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Redshift Calculator

Work out redshift instantly with clear inputs, formula shown and shareable results.

About Redshift Calculator

Redshift is the fractional wavelength shift, z = (lambda(obs) - lambda(rest))/lambda(rest). The H-alpha line at 656.3 nm observed at 700 nm gives z = 0.0666, implying a recession of about 19,300 km/s from the relativistic Doppler relation. Negative values are blueshifts, as seen from the approaching Andromeda galaxy.

Formulas

Redshift

z = (lambda(observed) - lambda(rest)) / lambda(rest)

Relativistic Doppler

beta = ((1+z)^2 - 1) / ((1+z)^2 + 1)

Worked example

With the default values below, Redshift Calculator returns Redshift z of 0.06659. Change any input above and every figure here is recalculated in your browser.

Inputs used

Observed wavelengthminimum 0 nm
700 nm
Rest wavelengthminimum 0 nm
656.3 nm

Results

Redshift z
0.06659
Recession Velocity
19,298.60 km/s
Speed As A Fraction Of Light Speed
0.06437
Motion
Redshifted - moving away

Step by step

  1. 1Values used
  2. 2Redshift
  3. 3Relativistic Doppler
  4. 4Redshift z= 0.06659
  5. 5Recession Velocity= 19,298.60 km/s
  6. 6Speed As A Fraction Of Light Speed= 0.06437
  7. 7Motion= Redshifted - moving away

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is cosmological redshift a Doppler shift?

Not strictly. For distant galaxies it comes from the expansion of space stretching the wave in transit, though at small z the two give the same answer.

Why use the relativistic formula?

Because the simple v = cz overestimates velocity once z passes about 0.1, and becomes badly wrong beyond z = 1 where it would imply superluminal motion.

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