The parsec (pc) is the professional unit for stellar distances: the distance at which 1 AU subtends 1 arcsecond. 1 pc = 3.262 ly. Multiples: kpc (clusters, galaxies), Mpc (nearby cosmos), Gpc (cosmology).
The parsec begins with a very concrete geometric idea. Observe a star from Earth in January, then again in July. In between, Earth has moved 2 AU (the diameter of its orbit). The star, seen from these two positions, seems to shift ever so slightly against the background stars — the annual parallax. The closer the star, the larger that angular shift.
The convention: call parallax p the half-angle at which 1 AU is seen from the star. Thus 1 pc is the distance at which 1 AU subtends exactly 1 arcsecond (1/3600 of a degree). That's a tiny angle: a 1-euro coin viewed from 5 km away.
This definition yields a formula of rare beauty: d(pc) = 1/p(arcsec). No constant, no c, no G. An astronomer measures the parallax angle and divides 1 by that value: out pops the distance in parsecs. This elegance is why professionals adopted the unit.
In practice, no star (besides the Sun) is close enough to reach p = 1 arcsec. Proxima Centauri, the nearest, has a parallax of 0.7687 arcsec and sits at 1/0.7687 ≈ 1.301 pc. The historical record for the first measured parallax (Bessel, 61 Cygni, 1838) was 0.314 arcsec, i.e. 3.18 pc.
The IAU gave an exact numerical definition in 2015: 1 pc = (648,000/π) AU, which is about 3.085 677 581 × 10¹⁶ m. Since the AU has itself been exact since 2012, the parsec is exact by derivation. The cosmological multiples (kpc, Mpc, Gpc) follow the same definition.
Fundamental formula:
d(pc) = 1 / p(arcsec)
where p is the annual parallax in arcseconds. For example, a star with p = 0.1 arcsec sits at 10 pc.
IAU 2015 definition (exact):
1 pc = (648,000/π) AU = 206,264.806... AU
Precise conversions:
• 1 pc ≈ 3.0857 × 10¹⁶ m • 1 pc ≈ 3.0857 × 10¹³ km • 1 pc ≈ 3.262 ly (exactly 206,264.806/63,241.077...) • 1 pc ≈ 206,264.806 AU • 1 kpc = 10³ pc ≈ 3,262 ly • 1 Mpc = 10⁶ pc ≈ 3.262 × 10⁶ ly • 1 Gpc = 10⁹ pc ≈ 3.262 × 10⁹ ly
Key parallaxes to know:
• Proxima Centauri: p = 0.7687 arcsec → 1.301 pc = 4.2465 ly • Sirius: p = 0.3792 arcsec → 2.637 pc = 8.59 ly • Vega: p = 0.1307 arcsec → 7.65 pc = 25 ly • Galactic centre: d ≈ 8.18 kpc = 26,700 ly (parallax too small to measure directly) • M31 Andromeda: d ≈ 0.78 Mpc = 2.54 × 10⁶ ly
For fun: in Star Wars (1977), Han Solo makes the Kessel Run in 'less than 12 parsecs'. That's a distance, not a time — a scripting error later retconned as 'the shortest shortcut'.
The parsec declines into a whole family of units, from stellar neighbourhoods to the edge of the observable Universe.
Parsec (pc, < 10³ pc). Nearby-to-intermediate stellar distances. A 100-pc radius around the Sun encloses almost all naked-eye stars (≈ 5,000). The Gaia mission (ESA, 2013-) reaches 20-microarcsecond parallaxes, accurate out to 50 kpc.
Kiloparsec (kpc, 10³ to 10⁶ pc). The preferred unit for mapping galaxies. The Milky Way is ≈ 32 kpc across; the Sun lies 8.18 kpc from the galactic centre; the disc thickness is 0.5 kpc. Open and globular clusters live in kpc (Beehive at 0.187 kpc, M13 at 7.2 kpc).
Megaparsec (Mpc, 10⁶ to 10⁹ pc). Intergalactic scale: M31 at 0.78 Mpc, Virgo Cluster at 16.5 Mpc, Laniakea Supercluster spanning 160 Mpc. It's the natural unit for the Hubble constant (H₀ ≈ 67-73 km/s/Mpc), which expresses galactic recession velocity per Mpc.
Gigaparsec (Gpc, > 10⁹ pc). The near-to-far observable Universe: ≈ 14 Gpc comoving radius. The most distant quasars, JWST's most primordial galaxies (z > 13), sit at 4-10 Gpc in light-travel distance. At these scales, astronomers also speak in terms of redshift z rather than parsecs.
