Last updated: 2026-06-16

The Hubble–Lemaître Law

In the 1920s Georges Lemaître and Edwin Hubble found that galaxies are moving away from us, and that the more distant a galaxy is, the faster it recedes. The relationship is strikingly simple:

$v = H_0 \, d$

where $v$ is the recession velocity, $d$ is the distance, and $H_0$ is the Hubble constant — the present-day expansion rate of the universe. This linear law is the foundational observational evidence that the universe is expanding.

The Hubble Constant

$H_0$ is conventionally expressed in kilometres per second per megaparsec (km/s/Mpc): for every megaparsec of distance, the recession velocity increases by $H_0$ km/s.

Two leading measurement methods currently disagree: the cosmic microwave background gives $H_0 \approx 67$ km/s/Mpc, while the local distance ladder of supernovae gives $H_0 \approx 73$ km/s/Mpc. This unresolved discrepancy is called the Hubble tension. The round value of 70 km/s/Mpc sits conveniently between them.

Worked Example

A galaxy lies 100 Mpc away. Using $H_0 = 70$ km/s/Mpc:

$v = H_0 d = 70 \times 100 = 7{,}000\ \text{km/s}$

That is about 2.3 % of the speed of light. To reverse the calculation and find distance from a measured velocity, rearrange to $d = v / H_0$.

A Window on Cosmic History

The inverse of the Hubble constant, $1/H_0$, has units of time and gives a rough estimate of the age of the universe — the Hubble time — of roughly 14 billion years. Because the expansion rate has changed over cosmic history, this is only an approximation, but it captures the right order of magnitude.

When the Linear Law Breaks Down

At small distances the law works well, but at very large distances the simple calculation can yield recession velocities greater than the speed of light. This is not a violation of relativity: the galaxies are not moving through space faster than light, rather the space between us and them is expanding. For high-redshift objects, astronomers replace the linear law with the full equations of cosmology, which account for how the expansion rate evolves over time. The companion redshift calculator handles the relativistic relationship between observed redshift and velocity.