Hubble's Law Calculator
Enter a distance, a recession velocity or a redshift and the calculator applies Hubble's law, v = H₀ × d, with the Hubble constant you choose: the Planck 2018, SH0ES 2022 or CCHP 2025 value, or your own. You also get the Hubble time and distance, the range allowed by H₀'s uncertainty, and a warning when the law stops being a good approximation. Free, no sign-up, and nothing leaves your browser.
Results
6740.0 km/s
Recession velocity
0.022482 c
Fraction of the speed of light
3.2616 × 10⁸ light-years
Distance in light-years
14.507 billion years
Hubble time 1/H₀
4448.0 Mpc
Hubble distance c/H₀
Range from the uncertainty in H₀: With H₀ = 67.400 ± 0.50000, the result runs from 6790.0 km/s to 6690.0 km/s.
The same input with each published H₀
| Hubble constant | H₀ (km/s/Mpc) | Result | Hubble time (Gyr) |
|---|---|---|---|
| Planck 2018 (cosmic microwave background) | 67.4 ± 0.5 | 6740.0 km/s | 14.507 |
| SH0ES 2022 (Cepheids and supernovae) | 73.04 ± 1.04 | 7304.0 km/s | 13.387 |
| CCHP 2025 (tip of the red giant branch) | 70.39 ± 1.94 | 7039.0 km/s | 13.891 |
| Round textbook value | 70 | 7000.0 km/s | 13.968 |
H₀ values: Planck Collaboration 2020 (A&A 641, A6), Riess et al. 2022 (ApJ 934, L7) and Freedman et al. 2025 (ApJ 985, 203, with its three errors added in quadrature). They disagree by more than their stated errors, which is the Hubble tension; nobody yet knows whether the cause is a measurement problem or new physics.
How to Use the Hubble's Law Calculator
- 1. Choose what to find. Recession velocity from distance is Hubble's law itself. Distance from recession velocity runs it backwards, and Velocity and distance from redshift starts from the quantity astronomers actually measure.
- 2. Choose the Hubble constant. The menu offers three published values, a rounded 70 for textbook problems and your own. The values disagree, which is why the results table shows all of them side by side.
- 3. Enter your number. A distance in megaparsecs, gigaparsecs or millions and billions of light-years; a velocity in km/s or as a fraction of the speed of light; or a redshift z. The redshift mode has three example objects.
- 4. Read the result. The headline gives the velocity or distance, with the uncertainty range from H₀, the fraction of the speed of light and the Hubble time. Notices appear when the answer needs a caveat.
What Hubble's Law Says
Galaxies recede from us, and the farther away they are the faster they go. In 1929 Edwin Hubble showed that the recession velocity v is proportional to distance d:
Hubble's law
v = H₀ × d
Hubble time
t_H = 1 ÷ H₀ = 977.79 Gyr ÷ H₀ (km/s/Mpc)
Hubble distance
d_H = c ÷ H₀
H₀, the Hubble constant, is the expansion rate today, in kilometres per second per megaparsec. At 67.4 km/s/Mpc a galaxy 100 Mpc away recedes at 6,740 km/s and one 200 Mpc away at 13,480 km/s. The speed is not motion through space but the stretching of space between us and the galaxy, which also stretches the light's wavelength: that is the cosmological redshift z. At low redshift the recession velocity is c·z, so distance follows from d = c·z ÷ H₀. Hubble's own 1929 value was about 500 km/s/Mpc, nearly seven times too large, because his distances were too small.
Which Value of H₀?
Two kinds of measurement give different answers, and the calculator lets you use either. Both are published with small error bars, so the gap is a real disagreement known as the Hubble tension:
| Source | Method | H₀ (km/s/Mpc) | Hubble time |
|---|---|---|---|
| Planck 2018 (A&A 641, A6) | Cosmic microwave background, assuming ΛCDM | 67.4 ± 0.5 | 14.507 Gyr |
| CCHP 2025 (ApJ 985, 203) | Tip of the red giant branch, HST and JWST | 70.39 ± 1.94 | 13.891 Gyr |
| SH0ES 2022 (ApJ 934, L7) | Cepheids calibrating Type Ia supernovae | 73.04 ± 1.04 | 13.387 Gyr |
The CCHP team gave 70.39 with three errors, 1.22 (statistical), 1.33 (systematic) and 0.70 (supernova sample); the calculator adds them in quadrature to ±1.94. The Planck value is inferred from the early universe and then run forward with a model; the SH0ES value is measured directly in the nearby one. Riess and colleagues put their gap with Planck at about five standard deviations. Whether the cause is an unrecognised error in one measurement or new physics, no one has yet established.
