Hubble's Law Calculator

Background.

A galaxy's spectrum shows its light stretched toward the red, and the stretch says it is moving away from us at 7,000 km/s. How far away is it? For most galaxies beyond our immediate neighbourhood the answer comes from a single proportion: recession velocity equals distance multiplied by the Hubble constant, v = H₀d. Divide 7,000 km/s by H₀ = 70 km/s per megaparsec and the galaxy is 100 Mpc away, about 326 million light-years. Run the law the other way and a distance gives the velocity the expansion of the universe should impart.

The arithmetic is the easy part. The uncomfortable part is that nobody agrees on H₀. The Planck satellite's fit of the standard cosmological model to the cosmic microwave background gives 67.4 ± 0.5 km/s/Mpc. The SH0ES team, measuring nearby distances step by step with Cepheid variables and Type Ia supernovae, gets 73.04 ± 1.04 and calls the gap a 5-sigma difference with no sign of measurement error. A third programme using the tip of the red giant branch, observed with Hubble and JWST, lands between them at 70.39. That disagreement, the Hubble tension, is why H₀ is an input you set rather than a fixed constant, and why every distance is also worked out at both 67.4 and 73.04, so you can see what the dispute is worth on your own galaxy. The default of 70 is a round number, not a verdict.

The law also has a range where it works. Close to home, galaxies have their own motions inside groups and clusters that can swamp the expansion; the Andromeda galaxy is actually approaching us. Far away, beyond about a tenth of the speed of light, distance depends on how the expansion rate has changed over time, which a single constant cannot capture. A short note under the result says which of those regimes your input falls in.

Two more numbers come with every answer: the Hubble time 1/H₀ and the Hubble distance c/H₀, scales set by the expansion rate itself.

What is hubble's law calculator?

Hubble's law is the observed proportionality between how fast distant galaxies recede and how far away they are. Georges Lemaître derived the relation and estimated its constant in 1927, and Edwin Hubble published the observational evidence in 1929; in 2018 the International Astronomical Union recommended calling it the Hubble–Lemaître law. The recession is not galaxies flying through space but space between them expanding, which stretches the light they emit. H₀, the present-day expansion rate, is quoted in kilometres per second per megaparsec, but those units reduce to an inverse time: 70 km/s/Mpc is 2.2685 × 10⁻¹⁸ per second. Put more intuitively, at that rate distances between well-separated galaxies are currently growing by about 7.2% per billion years. Turning H₀ upside down gives the Hubble time, and multiplying that by the speed of light gives the Hubble distance. In practice astronomers measure distances directly where they can, climbing a ladder from parallax to Cepheid variables to Type Ia supernovae, and fall back on velocity divided by H₀ for the many galaxies with nothing better than a redshift.

How to use this calculator.

1. 01Choose what to find: distance from a recession velocity, or recession velocity from a distance.
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 first; v = cz is only a small-redshift approximation. Velocities must be zero or positive.
3. 03Set H₀ to the value your source used: 67.4 for work based on Planck, 73.04 for SH0ES, or another published figure. The field accepts 1 to 500 km/s/Mpc.
4. 04Read the distance in megaparsecs and in millions of light-years, then compare the Planck and SH0ES distances beneath it. Both are always worked out from the recession velocity, so in velocity mode they show where that velocity would place the galaxy under each H₀.
5. 05Check the regime note before quoting the result. It tells you whether the velocity is small enough that the galaxy's own motion matters, large enough that a full cosmological model is needed, or in between.

The formula.

Hubble's law is v = H₀ × d, so solving for distance is d = v ÷ H₀. The units cancel neatly: km/s divided by km/s per Mpc leaves megaparsecs. To express the distance in light-years the calculator multiplies by 3.2615637772, the number of light-years in a parsec, which follows from two exact definitions — the parsec as (648,000/π) astronomical units of 149,597,870,700 m each, and the light-year as the distance light travels in a Julian year of 365.25 days. The Hubble time t_H = 1/H₀ needs the megaparsec in kilometres, 3.0857 × 10¹⁹ km: dividing that by H₀ gives seconds, and dividing by the 3.15576 × 10¹⁶ seconds in a billion Julian years gives gigayears. The Hubble distance is d_H = c ÷ H₀, with c = 299,792.458 km/s exactly. Because a light-year is defined through c, the Hubble time in billions of years and the Hubble distance in billions of light-years are always the same number. The two comparison distances repeat d = v ÷ H₀ with 67.4 and 73.04. Since distance is inversely proportional to H₀, the Planck figure is always 73.04 ÷ 67.4 = 1.0837 times the SH0ES figure, about 8.37% larger, whatever the object; the spread in megaparsecs grows in proportion to the velocity. Errors pass straight through the division: a 1% change in H₀ or in the velocity moves the distance by 1%. That is why nearby galaxies are awkward. A peculiar motion of 300 km/s, entirely separate from the expansion, is a 4.3% error on a galaxy receding at 7,000 km/s but a 30% error on one receding at 1,000 km/s. The regime note compares v with c. Below 1% of c it warns that the galaxy's own motion can dominate; from 1% to 10% it calls the galaxy part of the Hubble flow; above 10% it warns that the full cosmological model matters, and it adds a separate warning if the distance exceeds c ÷ H₀. Those 1% and 10% edges are round numbers chosen as a presentation convention, not thresholds published in the literature. H₀ must be above zero, since zero would describe a universe that is not expanding at all.

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.