's Law Calculator

Background.

Hubble's law — the IAU has recommended calling it the Hubble–Lemaître law since Resolution B4 in 2018 — says that a distant galaxy's recession velocity is proportional to its distance: v = H₀d. Give this calculator a recession velocity in km/s and it returns the distance in megaparsecs and in million light-years; give it a distance and it returns the velocity. It also reports the Hubble time 1/H₀ and the Hubble distance c/H₀, and tells you whether the linear law is actually valid at the velocity you entered.

The single most important thing about this calculation is that H₀ is not settled, and this page refuses to pretend otherwise. It is an editable input, not a baked-in constant, and every answer is computed a second and third time at the two headline determinations so you can see what the disagreement costs you. Planck Collaboration VI (2020), fitting the base-ΛCDM model to the cosmic microwave background, reports H₀ = 67.4 ± 0.5 km/s/Mpc. The SH0ES team (Riess et al. 2022), climbing the local distance ladder through Cepheid-calibrated Type Ia supernovae, reports H₀ = 73.04 ± 1.04 km/s/Mpc, and states plainly that this is "a 5-sigma difference with H₀ predicted by Planck+ΛCDM, with no indication this arises from measurement errors". That is the Hubble tension, and it has survived a decade of attempts to make it go away. A third, independent programme — the Chicago-Carnegie Hubble Program, using the tip of the red giant branch with HST and JWST — lands at 70.39 ± 1.22 (stat) ± 1.33 (sys), between the two.

What that means for your answer, concretely: a galaxy receding at 7,000 km/s is 103.86 Mpc away if Planck is right and 95.84 Mpc away if SH0ES is right. That is an 8.02 Mpc gap on a single object — about 26 million light-years of pure disagreement about the expansion rate, not about the measurement of that galaxy. The default here is 70 km/s/Mpc, chosen as a neutral round number that belongs to nobody; it is a placeholder, not an endorsement, and you should replace it with whichever value your source used.

The law itself is an approximation with a well-defined domain, and the page names it beside the answer rather than burying it. It works best in the Hubble flow: far enough out that a galaxy's own peculiar motion inside its group or cluster is small compared with the expansion, and near enough that the universe's changing expansion rate has not yet mattered. Close in, peculiar velocities dominate — the Andromeda Galaxy is blueshifted and approaching us, which the law simply cannot describe, and this calculator rejects negative velocities for exactly that reason. Far out, past roughly 10% of the speed of light, the distance stops depending on H₀ alone and starts depending on the whole cosmological model: the matter density, the dark-energy density and the expansion history. Beyond the Hubble distance c/H₀ the linear law returns recession speeds greater than c, which is not a paradox — cosmological recession is the expansion of space, not motion through it — but it is a loud signal that you are far outside the regime the formula was derived for.

One more distinction the page keeps explicit. The Hubble time, 1/H₀, is what you get by pretending the expansion rate has always been what it is now; at H₀ = 70 it comes out at 13.97 Gyr. That is tantalisingly close to the measured age of the universe, and it is not the same quantity. The real age integrates the whole expansion history, which has not been constant, and the numerical near-coincidence is a feature of our particular cosmology rather than an identity. Treat 1/H₀ as a characteristic timescale for the expansion, and get the age of the universe from a cosmological fit instead.

What is hubble's law calculator?

Hubble's law is the observed linear relation between the recession velocity of a distant galaxy and its distance from us: v = H₀d, where H₀ — the Hubble constant — is the present-day expansion rate, quoted in the slightly awkward but standard units of kilometres per second per megaparsec. Edwin Hubble published the relation in 1929 in the Proceedings of the National Academy of Sciences, building on Georges Lemaître's 1927 theoretical work; IAU Resolution B4 (2018) recommends the name Hubble–Lemaître law, adopted by 78% of the 4,060 members who voted.

H₀ has dimensions of inverse time, which is why it can be turned directly into two derived quantities. The Hubble time, 1/H₀, is a characteristic timescale for the expansion — 13.97 Gyr at H₀ = 70 — and the Hubble distance, c/H₀, is the distance at which the linear law would predict recession at exactly the speed of light: 4,282.75 Mpc at H₀ = 70. Numerically the Hubble time in gigayears and the Hubble distance in gigalight-years are the same number, because one is just c times the other.

What Hubble's law is not: it is not a Doppler shift caused by galaxies flying through space, it is not valid for objects bound into our own Local Group, and it is not a replacement for a cosmological model at large redshift. It is the leading-order term of a distance–redshift relation whose higher-order terms carry the information about dark energy, and it is exactly because those higher-order terms matter that supernova cosmology exists at all.

How to use this calculator.

1. 01Choose whether you are solving for distance or for velocity.
2. 02Enter the recession velocity in km/s, or the distance in megaparsecs. If you have a redshift z rather than a velocity, convert it on the redshift calculator first — v = cz is only valid at small z.
3. 03Set the Hubble constant. Use the value your source used; 67.4 for Planck-based work, 73.04 for SH0ES-based work, 70 if you genuinely have no preference.
4. 04Read the primary answer, then look at the two alternate distances underneath — they show what the unresolved H₀ disagreement costs on your specific object.
5. 05Check the regime note before quoting the number. Below about 1% of light speed the answer is contaminated by peculiar motion; above about 10% it needs a full cosmological model.

