Hubble's Law Distance Calculator

Edwin Hubble announced in 1929 that distant galaxies are receding from us, and that their recession speed is proportional to their distance. This was the first direct evidence that the universe is expanding.

The law

v = H0 x d

Where v is the recession velocity in km/s, d is the distance in megaparsecs (Mpc), and H0 is the Hubble constant in km/s/Mpc.

One megaparsec = 3.086 x 10^22 m = 3.2616 million light-years.

The Hubble constant tension

The value of H0 is currently a major unsolved problem in cosmology, known as the “Hubble tension.” Measurements from the Cosmic Microwave Background (Planck satellite) give H0 ≈ 67.4 km/s/Mpc. Measurements from the distance ladder (Cepheid variable stars, supernovae) give H0 ≈ 73 km/s/Mpc. The discrepancy is statistically significant and may point to new physics. The default here uses 70 km/s/Mpc as a round number between the two camps.

That 8% disagreement matters more than it sounds. It propagates straight into the age of the universe, into every distance derived from a redshift, and into the inferred amount of dark energy. Two careful teams measuring the same quantity with different methods and refusing to converge is either a systematic error nobody has found or a hole in the standard cosmological model.

Redshift

For recession velocities well below c, the redshift is approximately:

z ≈ v / c

where c = 299,792 km/s. The CMB sits at z ≈ 1100, meaning it was emitted when the universe was 1,101 times smaller than today. Note that the simple z = v/c relation fails badly above about z = 0.1; beyond that you need the relativistic Doppler formula, and beyond about z = 1 you need a full cosmological model with the expansion history built in.

Lookback time

For nearby galaxies the lookback time is simply the light travel time, which is the distance divided by the speed of light. Since one megaparsec is 3.2616 million light-years, the arithmetic is:

lookback time (years) ≈ d (Mpc) × 3.2616 × 10⁶

So a galaxy 100 Mpc away is seen as it was about 326 million years ago. This is only valid for small redshifts. Past z ≈ 0.1 the expansion of space during the journey matters, and the true lookback time falls increasingly below this straight-line figure.

The Hubble radius is not the edge of anything

c/H0 is about 4,280 Mpc, or 14 billion light-years. It is the distance at which the Hubble-law recession velocity formally reaches the speed of light, and it is often carelessly called the edge of the observable universe. It is not. The observable universe has a comoving radius of about 46.5 billion light-years, more than three times larger, because space has expanded while the light was in transit. Galaxies beyond the Hubble radius are receding faster than light and we can still see many of them, which sounds impossible until you remember that nothing is moving through space faster than light. Space itself is expanding.

The Andromeda galaxy (M31) at 0.78 Mpc is actually approaching us, at about 110 km/s. Local gravity overrides Hubble expansion at short distances, which is why this calculator is meaningless for anything inside the Local Group.