Hubble’s Law Calculator
Convert between a galaxy’s distance and its recession velocity with v = H₀ × d.
A galaxy at 100 Mpc (326.2 million ly) recedes at about 7,000 km/s with H₀ = 70.
With H₀ = 70 km/s/Mpc, the Hubble time 1 ÷ H₀ is about 13.97 billion years — a rough age-scale for the expanding universe. H₀ itself is debated: local measurements give ≈ 73 while the cosmic microwave background gives ≈ 67, a gap known as the Hubble tension.
Hubble’s law is v = H₀ × d: recession velocity equals the Hubble constant times distance. With H₀ = 70 km/s/Mpc, a galaxy at 100 Mpc recedes at 70 × 100 = 7,000 km/s. Reverse it with d = v ÷ H₀, so 7,000 km/s implies 100 Mpc. H₀ is uncertain — measured values span ≈ 67–74.
What Hubble’s law says
In the 1920s Edwin Hubble found that distant galaxies are receding from us, and the farther away a galaxy is, the faster it recedes. That proportionality is Hubble’s law, v = H₀ × d. It is the observational cornerstone of the expanding universe: space itself is stretching, carrying galaxies apart, so every observer sees the same outward flow. The Hubble constant H₀ is the current expansion rate, measured in km/s per megaparsec — it tells you how many extra km/s of recession you gain for each megaparsec of distance.
v = recession velocity (km/s), H₀ = Hubble constant (km/s/Mpc), d = distance (Mpc). Rearranged: d = v ÷ H₀. 1 Mpc ≈ 3.262 million light-years.
Worked example
Find the recession velocity of a galaxy 100 Mpc away, using H₀ = 70 km/s/Mpc:
- 1 Write the law. v = H₀ × d. Recession velocity equals the Hubble constant times distance.
- 2 Choose a Hubble constant. Use H₀ = 70 km/s/Mpc as a standard round value (real measurements span ≈ 67–74).
- 3 Put the distance in megaparsecs. Here d = 100 Mpc, which is about 326 million light-years.
- 4 Multiply. v = 70 × 100 = 7,000 km/s.
- 5 To go the other way, divide. Distance from a velocity is d = v ÷ H₀, so 7,000 ÷ 70 = 100 Mpc.
Distance to recession velocity (H₀ = 70 km/s/Mpc)
Velocity scales linearly with distance under Hubble’s law: double the distance, double the velocity. Change H₀ and every velocity rescales.
| Distance | In light-years | Recession velocity (v = 70 × d) |
|---|---|---|
| 10 Mpc | 32.6 million ly | 700 km/s |
| 16.5 Mpc (Virgo Cluster) | 53.8 million ly | 1,155 km/s |
| 50 Mpc | 163 million ly | 3,500 km/s |
| 100 Mpc (Coma Cluster) | 326 million ly | 7,000 km/s |
| 500 Mpc | 1.63 billion ly | 35,000 km/s |
Measured values of the Hubble constant (the tension)
Two rigorous methods disagree by more than their stated uncertainties — the unresolved “Hubble tension”. This tool defaults to a round 70 that sits between them.
| Method | H₀ (km/s/Mpc) | Implied Hubble time (1 ÷ H₀) |
|---|---|---|
| Cosmic microwave background (Planck) | ≈ 67.4 | ≈ 14.5 billion years |
| Round value used here | 70 | ≈ 14.0 billion years |
| Local distance ladder (Cepheids + supernovae) | ≈ 73 | ≈ 13.4 billion years |
How uncertain is H₀?
The Hubble constant is genuinely debated. Two careful, independent methods give different answers: measurements anchored to the local distance ladder land near 73 km/s/Mpc, while the value inferred from the cosmic microwave background sits near 67. The gap is larger than either method’s error bars, and it has not gone away as measurements have improved — this is the Hubble tension. Because of it, any velocity or distance you get from this tool is only as certain as the H₀ you choose, so treat single figures as estimates and try the range 67–74 to see how much the answer moves.
Hubble’s law is also an approximation. It works well for galaxies in the nearby, low-redshift universe. For very distant galaxies the simple v = H₀d relation breaks down: recession “velocities” can formally exceed the speed of light, the expansion rate changes over cosmic time, and different distance measures diverge. For those objects, redshift and a full cosmological model are needed rather than a single H₀.