The formula.

The core arithmetic is one division or one multiplication: d = v/H₀ when you know the velocity, v = H₀d when you know the distance. The units work out because H₀ is quoted in km/s per Mpc, so dividing a km/s by it leaves Mpc directly.

The derived quantities need the unit chain spelled out. The Hubble time is 1/H₀, but H₀ is not in inverse seconds, so the conversion runs through the megaparsec: 1 Mpc = 3.0856775814913673 × 10¹⁹ km exactly, so 1/H₀ = (3.0856775814913673 × 10¹⁹ km/Mpc) ÷ (H₀ km/s/Mpc) seconds. At H₀ = 70 that is 4.408 × 10¹⁷ s, and dividing by the Julian gigayear (3.15576 × 10¹⁶ s) gives 13.9684603 Gyr. The Hubble distance is simply c/H₀ = 299,792.458 ÷ 70 = 4,282.7494 Mpc. Converting that to gigalight-years gives 13.9684603 Gly — the same number as the Hubble time in Gyr, which is a useful arithmetic check that the unit chain is right rather than a coincidence.

The two comparison distances are the identical calculation run again at H₀ = 67.4 and H₀ = 73.04. Because d ∝ 1/H₀, their ratio is fixed at 73.04/67.4 = 1.08368 whatever the object: Planck's H₀ always puts a given recession velocity 8.37% further away than SH0ES' does. The tension spread output is the absolute difference in Mpc, which does scale with the object.

Rounding stage: there is no intermediate rounding anywhere. All arithmetic runs at 40 significant digits and is rounded once, at the return boundary, to ten decimal places. The regime bands are decided on the unrounded v/c ratio.

A scope note about the regime bands themselves, in the interests of not overclaiming: the two band edges used here, at 1% and 10% of the speed of light, are a presentation convention chosen for this page, not published thresholds from any paper. They are round numbers picked to separate three regimes that really are physically distinct — peculiar-motion-dominated, Hubble flow, and model-dependent. The Hubble-distance warning, by contrast, is exact: c/H₀ is where the linear law's own output reaches c.

Invalid-domain behaviour: H₀ ≤ 0 raises a field error, because H₀ = 0 is the singularity of d = v/H₀ and describes a static universe in which the law has no distance solution. A negative recession velocity also raises an error rather than returning a negative distance — blueshifted galaxies exist, but their motion is peculiar velocity within a gravitationally bound system, which Hubble's law does not describe.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Planck Collaboration VI (2020), "Planck 2018 results VI: Cosmological parameters", Astronomy & Astrophysics 641, A6; arXiv:1807.06209 (abstract retrieved 2026-07-29). Abstract quotes "Hubble constant H₀ = (67.4 ± 0.5) km/s/Mpc" for base-ΛCDM. Peer-reviewed; open-access preprint.
2. [2]Riess, A. G., et al. (2022), "A Comprehensive Measurement of the Local Value of the Hubble Constant…" (SH0ES), Astrophysical Journal Letters 934, L7, doi:10.3847/2041-8213/ac5c5b; arXiv:2112.04510 (abstract retrieved 2026-07-29). Abstract: "Our baseline result from the Cepheid-SN sample is H0=73.04+-1.04 km/s/Mpc" and "We find a 5-sigma difference with H0 predicted by Planck+LCDM, with no indication this arises from measurement errors". Peer-reviewed; open-access preprint.
3. [3]Freedman, W. L., et al., Chicago-Carnegie Hubble Program, "Status Report on the CCHP: Measurement of the Hubble Constant Using the Hubble and James Webb Space Telescopes", arXiv:2408.06153 (abstract retrieved 2026-07-29). Reports JWST TRGB H₀ = 68.81 ± 1.79 (stat) ± 1.32 (sys) and a best HST+JWST TRGB combination of 70.39 ± 1.22 (stat) ± 1.33 (sys) ± 0.70 (σ_SN) km/s/Mpc — an independent third determination. Open-access preprint.
4. [4]Hubble, E. (1929), "A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae", Proceedings of the National Academy of Sciences 15(3), 168–173. The original observational paper establishing the linear velocity–distance relation. Free full text via PubMed Central (page images); retrieved 2026-07-29.
5. [5]International Astronomical Union, press release iau1812 (2018), "IAU members vote to recommend renaming the Hubble law as the Hubble–Lemaître law" (retrieved 2026-07-29). Records IAU 2018 Resolution B4 and the electronic vote closing 26 October 2018: 4,060 members voting (37% turnout), 78% in favour, 20% against, 2% abstaining.
6. [6]Mamajek, E. E., et al. (2015), "IAU 2015 Resolution B2…", arXiv:1510.06262 (retrieved 2026-07-29). Source of the exact parsec definition, (648 000/π) au = 3.085 677 581 × 10¹⁶ m, used for every Mpc↔km and Mpc↔Mly conversion on this page. Open-access preprint of an adopted IAU resolution.
7. [7]NIST/CODATA 2022, "Speed of light in vacuum": c = 299 792 458 m s⁻¹, exact. Retrieved 2026-07-29. Used for the Hubble distance c/H₀ and the v/c regime bands.