# Redshift Calculator

Created by Davide Borchia
Last updated: Jul 04, 2023

Discover one of the most important discoveries of astronomy with our redshift calculator: why do galaxies look redder than they should? What does it imply for our comprehension of the universe? Everything is moving away from us: here we will teach you the physics phenomenon at the basis of this!

Here you will learn:

• What is the redshift: Doppler effect for light;
• Why redshift is important in astronomy;
• How to calculate redshift from wavelength; and
• How to calculate the redshift from the frequency.

## Before the redshift: Doppler effect

You experienced Doppler effect in your life, knowingly or not. When the sound of a siren (like an ambulance) approaches you, you can hear a change in its pitch. The key of the Doppler effect is that a wave-like phenomenon is affected by speed.

Imagine standing while an ambulance approaches (someone called it, but not for me).

We can identify three moments:

• The ambulance approaches;
• The ambulance reaches the shortest distance from you;
• The ambulance moves away.

Let's analyze each step:

• During the approach, the vehicle moves in your direction, thus reducing the distance. While the frequency of the sound itself doesn't change, the wave is compressed by the approach (each point of the wave happens slightly before in space than it should without movements): you hear a higher-pitched sound.
• At the shortest distance, you would hear the sound unperturbed.
• When moving away from you, the position at which the sound starts gets increasingly larger: the wavelength is somehow increased; thus, you hear a lower-pitched sound.

Since De Broglie taught us that light is both a particle and a wave, can we define a phenomenon similar to the Doppler effect but for electromagnetic radiation? Let's introduce redshift.

## What is the redshift?

Redshift is the electromagnetic analog of the Doppler effect. The resemblance runs on the fact that a sound's pitch corresponds to the light's color.

While sound is — literally — down to Earth, to observe the redshift, it's better to move up a bit and look at the star.

Doppler effect was actually thought for light first! Some stars vary their color, and Christian Doppler thought this was due to their periodic shift with regard to Earth: now we know that that variation was due to temperature.

Redshift was later proved to be true: the Earth's movement in its orbit and the relative motions of stars contribute to the change in frequency of the received light.

So, how do we observe redshift? Consider the light spectrum: it spans from violet (shorter wavelength) to red (longer wavelength). So, for a light source getting away from us, we should observe a shift towards redder colors. That's exactly what we see!

But how do we calculate the redshift?

## How to calculate redshift

To calculate redshift from the wavelength, we find the redshift factor $z$. The redshift equation is:

$z = \frac {\lambda_{\text{obs}}-\lambda_{\text{emit}}}{\lambda_{\text{emit}}}$

Where:

• $\lambda_{\text{emit}}$ is the wavelength of the emitted light; and
• $\lambda_{\text{obs}}$ is the wavelength of the observed light.

Take a closer look at the formula for redshift: the wavelengths control the value of $z$.

• If the observed wavelength is longer than the emitted one, $\lambda_{\text{obs}}\text{\textgreater}\lambda_{\text{emit}}$, the light will shift toward the red. This would signal that the object is moving away from us.
• If the observed wavelength is shorter than the emitted one $\lambda_{\text{obs}}\text{\textless}\lambda_{\text{emit}}$, the light shifts toward the blue. The object is getting closer to us.

You can easily calculate the redshift using the frequency of the emitted and observed light:

$z = \frac {f_{\text{emit}}-f_{\text{obs}}}{f_{\text{obs}}}$

## How do I find the emitted wavelength in the redshift equation?

While measuring the observed wavelength would be super easy, barely an inconvenience (you only need a spectrometer), measuring the emitted wavelength requires a bit more thought.

Luckily, physics is pretty consistent across our universe, and stars shine pretty much the same way in our surroundings and on the other side of the galaxy, or even in other galaxies; thus, we can recognize features in the spectra we measure on Earth that allows us to quantify the emitted wavelength.

Consider hydrogen: being the most common element in the universe and the main fuel for the nuclear fusion processes inside stars, it's an easy catch during the analysis of a spectrum. If you can identify the region of the spectrum by the pattern of absorption lines (they are all shifted in the same way), you can easily measure the shift of the spectrum.

## Redshift and astronomy

The formula for redshift allowed astronomers to understand one of the key features of our universe: galaxies are moving away from us, and not just randomly, but following the underlying expansion of the universe. Find out more at our Hubble law distance calculator.

Davide Borchia
Emitted light
Wavelengh
nm
Frequency
THz
Observed light
Wavelength
nm
Frequency
THz
Redshift
z
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