# Parallax Calculator

Created by Purnima Singh, PhD
Reviewed by Steven Wooding
Last updated: Feb 15, 2022

Omni's parallax calculator allows you to compute the distance of nearby stars by using the stellar parallax method.

Do you know how astronomers measure the distance between our Earth and nearby stars? The answer is that they use a technique called the parallax method to make these astronomical measurements. The method relies on measuring the parallax angle and using it to compute the stellar distances.

Continue reading this article to know the definition of parallax and the formula for calculating it. You will also find an example of calculating stellar distance using the technique.

Before going any further, let us first try to understand what parallax is.

## What is parallax? – Parallax definition

Have you ever tried holding out a pencil at arm's length and looking at it with your left and right eye closed sequentially? If you have never done this, then try it right now. Observe the position of the pencil with respect to some distant background object like a tree or a wall.

You will notice that the relative position of the pencil with respect to the background will change depending upon whether you are looking at it with your left or right eye closed. Another thing worth noting is that as you move the pencil closer to your face, the gap between the left and right images will increase.

That is the parallax effect; a change in the apparent position of an object due to a change in the position of observation point. This result is a very useful tool in astronomy for calculating the distance between the earth and far away stars.

## Stellar parallax

You must be thinking about how we can utilize parallax to determine the distance of stars. It's not as if we can use our two eyes to do the trick.

As we know, our Earth moves around the Sun in its orbit (see the given figure). In fact, it changes its position by about 300 million kilometers or 2 AU in six months. This movement allows us to look at the stars from different locations that are approximately two astronomical units apart.

For example, we can measure the position of a star, say in June, when the Earth is at a specific point in its orbit (shown as point A in figure 1). We then repeat the measurement after six months, i.e., in December (point B).

Due to the change in the position of the Earth around the Sun (or a change in our observation point), a nearby star would appear to move against the distant background stars. This apparent change in position or motion of the star is called stellar parallax.

Since we know the size of Earth's orbit, we can calculate the distance to the star by measuring the angles of the light from the star at two points in the trajectory using a telescope.

## Parallax formula for distance calculation

As shown in figure 1, the two observation positions, A and B, and the star's position, form a triangle. Since we know the baseline between the two observation points (2 AU), by measuring the parallax, we can easily calculate the distance of the object using trigonometry.

The parallax formula for calculating approximate distance is:

$\quad D = \frac{1}{P}$

where:

• $D$ – Distance between the star and the Earth, measured in parsecs; and

• $P$ – Parallax angle, measured in arcseconds.

Using the above parallax equation, we can also define 1 parsec as the distance at which an object has a parallax of 1 arcsecond.

## Stellar parallax calculation example

Let's calculate the distance between Earth and Sirius, the brightest star in the night sky. According to the the parallax for this star is 379.2 milliarcseconds (mas), i.e., $P = 379.2 \times 10^{-3} ~\rm arcsec$.

To calculate the star's distance, we will use the parallax formula:

\quad \begin{align*} D& = \frac{1}{P}\\\\ & = \frac{1}{379.2 \times 10^{-3} ~\rm arcsec}\\\\ & = 2.64 ~ \rm parsecs \end{align*}

Using 1 parsec = 3.26 light-year, we can convert the distance in light-year as:

\quad \begin{align*} D& = 2.64 ~ \rm parsecs\\ & = 2.64 \times 3.26~ \rm ly\\ & = 8.60 ~ \rm ly \end{align*}

## How to use the parallax calculator

Now let us see how we can find the distance between our planet and stars using the parallax calculator:

1. Using the drop-down menu, select the star that you are interested in. If you want to calculate the distance for a star not given in the menu, choose the custom option.

2. The fields parallax and distance will auto-populate. You can also enter the parallax if you know the value.

3. You can also use this tool as a parallax angle calculator. Just enter the star's distance, and you will get the calculated parallax angle in a fraction of a second.

## FAQ

### What is parallax angle?

The parallax angle is half of the angle between the position of our Earth at one specific time of the year and after six months, as measured with respect to a nearby star.

### How do I calculate distance of a star using the stellar parallax method?

To calculate the distance of a star using the stellar parallax method, proceed as follows:

1. Find out the measured stellar parallax angle of the star.

2. Determine the distance of the star using the stellar parallax equation, distance = 1 / stellar parallax.

3. Congratulations! You have calculated the distance of the star.

### What are the limitations of stellar parallax method?

The stellar parallax method can't be used to measure the distance of stars that are more than 100 light-years from the earth. This is because the parallax angle is inversely proportional to the distance, and for very large distances, the angle is too small to be measured.

### What is the stellar parallax of the nearest star to Earth?

0.772 arcsec. The nearest star to Earth is the Proxima Centauri. It has a stellar parallax of 0.772 arc seconds and is approximately 1.30 parsecs away from the Earth.

Purnima Singh, PhD
Star
Arcturus (α Boötis)
Parallax (P)
marcsec
Distance (D)
pcs
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