Redshift Calculator: z, Recession Speed and Distance of a Galaxy from Its Spectrum

Redshift, speed and distance from a spectral line.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose whether you know the two wavelengths or the redshift.

Enter the observed and emitted wavelengths, or z, and the Hubble constant.

The calculator gives z, the speed and the distance.

Formulas used

  • z = \frac{\lambda_{obs} - \lambda_{emit}}{\lambda_{emit}}
  • v = c\,\frac{(1+z)^2 - 1}{(1+z)^2 + 1}
  • d = \frac{v}{H_0}

Worked example

With the default numbers in the calculator above:

  1. Redshift z: 0.0666179
  2. Recession speed (relativistic Doppler formula): 19307.7 km/s
  3. Speed as a fraction of the speed of light: 0.0644035
  4. Distance by Hubble's law (good for small z): 275.82 Mpc (899.62 million light years)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you know? The redshift z; Redshift z (used when you choose z) 0.5.

  1. Redshift z: 0.5
  2. Recession speed (relativistic Doppler formula): 115305 km/s
  3. Speed as a fraction of the speed of light: 0.384615
  4. Distance by Hubble's law (good for small z): 1647.2 Mpc (5372.5 million light years)

Common questions

What is redshift?

The stretching of the wavelength of light from a source that moves away from us, or from the expansion of space.

What does a negative redshift mean?

A blueshift: the source is coming toward us.

Why is the distance not accurate for large z?

Hubble's law is a simple low-redshift approximation. For large z, the way the expansion rate changed over time must be included.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any astronomy or physics text (redshift and the Doppler effect).

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