Hubble's law calculator
Enter the Hubble constant and a galaxy's distance in megaparsecs or light years to get its recession velocity, or enter the velocity to get the distance. The calculator also shows the approximate redshift and, for your value of H₀, the Hubble time and the Hubble radius.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: the velocity or the distance.
- Enter H₀ in km/s per megaparsec.
- Enter the distance in megaparsecs, millions or billions of light years, or the recession velocity in km/s.
- Hubble’s law: v = H₀ × d, so d = v ÷ H₀.
- Low-redshift approximation: z ≈ v ÷ c.
- Hubble time: t_H = 1 ÷ H₀; Hubble radius: c ÷ H₀. 1 Mpc = 3.0857 × 10¹⁹ km = 3.2616 million light years.
Worked example
With H₀ = 70 km/s/Mpc, a galaxy 100 Mpc away (326.16 million light years) recedes at 70 × 100 = 7,000 km/s, a redshift of about 0.023349. The Hubble time is 3.0857 × 10¹⁹ ÷ 70 s = 13.968 billion years.
A galaxy receding at 21,000 km/s is 21,000 ÷ 70 = 300 Mpc away.
Tips
- Nearby galaxies have their own motions of a few hundred km/s, so Hubble’s law works best beyond about 10 Mpc.
- Andromeda is approaching us; local gravity wins over the expansion there.
- A Hubble radius in billions of light years equals the Hubble time in billions of years, since light covers one light year per year.
Frequently asked questions
What is Hubble's law?
Distant galaxies move away from us with a speed proportional to their distance, v = H₀ × d. With H₀ = 70 km/s per megaparsec, a galaxy 100 Mpc away recedes at about 7000 km/s.
What value of the Hubble constant should I use?
Measurements disagree slightly. Results from the cosmic microwave background give about 67 to 68 km/s/Mpc, while nearby supernovae and Cepheids give about 73. 70 is a common round value; enter whichever you need.
What is the Hubble time?
1 ÷ H₀, the age the universe would have if it had always expanded at today's rate. For H₀ = 70 km/s/Mpc it is about 13.97 billion years, close to the measured age of about 13.8 billion years.
Is z = v ÷ c exact?
No, it holds only for nearby galaxies, roughly z below 0.1. Further away, distances and velocities depend on the cosmological model; the redshift calculator gives the relativistic Doppler relation instead.