Hubble Constant Calculator
Current best estimate is 67.4–73.0 km/s/Mpc depending on measurement method.
Distance in your selected unit; 1 Mpc = 3.26 million light-years.
Select a Mode and Enter Values
Choose a calculation mode above, enter the known values, and the calculator will instantly solve for recession velocity, distance, Hubble constant, or redshift.
How to Use the Hubble Constant Calculator
Choose a Calculation Mode
Select one of the four tabs at the top: Solve Velocity (need distance and H₀), Solve Distance (need velocity and H₀), Solve H₀ (need both velocity and distance), or Wavelength/Redshift (need spectral line wavelengths). The input fields will update automatically for the chosen mode.
Set the Hubble Constant
The Hubble constant field defaults to 70.3 km/s/Mpc. Use the preset buttons to switch between Planck 2018 (67.4), SH0ES (73.0), or Hubble’s original 1929 estimate (50). You can also type any custom value. The universe age and H(z) will update instantly.
Enter Your Galaxy Data
Type the known values into the input fields. For velocity, choose units (km/s, m/s, or fraction of c). For distance, choose Mpc, light-years, parsecs, or km. In Wavelength mode, use the spectral line preset buttons (Ca II K, H-alpha, etc.) to populate the rest wavelength automatically, then enter the observed wavelength from your spectrum.
Read Results and Export
Results appear instantly on the right. You will see the primary solved quantity, recession speed as a percentage of c, distance in four unit systems, estimated universe age, and H(z) at the computed redshift. A comparative bar chart shows how the universe age varies between Planck, SH0ES, and your chosen H₀. Click Export CSV to download all values, or Print Results for a clean printout.
Frequently Asked Questions
What is the Hubble constant and what are its units?
The Hubble constant H₀ describes how fast the universe is expanding today. Its units are kilometers per second per megaparsec (km/s/Mpc), meaning that for every additional megaparsec of distance from Earth, a galaxy appears to recede at H₀ more km/s. A galaxy 100 Mpc away recedes at roughly 7,000 km/s if H₀ = 70. H₀ can also be expressed in SI units of inverse seconds (s⁻¹), but the km/s/Mpc convention is nearly universal in observational astronomy. Its value changes over cosmic time as the expansion rate evolves; the subscript zero denotes the present-epoch value. Current best estimates range from 67.4 (Planck CMB) to 73.0 (SH0ES distance ladder) km/s/Mpc.
What is the Hubble Tension?
The Hubble Tension is the statistically significant discrepancy between two independent measurements of H₀. Measurements using the cosmic microwave background and the standard ΛCDM cosmological model (Planck 2018) give H₀ ≈ 67.4 km/s/Mpc, while measurements using the local distance ladder — Cepheid variable stars calibrating Type Ia supernovae — (SH0ES team) give H₀ ≈ 73.0 km/s/Mpc. The disagreement is now at the 5-sigma level, making systematic error increasingly implausible as the sole explanation. Proposed resolutions include early dark energy, extra relativistic species, or modifications to the recombination epoch. As of 2026, the tension remains unresolved and is one of the leading open problems in cosmology.
When do I need to use the relativistic formula?
The simple formula v = cz is only valid for small redshifts (roughly z < 0.1, corresponding to velocities less than about 10% of the speed of light). At higher redshifts, the non-relativistic approximation overestimates the true recession velocity and can even give results exceeding c, which is physically impossible. The relativistic Doppler formula v = c×[(z+1)²−1]/[(z+1)²+1] should be used for z ≥ 0.1. This calculator applies the correction automatically and displays a note when it has been used. For context, a galaxy at z = 1 has a true recession velocity of about 0.6c using the relativistic formula, whereas v = cz would incorrectly give exactly c.
How is the universe age calculated from H₀?
The simplest estimate of the universe age is the Hubble time: t_H = 1/H₀. After converting H₀ from km/s/Mpc to inverse seconds (by dividing by the number of kilometers in a megaparsec, 3.086×10¹⁹ km), the result is a time in seconds which is then converted to gigayears. At H₀ = 70 km/s/Mpc, t_H ≈ 13.97 Gyr. In reality the true age is slightly less because the expansion was decelerating in the matter-dominated era and is now accelerating due to dark energy. The ΛCDM correction gives an age of about 13.8 Gyr for H₀ = 67.4. This calculator uses the pure Hubble time without the ΛCDM correction factor, so the displayed age is a slight overestimate.
How do spectral lines reveal a galaxy's recession velocity?
Galaxies contain familiar elements like hydrogen, calcium, magnesium, and sodium. These elements emit and absorb light at precise, laboratory-measured wavelengths called rest wavelengths. When a galaxy is moving away from us, the Doppler effect stretches the wavelengths of its light toward the red end of the spectrum — a phenomenon called cosmological redshift. By comparing the observed wavelength of a spectral line in a galaxy's spectrum to its known rest wavelength, astronomers compute the redshift z = (λ_obs − λ_rest)/λ_rest. This z value then gives the recession velocity via Hubble's Law. The Ca II K (3934 Å) and H-alpha (6563 Å) lines are among the most commonly used for this purpose in optical spectroscopy.
What is H(z) and why does the Hubble parameter change with redshift?
The Hubble parameter H(z) describes the expansion rate of the universe at the cosmic epoch corresponding to redshift z. Because the universe was smaller and denser in the past, its expansion rate was different — faster during the matter-dominated era and slower before dark energy began to dominate. In the matter-dominated approximation (valid roughly for 1 < z < 100), H(z) ≈ H₀×(1+z)^1.5. The full ΛCDM formula is H(z) = H₀×√[Ω_m(1+z)³ + Ω_Λ], where Ω_m ≈ 0.31 is the matter density parameter and Ω_Λ ≈ 0.69 is the dark energy density parameter. This calculator uses the simplified matter-dominated formula, which overestimates H(z) at low redshift where dark energy is important.