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How is the distance in parsecs calculated from a parallax measured in arcseconds?

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Diagram illustrating how astronomers calculate the distance to a star using parallax: Earth is shown in two positions on opposite sides of its orbit around the Sun, with lines extending to a nearby star X and further to distant background stars. The apparent shift in star X's position, measured as angle A, is used to determine its distance, with the baseline labeled as 186,000,000 miles. — Parallax Calculating stellar distances.

To calculate the distance to a star in parsecs when the parallax is measured in arcseconds, you use a simple reciprocal relationship.

The distance $d$ in parsecs is defined as the reciprocal of the parallax angle $p$ in seconds of arc, expressed by the formula:

$d = \frac{1}{p}$

In this relationship, a parsec represents the distance at which the radius of Earth’s orbit subtends an angle of one second of arc. Consequently, a star with a parallax of 1 arcsecond is exactly 1 parsec away, which is equivalent to approximately 3.26 light-years.123