Astronomical redshift conversion calculator

Calculate redshift z and observed/rest wavelength ratio with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use redshift z and observed/rest wavelength ratio to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Observed wavelength (nm)
660
Rest wavelength (nm)
656.28
Redshift z
0.005668
Observed/rest wavelength ratio
1.005668
Special-relativistic radial Doppler equivalent (km/s)
1,694.501225

Try another scenario

Observed wavelength (nm)
726.0000000000001
Rest wavelength (nm)
656.28
Redshift z
0.106235
Observed/rest wavelength ratio
1.106235
Special-relativistic radial Doppler equivalent (km/s)
30,165.365811
Calculation method

Calculation method

Redshift z

z=lambdaObs/lambdaRest-1; beta=((1+z)²-1)/((1+z)²+1).

Observed/rest wavelength ratio

z=lambdaObs/lambdaRest-1; beta=((1+z)²-1)/((1+z)²+1).

Special-relativistic radial Doppler equivalent (km/s)

z=lambdaObs/lambdaRest-1; beta=((1+z)²-1)/((1+z)²+1).

Symbols and units
a
Observed wavelength (nm)
b
Rest wavelength (nm)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Radial Doppler equivalent in vacuum; not a cosmological recession-distance estimate. Supported limits: All required fields must be finite values of the exact declared type and within displayed bounds. Lists contain1–1000 finite numbers. JSON tables are numeric rectangular rows, at most100 rows and30 columns; individual tools have stricter shape/domain constraints. Radial Doppler equivalent in vacuum; not a cosmological recession-distance estimate.
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