Hubble Distance from Redshift Calculator

How it is calculated

Hubble's law says a galaxy's recession velocity grows in proportion to its distance, v = H₀ × d, so the tool uses d = v / H₀. Here v is the recession velocity in km/s, H₀ is the Hubble constant in km/s per megaparsec, and d comes out in megaparsecs (Mpc). It then converts to millions of light-years by multiplying by 3.2615637772, the number of million light-years in one megaparsec. If the Hubble constant is left empty the tool assumes 70. The velocity may not be negative and H₀ must be above zero. The relation is linear and has no relativistic correction, so it is a good approximation only for relatively nearby galaxies where the velocity is a small fraction of the speed of light.

Common mistakes

• Entering the redshift z instead of the velocity. The field takes km/s, so a redshift of 0.0233 must first be turned into about 7,000 km/s (z × 299,792 km/s) for small z.
• Entering the velocity in m/s or in fractions of c. The tool expects km/s, so 7,000,000 m/s typed as is gives a distance a thousand times too large.
• Using the linear law for very distant galaxies. A velocity of 150,000 km/s gives 2,142.86 Mpc here, but at that speed the expansion history and relativistic effects matter, so the result is not reliable.
• Treating the output as a precise distance. It scales as 1/H₀, and the commonly quoted values vary from about 67 to 73, so the answer carries several percent of uncertainty before the galaxy's own motion is considered.
• Entering a blueshifted (approaching) object as a negative velocity. Negative values are rejected, and for nearby galaxies like Andromeda the Hubble law does not apply because local motion dominates.