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Calcimator

Hubble's Law Calculator

Calculate recession velocity and distance from cosmological redshift using Hubble's Law. Includes lookback time, scale factor, and relativistic corrections.

Inputs

km/s/Mpc

Results

Recession Velocity (classical)

29,979.25 km/s

Recession Velocity (relativistic)

28,487.07 km/s

Distance

428.27 Mpc

Distance1,396.86 Mly
Distance1.397 Gly
Lookback Time1.27 Gyr
Hubble Time (1/H₀)13.97 Gyr
Scale Factor at Emission0.9091
Wavelength Stretch1.1×
Age At Emission12.7
How to Use This Calculator
  1. Enter the spectroscopic Redshift (z) of the galaxy — nearby galaxies are 0.001–0.1, distant quasars can exceed 6.
  2. Set the Hubble Constant (H₀) in km/s/Mpc — Planck gives 67.4, SH0ES gives 73.0; 70 is a common compromise.
  3. Read Distance (Mpc) and Distance (Gly) for the galaxy's comoving distance from Earth.
  4. Use Lookback Time (Gyr) to determine how far into the past you are observing the object.
  5. Compare Classical and Relativistic recession velocities — for high-z objects, the relativistic formula is more accurate.

How the result changes with Redshift (z)

Redshift (z)Recession Velocity (classical)Recession Velocity (relativistic)Distance
2599,584.92 km/s239,833.97 km/s8,565.5 Mpc
72,098,547.21 km/s290,568.07 km/s29,979.25 Mpc
133,897,301.95 km/s296,748.88 km/s55,675.74 Mpc
185,396,264.24 km/s298,136.15 km/s77,089.49 Mpc

What each input means

Redshift (z)
Cosmological redshift measured from spectral lines (nearby galaxies ~0.001-0.1, distant ~1-10)
Hubble Constant (H₀)
Current expansion rate (Planck 2018: 67.4, SH0ES: 73.0; default 70 is a compromise)

How this is calculated

Formula

v = H₀ × d; d = cz / H₀

Worked example, using the default values

  1. Identify Input Parameters
    Redshift (z) = 0.1, Hubble Constant (H₀) = 70 = 2 input(s) provided
  2. Calculate Recession Velocity
    Recession Velocity
    29979.25 = 29979.25
  3. Calculate Recession Velocity
    Recession Velocity
    28487.07 = 28487.07
  4. Calculate Distance
    Distance
    428.27 = 428.27
  5. Calculate Distance
    Distance
    1396.86 = 1396.86
  6. Calculate Distance
    Distance
    1.397 = 1.397

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