Hubble's Law Calculator
Compute galaxy recession velocity, universe age, and redshift using Hubble's Law v = H₀ × d. Enter distance and Hubble constant H₀ for instant results.
About This Calculator
Hubble's Law describes the observation that galaxies are moving away from Earth at speeds proportional to their distance. The relationship v = H0 × d is one of the most important formulas in cosmology, providing the primary evidence for the expanding universe and enabling distance measurements to remote galaxies. Discovered by Edwin Hubble in 1929, this law forms the foundation of modern observational cosmology and our understanding of the Big Bang theory.
This free online calculator computes recession velocity from distance and the Hubble constant, and also derives the age of the universe (1/H0) and the approximate redshift (z ≈ v/c). You can adjust the Hubble constant to see how different values affect results — current measurements range from 67 to 74 km/s/Mpc depending on the method used, a discrepancy known as the "Hubble tension" that represents one of the most exciting open problems in cosmology.
The calculator is useful for students studying astronomy and cosmology, educators demonstrating the expanding universe, and anyone curious about how we measure the scale of the cosmos. By entering the distance to a galaxy in megaparsecs (Mpc) and an appropriate Hubble constant, you instantly get the recession velocity in km/s, the Hubble time (an estimate of the universe's age), and the approximate redshift value.
Key Formulas
- Recession velocity: v = H0 × d
- Universe age (Hubble time): t = 1 / H0
- Redshift (low z approximation): z ≈ v / c
- Distance from velocity: d = v / H0
How the Calculations Work
Entering a distance of 10 Mpc with H0 = 70 km/s/Mpc gives a recession velocity of 700 km/s. The universe age estimate uses the Hubble time formula t = 1/H0, which with H0 = 70 km/s/Mpc yields approximately 13.97 billion years — close to the Planck satellite value of about 13.8 billion years from the Lambda-CDM model. The redshift z is computed as v/c for the non-relativistic case (z < 0.1), which covers the vast majority of observable galaxies.
Note that the simple 1/H0 universe age estimate assumes a constant expansion rate throughout cosmic history. In reality, the expansion has been decelerated by gravity and later accelerated by dark energy, so the actual age is slightly different from the simple Hubble time. Our result of ~13.97 Gyr with the default H0 is a useful approximation for educational purposes.
Frequently Asked Questions
What is Hubble's Law?
Hubble's Law states that galaxies are moving away from Earth at a velocity proportional to their distance: v = H0 × d. The Hubble constant H0 is approximately 70 km/s/Mpc. This observation provides the primary evidence for the expansion of the universe.
How is the age of the universe estimated from Hubble's Law?
The inverse of the Hubble constant (1/H0) provides an estimate of the age of the universe. With H0 = 70 km/s/Mpc, the estimated age is about 13.8 billion years. This matches results from the Planck satellite measurements of the cosmic microwave background.
What is the relationship between redshift and recession velocity?
For galaxies at non-relativistic speeds, the redshift z approximately equals v/c where v is recession velocity and c is the speed of light. This redshift is observed as a shift in spectral lines toward longer (redder) wavelengths.
How do you calculate the distance to a galaxy using Hubble's Law?
The distance d to a galaxy can be calculated as d = v / H0 where v is the recession velocity from redshift measurements. This makes Hubble's Law one of the primary tools for mapping the large-scale structure of the universe.
What is the Hubble constant and why is it important?
The Hubble constant H0 describes the rate at which the universe is expanding. Current measurements place it around 70 km/s/Mpc. Its precise value is critical for determining the size, age, and fate of the universe.
How accurate is the Hubble's Law Calculator?
Results use the standard formula v = H0 × d rounded to 2 decimal places. The universe age estimate (1/H0) assumes a constant expansion rate and matches the Planck satellite value of ~13.8 billion years when using H0 = 70 km/s/Mpc.
What units does the calculator use?
Distance is entered in megaparsecs (Mpc), the Hubble constant in km/s/Mpc, and recession velocity is returned in km/s. The universe age is given in gigayears (Gyr, billions of years).
Can I share my Hubble's Law calculation?
Yes, the URL automatically saves your input values so you can bookmark or share the exact calculation with others. Simply copy the URL after calculating to share your results.