Parallax Calculator

Created by Luis Hoyos
Last updated: Nov 21, 2022

Omni's parallax calculator determines the distance from Earth to different stars using the stellar parallax method.

The article below explains how that method works by showing the parallax equation. In that formula, the parallax angle (P) is related to stellar distances (D) using trigonometric principles.

The stellar parallax method

The stellar parallax method is a technique astronomers use to measure the distance from Earth to stars. It's been used for centuries and is still considered one of the most accurate ways to measure star distances. Recent technological advances have allowed astronomers to measure distances to stars with greater precision.

The method relies on the fact that stars will appear to shift their position as Earth orbits around the sun. We can detect this shift by measuring the angles of the light from the star at two different points in Earth's orbit.

For example, in the following image, you can observe how the same nearby star looks different at two opposite points of Earth's orbit. The parallax angle (P) is simply half the difference between the two observed angles. The formula to calculate the distance to the star arises from using the tangent (tan) trigonometric function, the radius of Earth's orbit, and the parallax angle. We present that formula in the following section, and you can look at its derivation in this Wikipedia article.

Parallax effect of a star seen from two positions of Earth's orbit.
The parallax effect.

🔎 If you want to learn about the motion of satellites around the Earth, visit the earth orbit calculator

Parallax formula to calculate distance

Once we know the parallax angle, we only need to use the parallax equation:

D = 1/P

, where:

  • DDistance between the star and the Earth, in parsecs (pcs) units; and
  • PParallax angle, in arcseconds (arcsec) units.

Some important points about the previous relationship:

  • The distance to stars is usually a huge number, so the parallax angle is really tiny. An arcsecond is a unit for small angles, such as the parallax one. For example, 1 arcsec = 0.000277778 deg, as you can check in our angle conversion tool.
  • On the other side, the parsec is a length unit made up to conveniently use the previous parallax formula without needing any conversion factor, just inputting D in pcs and P in arcsec.
  • Contrary to arcsecond, the parsec is helpful for enormous distances, such as those to objects outside the Solar System. You can find and interact with that unit in our length converter.
  • We can also solve for P and obtain the parallax angle formula: P = 1/D. In fact, in this parallax calculator, the parallax angle can be obtained by inputting D.
Luis Hoyos
Star
Arcturus (α Boötis)
Parallax (P)
marcsec
Distance (D)
pcs
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