The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to 3.26 light-years or 206,265 astronomical units (AU), i.e. 30.9 trillion kilometres (19.2 trillion miles).

[a] The parsec unit is obtained by the use of parallax and trigonometry, and is defined as the distance at which 1 AU subtends an angle of one arcsecond[1] (⁠1/3600⁠ of a degree).

[3] The word parsec is a shortened form of a distance corresponding to a parallax of one second, coined by the British astronomer Herbert Hall Turner in 1913.

[4] The unit was introduced to simplify the calculation of astronomical distances from raw observational data.

Partly for this reason, it is the unit preferred in astronomy and astrophysics, though in popular science texts and common usage the light-year remains prominent.

Although parsecs are used for the shorter distances within the Milky Way, multiples of parsecs are required for the larger scales in the universe, including kiloparsecs (kpc) for the more distant objects within and around the Milky Way, megaparsecs (Mpc) for mid-distance galaxies, and gigaparsecs (Gpc) for many quasars and the most distant galaxies.

Equivalently, it is the subtended angle, from that star's perspective, of the semimajor axis of the Earth's orbit.

A parsec can be defined as the length of the right triangle side adjacent to the vertex occupied by a star whose parallax angle is one arcsecond.

No trigonometric functions are required in this relationship because the very small angles involved mean that the approximate solution of the skinny triangle can be applied.

Astronomer Royal Frank Watson Dyson expressed his concern for the need of a name for that unit of distance.

By the 2015 definition, 1 au of arc length subtends an angle of 1″ at the center of the circle of radius 1 pc.

Approximately, In the diagram above (not to scale), S represents the Sun, and E the Earth at one point in its orbit (such as to form a right angle at S[b]).

The angle SDE is one arcsecond (⁠1/3600⁠ of a degree) so by definition D is a point in space at a distance of one parsec from the Sun.

Because the astronomical unit is defined to be 149597870700 m,[10] the following can be calculated: Therefore, if 1 ly ≈ 9.46×1015 m, A corollary states that a parsec is also the distance from which a disc that is one au in diameter must be viewed for it to have an angular diameter of one arcsecond (by placing the observer at D and a disc spanning ES).

Mathematically, to calculate distance, given obtained angular measurements from instruments in arcseconds, the formula would be:

where θ is the measured angle in arcseconds, Distanceearth-sun is a constant (1 au or 1.5813×10−5 ly).

To the nearest meter, the small-angle parsec corresponds to 30856775814913673 m. The parallax method is the fundamental calibration step for distance determination in astrophysics; however, the accuracy of ground-based telescope measurements of parallax angle is limited to about 0.01″, and thus to stars no more than 100 pc distant.

Between 1989 and 1993, the Hipparcos satellite, launched by the European Space Agency (ESA), measured parallaxes for about 100000 stars with an astrometric precision of about 0.97 mas, and obtained accurate measurements for stellar distances of stars up to 1000 pc away.

[15] Distances expressed in fractions of a parsec usually involve objects within a single star system.

The Hubble constant becomes relevant when converting an observed redshift z into a distance d using the formula d ≈ ⁠c/H⁠ × z.

[23] One gigaparsec (Gpc) is one billion parsecs — one of the largest units of length commonly used.

One gigaparsec is about 3.26 billion ly, or roughly ⁠1/14⁠ of the distance to the horizon of the observable universe (dictated by the cosmic microwave background radiation).

For example: To determine the number of stars in the Milky Way, volumes in cubic kiloparsecs[c] (kpc3) are selected in various directions.

The number of globular clusters, dust clouds, and interstellar gas is determined in a similar fashion.

To determine the number of galaxies in superclusters, volumes in cubic megaparsecs[c] (Mpc3) are selected.

The Sun is currently the only star in its cubic parsec,[c] (pc3) but in globular clusters the stellar density could be from 100–1000 pc−3.

The observational volume of gravitational wave interferometers (e.g., LIGO, Virgo) is stated in terms of cubic megaparsecs[c] (Mpc3) and is essentially the value of the effective distance cubed.

The parsec was used incorrectly as a measurement of time by Han Solo in the first Star Wars film, when he claimed his ship, the Millennium Falcon "made the Kessel Run in less than 12 parsecs", originally with the intention of presenting Solo as "something of a bull artist who didn't always know precisely what he was talking about".

The claim was repeated in The Force Awakens, but this was retconned in Solo: A Star Wars Story, by stating the Millennium Falcon traveled a shorter distance (as opposed to a quicker time) due to a more dangerous route through the Kessel Run, enabled by its speed and maneuverability.