Hubble Law Calculator

Hubble law states that galaxies recede at a rate proportional to their distance. More distant galaxies move away faster. The Hubble constant H0 gives the expansion rate of the universe.

🌀 Cosmology📐 v = H₀ d🔭 Astrophysics

Distance d (Mpc)

Hubble constant H₀ (km/s/Mpc)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Recession Velocity	v	v = H₀ d	km/s
Distance	d	d = v/H₀	Mpc
Hubble Constant	H₀	~70 km/s/Mpc	km/s/Mpc
Age of Universe	t	1/H₀ ≈ 14 Gyr	Gyr
1 Mpc	—	3.086 × 10²⁲ m	m

Step-by-Step Examples

Example 1

Andromeda (not receding)

M31 at ~0.77 Mpc. Local Group is gravitationally bound.

v = 70 * 0.77 = 54 km/s (Hubble recession)
Actual velocity: -110 km/s (approaching!)
Local Group gravity dominates at this scale

✓ Andromeda approaches us despite Hubble expansion

Example 2

Virgo Cluster

D = 16.5 Mpc, H0 = 70.

v = 70 * 16.5 = 1155 km/s
Observed: ~1200 km/s (close!)

✓ 1155 km/s recession velocity

Example 3

Very Distant Galaxy

d = 4000 Mpc (z~1).

v = 70 * 4000 = 280,000 km/s = 0.93c
At larger d: v > c (expansion of space, not motion)

✓ Recession at 93% speed of light

Real-World Applications

🔭

Cosmology

Hubble law is the primary evidence for universe expansion and the Big Bang.

🌀

Galaxy Distances

Hubble law gives distance to galaxies too far for other methods: d = v/H0 from measured redshift.

🌟

Dark Energy

Acceleration of expansion (distant supernovae recede faster than Hubble law predicts) revealed dark energy.

📶

Redshift Surveys

Large galaxy surveys map 3D universe using v = H0*d to convert redshift to distance.

Common Mistakes to Avoid

⚠️

Hubble law fails for nearby galaxies

At d < ~10 Mpc, peculiar velocities (gravitational interactions) dominate over Hubble flow. Only use for distant galaxies.

⚠️

Recession > c is allowed

For d > c/H0 ~ 4280 Mpc, v > c. This is expansion of space, not motion through space. Special relativity allows this.

⚠️

H0 value is uncertain

H0 is ~67-73 km/s/Mpc depending on measurement method. The Hubble tension is a major open problem in cosmology.

Frequently Asked Questions

What is the Hubble constant? ▾

H0 = 70 km/s/Mpc means a galaxy 1 Mpc away recedes at 70 km/s. 2 Mpc away: 140 km/s. The rate of cosmic expansion.

Why do distant galaxies recede faster than light? ▾

It is space itself expanding, not galaxies moving through space. Special relativity limits objects moving through space to c, but space can expand at any rate.

What is the Hubble tension? ▾

Early universe (CMB) gives H0 = 67.4 km/s/Mpc. Local universe (Cepheids+supernovae) gives H0 = 73.0. The discrepancy is a major unsolved problem.

How is Hubble law used to find distances? ▾

Measure galaxy redshift z: v = cz for small z. Then d = v/H0. This is the basis of the cosmic distance ladder beyond ~100 Mpc.

What is the observable universe size? ▾

~13.8 Gyr after Big Bang, but proper distance to edge is ~46.5 billion light-years due to expansion during travel time.

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Formula Explorer connections

Interpretation: This relationship connects mass, distance, orbit or spacetime behavior through gravitation and astrophysical scaling. Assumption: Many calculations assume spherical bodies, point masses, circular orbits, weak fields or Newtonian gravity; relativistic regimes require the stated correction.

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