Hubble's Law Calculator
Enter distance or recession velocity to compute the other via v = H₀·d, plus redshift and light-travel time.
Input Data
Results
At a glance:Hubble's law (Hubble & Lemaître, 1929) relates a galaxy's recession velocity to its distance: v = H₀·d, where H₀ ≈ 70 km/s/Mpc is the Hubble constant (the expansion rate of the universe). The corresponding redshift z ≈ v/c for small z; more precisely 1+z = √((1+β)/(1−β)) in special relativity (cosmological redshifts use the scale factor). The lookback/light-travel time grows roughly with z. This linear relation is the key evidence for an expanding universe and lets us estimate distances to far galaxies from their redshift. Locally, peculiar velocities (e.g. Virgo infall) add scatter, so the law applies statistically at large distances.
Formula
v = H₀·d
z ≈ v/c (low redshift)
H₀ ≈ 70 km/s/Mpc
$$v = H_0 d, \quad z \approx \frac{v}{c}, \quad t \approx \frac{d}{c}, \quad t_H = \frac{1}{H_0} \approx 14 \text{ Gyr}$$How to Use
- Enter the distance d (Mpc) or recession velocity v (km/s) and the Hubble constant.
- The calculator returns v (or d), redshift z and light-travel time.
Case Studies
Distance to a galaxy
v = 21000 km/s, H₀ = 70.
d = 21000/70 = 300 Mpc ≈ 1 Gyr light-travel (≈978 Mly).
z ≈ 21000/3e5 ≈ 0.07.
Calibrating distance
d = 100 Mpc, H₀ = 70 km/s/Mpc.
v = 70×100 = 7000 km/s.
Confirms linear expansion; scatter from peculiar velocities <~1000 km/s locally.
FAQ
Why does the universe expand?
Solutions of general relativity with uniform matter show space itself stretches; galaxies separated by expanding space recede at v = H₀d. This is not motion through space but the growth of distances.
Is the Hubble constant really constant?
It is constant in space today but changes with cosmic time; 'constant' refers to its value across space at a given epoch. Measurements (Planck vs local Cepheids) currently differ ~67–74 km/s/Mpc — the 'Hubble tension'.
What is redshift z?
The fractional stretching of light wavelength: z = (λ_obs−λ_emit)/λ_emit. Larger z means farther and younger light; for low z, z ≈ v/c.
Can v exceed c?
Yes for very distant galaxies — but that is recession of space, not local motion, so it does not violate special relativity (which limits motion through space to c).
How old is the universe from H₀?
Roughly the Hubble time t_H ≈ 1/H₀ ≈ 14 Gyr, modified by matter/dark-energy content to the actual age ~13.8 Gyr.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.