Worked Examples
| Input | Planck 67.4 | CCHP 70.39 | SH0ES 73.04 |
|---|---|---|---|
| 100 Mpc → velocity | 6740.0 km/s | 7039.0 km/s | 7304.0 km/s |
| 7000 km/s → distance | 103.86 Mpc | 99.446 Mpc | 95.838 Mpc |
| Hubble distance c/H₀ | 4448.0 Mpc | 4259.0 Mpc | 4104.5 Mpc |
The Coma Cluster has a redshift of 0.0231, so c·z is 6925.2 km/s and the Hubble-law distance with Planck's H₀ is 102.75 Mpc, about 335 million light-years. The quasar 3C 273, at z = 0.158, gives 47,367 km/s and 702.78 Mpc. In a flat ΛCDM universe with Ωₘ = 0.315 the comoving distances are 102.18 Mpc and 675.91 Mpc, 0.5% and 3.8% below the simple figures, so the law is excellent for Coma and a little off for 3C 273.
When Hubble's Law Breaks Down
- High redshift. Because the expansion rate has changed over time, v = c·z fails once z passes about 0.1. At z = 0.1 the full ΛCDM comoving distance is 2.4% below the Hubble-law one with Planck's H₀, and for a z = 10.6 galaxy such as GN-z11 the true figure is 9758.9 Mpc against 47148 Mpc from the law. Use a cosmology calculator beyond z ≈ 0.1.
- Nearby galaxies. Galaxies within a few Mpc are dominated by their own motions in gravity, not by the expansion; Andromeda is falling towards us.
- Velocities above c. The law formally gives v > c for d > c/H₀ (4448.0 Mpc, or 14.507 billion light-years for Planck's H₀). That is the expansion of space, not motion through it, so it does not violate relativity. Light from such galaxies can still reach us because the Hubble sphere itself grows.
Frequently Asked Questions
- What is the Hubble constant?
- It is the present rate of cosmic expansion: the extra recession velocity per unit of distance. At 70 km/s/Mpc, a galaxy 1 megaparsec (3.26 million light-years) away recedes at 70 km/s, one at 10 Mpc at 700 km/s. Expressed in other units it is about 2.2 × 10⁻¹⁸ per second.
- What is the value of the Hubble constant?
- There is no agreed value. Planck's cosmic microwave background analysis gives 67.4 ± 0.5 km/s/Mpc, the SH0ES team's supernova distance ladder gives 73.04 ± 1.04, and the CCHP's red giant branch work gives 70.39 ± 1.94. The discrepancy is called the Hubble tension, and a value of 70 is a convenient round number in between.
- How do you calculate distance from redshift?
- For small redshift, multiply z by the speed of light to get a velocity, then divide by H₀: d = c·z ÷ H₀. For Coma, z = 0.0231 gives 6925.2 km/s and, with H₀ = 67.4, 102.75 Mpc. Above z ≈ 0.1 you need a full cosmological model, not this shortcut.
- How old is the universe from the Hubble constant?
- The Hubble time 1 ÷ H₀ is 14.507 billion years for H₀ = 67.4 and 13.387 billion years for 73.04. It is only a rough guide to the age, because the expansion has not been constant. Planck's full ΛCDM fit gives 13.787 ± 0.020 billion years.
- Can galaxies move faster than light?
- They can recede faster than light, but they are not moving through space that fast. Space between us and a distant galaxy expands, and beyond the Hubble distance c ÷ H₀ the recession speed exceeds c. Nothing locally outruns light, so special relativity is not violated.
- Why do the results differ between H₀ choices?
- Velocity scales directly with H₀ and distance inversely. A 100 Mpc galaxy recedes at 6740.0 km/s with Planck's value and 7304.0 km/s with SH0ES, a difference of 8.4%. Always state which H₀ you used; the table below the result shows each side by side.