# Redshift Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Oct 21, 2022

The redshift calculator will help you to estimate the redshift parameter $z$. The discovery of the redshift in astrophysics has become a crucial point in understanding the history of our universe.

In the further text, we explain what redshift is and how you can estimate its magnitude using the mathematical definition of redshift. Finally, we are also discussing the differences between redshift and blueshift.

## What is redshift?

Redshift is a phenomenon where the spectral lines of electromagnetic radiation coming from some stars or galaxies are shifted towards longer wavelengths (or lower frequencies). The term redshift was introduced since the visible light of the longest wavelength is red (approximately 700 nm). Several reasons can cause the redshift:

• Relativistic Doppler effect – Occurs whenever a light source moves away from an observer. You can check out our Doppler effect calculator which is a classical version of Doppler effect.

• Expansion of the universe – The more distant galaxies are, the faster they seem to move away from us.

• Gravitational effect – Light loses energy by "overcoming" gravity of the star, i.e., the light increases its wavelength.

💡 Learn more about how Hubble discovered that the Universe is expanding by looking at the redshift of galaxies with our hubble law distance calculator.

## Redshift definition

In astronomy, the redshift is characterized by a dimensionless quantity called $z$. Our redshift calculator can estimate $z$ parameter in two ways:

$\begin{split} z &= \frac{\lambda_{\rm{obsv}} - \lambda_{\rm{emit}}}{\lambda_{\rm{emit}}}\\[1em] &\rm{or}\\[1em] z &= \frac{f_{\rm{emit}} - f_{\rm{obsv}}}{f_{\rm{obsv}}}, \end{split}$

where:

• $z$ – Redshift parameter;
• $\lambda_{\rm{emit}}$ and $f_{\rm{emit}}$ – Wavelength and the frequency of emitted light, respectively; and
• $\lambda_{\rm{obsv}}$ and $f_{\rm{obsv}}$ – Wavelength and the frequency of observed light, respectively.

The possibility to use both wavelength and frequency results from Planck's equation. You can see from the above redshift formula that the greater $z$, the bigger the difference between emitted and observed light.

## Redshift and blueshift

When the observed wavelength is smaller than emitted, the $z$ parameter is negative $(z \lt 0)$, and the blueshift phenomenon occurs. In this case, the spectral lines are shifted towards shorter wavelengths (blue light has the shortest wavelength, approximately 450 nm).

There are different interpretations of the $z$ parameter, for example:

• When the Doppler effect causes the shift, the object approaches (blueshift) or recedes (redshift) from the observer.

• We would observe a blueshift if the universe is shrinking and a redshift if the universe is expanding.

• When a gravitational effect causes the shift, the light is emitted from a source with a weaker (blueshift) or a stronger (redshift) gravitational field than the gravitational field in which the observer resides.

Dominik Czernia, PhD
Emitted light
Wavelengh
nm
Frequency
THz
Observed light
Wavelength
nm
Frequency
THz
Redshift
z
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