Hubble Law Distance Calculator
Enter a galaxy's distance (or its recessional velocity) to apply Hubble's Law and solve for the other quantity. You can customize the Hubble constant to compare the Planck and SH0ES measurements, switch between Megaparsecs, kiloparsecs, and light-years, and view a velocity-distance chart across the observable universe. The step-by-step panel shows every calculation with your live numbers.
Formula
Worked example
A galaxy at 100 Mpc with H0 = 67.4 km/s/Mpc: v = 67.4 x 100 = 6,740 km/s, about 2.25% of the speed of light. The Hubble radius (where recession = c) is 299,792 / 67.4 = 4,448 Mpc = 14.5 billion light-years.
What is Hubble's Law?
Hubble's Law states that galaxies recede from us at a speed proportional to their distance: v = H0 x d, where v is the recessional velocity in km/s, d is the proper distance in Megaparsecs (Mpc), and H0 is the Hubble constant in km/s/Mpc. It was formulated by Edwin Hubble in 1929 from observations of galaxy redshifts, and it is the empirical cornerstone of the standard Big Bang cosmological model. The law does not mean galaxies are flying through space; it means the fabric of space between us and them is expanding, carrying the galaxies with it.
How to use this calculator
- Solve for velocity: select "Recessional velocity" from the "Solve for" dropdown, enter the galaxy's distance, choose the distance unit (Mpc, kpc, or light-years), and the calculator returns the recessional velocity in km/s and as a fraction of the speed of light.
- Solve for distance: select "Distance", enter the recessional velocity (derived from the galaxy's redshift via v = z x c for small z), and the calculator returns the distance in Mpc and in millions of light-years.
- Hubble constant: the default H0 is 67.4 km/s/Mpc from the Planck 2018 CMB analysis. Change it to 73.0 to use the SH0ES Cepheid-calibrated value. The chart and Hubble radius update instantly.
The Hubble constant and the 'Hubble Tension'
Two independent measurement methods give different values for H0, and the disagreement (about 5 sigma as of 2024) is called the Hubble Tension. The CMB-based method (Planck satellite, 2018) gives H0 = 67.4 +/- 0.5 km/s/Mpc. The distance-ladder method (SH0ES team, using Cepheid stars and Type Ia supernovae) gives H0 = 73.0 +/- 1.0 km/s/Mpc. This gap is significant: a higher H0 implies a younger, faster-expanding universe. No measurement error or systematic bias has yet resolved the discrepancy, making it one of the most important open problems in cosmology. Use this calculator's H0 field to see how the choice of constant changes the distance estimate by about 8%.
The Hubble radius and superluminal recession
The Hubble radius (also called the Hubble sphere or Hubble horizon) is the distance at which recession velocity equals the speed of light: r_H = c / H0. For H0 = 67.4 km/s/Mpc this is about 4,450 Mpc or 14.5 billion light-years. Galaxies beyond this radius recede faster than light, which does not violate special relativity because no object is moving through space at superluminal speed. The expansion itself carries space apart. Light emitted today by objects beyond the Hubble radius will never reach us, but light emitted earlier, when those objects were closer, may still be arriving. The observable universe (radius about 46 billion light-years) is therefore much larger than the Hubble radius.
Converting redshift to velocity
Astronomers measure recessional velocity indirectly from redshift (z): the fractional shift in the wavelength of known spectral lines. For small redshifts (z < 0.1), the approximation v = z x c is accurate to within about 1%. For example, z = 0.05 gives v = 0.05 x 299,792 = 14,990 km/s, implying a distance of 14,990 / 67.4 = 222 Mpc. At higher redshifts, the full relativistic Doppler formula or a proper Friedmann-equation integral is needed. The Hubble Law calculator on this page is accurate for z up to about 0.1 (distances up to roughly 400 Mpc for H0 = 67.4).
