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How far away is a star with a parallax of one arcsecond?

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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.

A star with a parallax of one arcsecond is at a distance of one parsec.12

This distance is equivalent to approximately 3.26 light-years, or about 30 trillion kilometers. In astronomy, the distance $d$ in parsecs is calculated as the reciprocal of the parallax $p$ in seconds of arc, expressed by the formula:23

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

Because the parallax angle is defined as the angle subtended by the radius of Earth’s orbit, a parallax of one arcsecond serves as the fundamental basis for the parsec unit.12