Hubble's Law Recession Velocity Calculator

Hubble’s Law states that galaxies recede from us at a speed proportional to their distance. The farther away a galaxy is, the faster it moves away from us.

v = H₀ × d

Where:

• v = recession velocity (km/s)
• H₀ = Hubble constant (km/s per Megaparsec)
• d = distance to the galaxy (Megaparsecs or Gigalightyears)

The Hubble constant controversy: There is an ongoing debate about the precise value of H₀:

• Planck 2018 (CMB method): H₀ = 67.4 km/s/Mpc
• Standard value (widely used): H₀ = 70 km/s/Mpc
• Local measurements (distance ladder): H₀ = 73 km/s/Mpc

This discrepancy, known as the Hubble tension, may point to new physics beyond the standard cosmological model.

The Hubble sphere: At a certain distance, the recession velocity equals the speed of light (c). This distance is called the Hubble radius or Hubble sphere:

d_H = c / H₀

Galaxies beyond this radius recede faster than light, which puts them outside our Hubble sphere. Light from some of them can still reach us, because the geometry of spacetime is on their side.

Note on lookback time: For nearby galaxies (d much smaller than the Hubble radius), lookback time is close to d/c in light-years.
For distant ones that shortcut breaks down and a full cosmological calculation is needed.
The observable universe has a radius of about 46.5 billion light-years.

That 46.5 billion figure surprises people, because the universe is only 13.8 billion years old and nothing outruns light. The resolution is that space itself expanded while the light was in transit. A photon that set out 13.8 billion years ago covered 13.8 billion light-years of ground, but the ground kept stretching behind it, so the object that emitted it now sits roughly 46.5 billion light-years away. Nothing moved through space faster than light; there is simply more space now than there was then.

Where the simple v = H₀d picture stops working. It is a local law. Feed it a distance of 5,000 Mpc and it hands back a velocity above c quite happily, and the number is not wrong so much as no longer the thing you wanted: at those separations distance itself has several definitions (comoving, proper, light-travel, angular diameter) and they disagree by billions of light-years. This page reports the proper distance version, which is the one Hubble’s law is actually written in. Treat anything past a few hundred Mpc as an illustration of the law rather than a measurement of a real galaxy.