Notable galaxy distances and recessional velocities (H0 = 67.4 km/s/Mpc)
| Object | Distance (Mpc) | Recession velocity (km/s) | Fraction of c |
|---|---|---|---|
| Andromeda Galaxy (M31) | 0.785 | 52.9 | 0.000177 c |
| Virgo Cluster | 16.5 | 1112 | 0.0037 c |
| Coma Cluster | 99 | 6673 | 0.022 c |
| Perseus Cluster | 74 | 4988 | 0.017 c |
| Fornax Cluster | 20 | 1348 | 0.0045 c |
| Great Attractor region | 75 | 5055 | 0.017 c |
| Hubble radius (c/H0) | 4447 | 299 792 | 1.000 c |
Approximate values for orientation. Distances from NASA/IPAC Extragalactic Database.
Frequently asked questions
What is the Hubble constant and which value should I use?
The Hubble constant H0 quantifies how fast the universe is expanding per unit distance. Two competing measurements give 67.4 km/s/Mpc (Planck CMB) and 73.0 km/s/Mpc (SH0ES Cepheid ladder). The difference is the unresolved Hubble Tension. For cosmological calculations tied to the CMB era, use 67.4; for local-universe distance ladder work, 73.0 is more consistent with direct observations.
Can recession velocity exceed the speed of light?
Yes, and it does for galaxies beyond the Hubble radius (about 4,450 Mpc for H0 = 67.4). This does not violate special relativity because the recession is due to the expansion of space, not motion through space. No information or matter is being transmitted faster than light; the spatial fabric between us and those galaxies is simply expanding.
How do I convert redshift (z) to recessional velocity for use in this calculator?
For small redshifts (z < 0.1), use v = z x c = z x 299,792 km/s. For larger redshifts, the special-relativistic formula is v = c x ((1+z)^2 - 1) / ((1+z)^2 + 1). Enter the resulting velocity in km/s into the "Recessional velocity" field with the mode set to "Distance" to find the distance.
What is the Hubble time and what does it tell us?
The Hubble time is 1/H0 expressed in units of time (after converting km/s/Mpc to 1/seconds). For H0 = 67.4 km/s/Mpc it equals about 14.5 billion years; for 73.0 it is about 13.4 billion years. It represents the age the universe would have if it had always expanded at today's rate. The actual age (from the CMB) is about 13.8 billion years, slightly less than the Hubble time because expansion has been decelerating (matter era) and then accelerating (dark energy era).
Why does Hubble's Law break down at large distances?
Hubble's Law v = H0 x d is a linear approximation valid for small redshifts (z << 1, distances up to a few hundred Mpc). At larger distances, the expansion history matters: during the matter-dominated era the expansion decelerated, and since about 5 billion years ago dark energy has caused re-acceleration. The full relationship requires integrating the Friedmann equations with matter density, dark energy density, and radiation density. At z = 1 the linear law overestimates velocity by roughly 30%.
What units does this calculator use for distance?
The calculator accepts Megaparsecs (Mpc), kiloparsecs (kpc), or light-years (ly) and converts internally to Mpc before applying Hubble's Law. Results are always shown in both Mpc and millions of light-years. One Megaparsec equals 3.262 million light-years or 3.086 x 10^19 km.
Does Hubble's Law apply to objects within our galaxy or Local Group?
No. The Milky Way, Andromeda, and the other Local Group galaxies are gravitationally bound to each other. Local gravity dominates over the Hubble flow at scales below about 1-2 Mpc. Andromeda is actually approaching us at about 110 km/s despite being 0.785 Mpc away. Hubble's Law applies reliably only to galaxies in the field (unbound systems) at distances beyond a few Mpc.
Sources
- Hubble E. (1929). A relation between distance and radial velocity among extra-galactic nebulae. PNAS 15(3):168-173.
- Planck Collaboration (2020). Planck 2018 results VI: Cosmological parameters. A&A 641, A6.
- Riess A.G. et al. (2022). A comprehensive measurement of the local value of the Hubble constant with 1 km/s/Mpc uncertainty. ApJL 934 L7.