Hubble’s Law Calculator
Compute galaxy recession velocities with v = H₀ × d — three-way solver (v / d / H₀), Planck 2018 & SH0ES H₀ presets, Hubble time tᴴ = 1/H₀, and redshift approximation.
Calculator
The H₀ value is still debated (“Hubble tension”) — compare both presets before concluding.
Preset comparison at the same distance
For d = 100 Mpc, recession velocity per H₀ value:
| Sumber H₀ | H₀ value | v = H₀ × d |
|---|---|---|
| Planck 2018 (CMB) | 67.4 km/s/Mpc | 6,740 km/s |
| SH0ES (supernova lokal) | 73.04 km/s/Mpc | 7,304 km/s |
| Value you use | — | 7,000 km/s |
Verified examples
Pertanyaan umum
What is Hubble’s law?
Hubble’s law states that distant galaxies recede from us with a recession velocity v proportional to their distance d: v = H₀ × d. Discovered by Edwin Hubble in 1929 from galaxy observations, it is the primary observational evidence that the universe is expanding.
What are the units of the Hubble constant H₀?
H₀ has units km/s/Mpc (kilometers per second per megaparsec): each additional megaparsec of distance adds H₀ km/s of recession velocity. Since v [km/s] = H₀ [km/s/Mpc] × d [Mpc], the Mpc units cancel. H₀ can also be read as the expansion rate per unit distance — which is why 1/H₀ yields a time unit.
What is the correct value of H₀? What is the “Hubble tension”?
Its value is still debated — this is the “Hubble tension,” one of modern cosmology’s open problems. Cosmic microwave background measurements (Planck 2018) give 67.4 ± 0.5 km/s/Mpc, while the local supernova distance ladder (SH0ES) gives 73.04 ± 1.04 km/s/Mpc. The 5.64 km/s/Mpc (~8%) gap is too large to explain by measurement error alone. This calculator provides both presets plus a custom value so you can compare yourself.
What is the Hubble time?
The Hubble time tᴴ = 1/H₀ is a rough estimate of the universe’s age if the expansion rate were always constant. For H₀ = 70 km/s/Mpc, tᴴ = 13.968 billion years; for the Planck 67.4 preset it becomes 14.507 billion years and SH0ES 73.04 becomes 13.387 billion years. This is not the exact age of the universe (Planck: 13.8 billion years) because expansion first slowed then accelerated due to dark energy.
Hubble’s law calculation example?
Take H₀ = 70 km/s/Mpc and a galaxy at d = 100 Mpc. Then v = 70 × 100 = 7,000 km/s. Its approximate redshift z ≈ v/c = 0.02335, and its Hubble time 13.968 billion years.
Does Hubble’s law apply to the Andromeda galaxy?
No. Hubble’s law only holds on cosmological scales where universal expansion overwhelms local gravity. Andromeda is gravitationally bound to the Milky Way and is actually approaching (~110 km/s, blueshift). Do not use this calculator for gravitationally bound objects like neighboring galaxies or the local group.
How does recession velocity relate to redshift z?
For small redshifts (z ≪ 1), the non-relativistic approximation z ≈ v/c holds. Example: v = 7,000 km/s gives z ≈ 0.02335. For z ≥ 0.1 (v ≥ 29,979.25 km/s) this approximation starts to fail and you need the relativistic formula or a ΛCDM cosmology model — this calculator shows a warning in that range.
Can you compute H₀ from observational data?
Yes — select “Calculate H₀” mode then enter the observed recession velocity and distance. Example: v = 7,000 km/s at d = 100 Mpc gives H₀ = 70 km/s/Mpc. This is how Hubble did it in 1929 (his estimate then ~500 km/s/Mpc — wrong because his distance calibration was off).
Can recession velocity exceed the speed of light?
Formally yes: at the Hubble radius c/H₀ ≈ 4,283 Mpc (for H₀ = 70), the formula v = H₀×d gives v = c, and more distant galaxies “recede” faster than light. This is not local motion violating relativity — it is space itself expanding. This calculator still uses the non-relativistic approximation, so treat z ≥ 0.1 results with care.
What are this calculator’s limitations?
Three main limits: (1) it uses the non-relativistic approximation v = H₀×d, accurate only for z ≪ 1; distant galaxies need a ΛCDM cosmology model with matter and dark-energy density parameters; (2) it does not apply to gravitationally bound objects (see Andromeda above); (3) the H₀ value itself is still debated (Hubble tension) — compare results across presets before concluding.
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