Hubble's Law Calculator (Recession Velocity ↔ Distance)

How it works

v = H₀ × d · d (Mpc) = v (km/s) ÷ H₀ (km/s/Mpc) · 1 + z = √((1 + v/c) ÷ (1 − v/c)) · Hubble time = 977.8 ÷ H₀ Gyr · 1 Mpc = 3.2616 million light-years

Edwin Hubble found that galaxies recede at speeds proportional to their distance — the signature of a uniformly expanding universe — and the constant of proportionality, H₀, turns an easily measured spectral redshift into a distance. The relation is linear only while the recession speed is a small fraction of light speed; farther out, the expansion history matters and cosmologists integrate the Friedmann equations instead. The redshift itself is converted to velocity here with the relativistic Doppler formula so the tool degrades gracefully, and because H₀ is still uncertain at the 10% level the distance inherits that uncertainty, which is why the calculator shows both leading values.

Worked example

A galaxy receding at 7,000 km/s (redshift z ≈ 0.024) lies at 7,000 ÷ 70 = 100 Mpc, about 326 million light-years, so its light left roughly 326 million years ago. At H₀ = 67.4 the same galaxy would be placed at 103.9 Mpc, at 73 only 95.9 Mpc.

Frequently asked questions