Rarely-used submultiples: the milliparsec (mpc, 10⁻³ pc) and microparsec (µpc) appear in proper-motion studies or extreme Oort-cloud distances, but stay confidential.
The parsec is naturally measured by parallax — that's its whole point.
Trigonometric parallax. Photograph a star six months apart, measure its angular shift against far-distant background stars (treated as fixed). The half-shift is the annual parallax p. Distance is 1/p in parsecs. Simple, elegant, but limited by angular precision. From the ground, you cap at 0.01 arcsec (100 pc). Hipparcos (ESA, 1989-1993) reached 1 milliarcsec (1 kpc), Gaia (ESA, 2013-) goes to 20 microarcsec (50 kpc).
Gaia in particular has revolutionised the field. Its DR3 catalogue (2022) holds nearly 2 billion stars with parallaxes, proper motions and magnitudes. For the first time, we have a precise 3D map of the Milky Way out to the galactic centre — a leap comparable to the invention of the telescope.
Beyond Gaia. For distances > 10 kpc, parallax becomes insufficient and we chain onto the cosmic distance ladder: Cepheid variables (period-luminosity law), RR Lyrae, horizontal branches of globular clusters, Type Ia supernovae, Tully-Fisher (spiral galaxies) and Fundamental Plane (ellipticals). Each rung calibrates on the previous — hence the importance of Gaia's precision for Cepheid calibration.
Cosmological redshift. From ≈ 100 Mpc, we use the Hubble-Lemaître law: d ≈ cz/H₀, where z is the spectral redshift. JWST observations keep pushing the record beyond z > 14.
What about amateurs? Parallax is out of reach for amateur telescopes (except collaborative work via the AAVSO). You can, however, estimate the distance of well-known clusters via tabulated apparent and absolute magnitudes. Our sky map tool shows distances in parsecs and light-years for pointed objects.
Several pitfalls surround the parsec.
Parsec vs light-year. Both measure stellar distances, but 1 pc = 3.262 ly (not the other way round). Multiply parsecs by 3.262 to get light-years; divide light-years by 3.262 to get parsecs. Scientific papers overwhelmingly use the parsec; outreach prefers the light-year.
Parsec vs astronomical unit. 1 pc = 206,265 AU exactly. The AU describes the Solar System, the parsec stars and galaxies. Scale → unit: AU (Solar System), pc-kpc (stars-galaxy), Mpc-Gpc (cosmology).
Parallax vs proper motion. Parallax is an apparent shift due to Earth's orbit (cyclic, yearly). Proper motion is the star's real motion across the celestial sphere (linear, cumulative). Barnard's Star has the largest known proper motion (10.3 arcsec/year) — don't confuse it with its parallax (0.547 arcsec).
Parsec vs 'parsecs of time'. In Star Wars, the parsec is used as a duration ('in less than 12 parsecs'). Mathematically absurd: a parsec is a distance. A shorter voyage geographically can take more or less time depending on speed and obstacles — that's the official retcon reading.
Modern vs old parsec. Until 2015, the parsec had no exact numerical definition; it was implicitly tied to the pre-2012 AU. Earlier numerical values differ at the 8th decimal place. Since Resolution B2 (2015), the parsec equals exactly (648,000/π) AU.
Because the parsec drops naturally from the parallax method, the main technique for measuring stellar distances. The formula d(pc) = 1/p(arcsec) is unbeatably simple: no intermediate constant, no speed of light. The Hipparcos and Gaia catalogues deliver parallaxes directly in milli- or microarcseconds — inversion gives parsecs with no further calculation. The light-year, though more evocative for the public, forces multiplication by c and by 365.25 × 86,400 — adding needless conversions for a professional.
Annual parallax is the half-angle of a star's apparent shift when observed six months apart — from the two ends of Earth's orbit, 2 AU apart. Nearby stars 'seem' to shift against distant stars that serve as a fixed backdrop. Photograph the field in January and July, measure the angle, divide 1 by that value in arcseconds. The Gaia mission (ESA, 2013-, extended) does this for 2 billion stars with precision down to 20 microarcsec, corresponding to distances up to 50,000 pc.
No formal limit: Gpc is used for the observable Universe (≈ 14 Gpc comoving radius), and one could in principle go further. In practice, direct parallax caps at about 50 kpc (Gaia). Beyond that, we chain indirect methods (Cepheids to ≈ 30 Mpc, Type Ia supernovae to ≈ 10 Gpc, cosmological redshift beyond). The most distant galaxies seen by JWST in 2024-2025 (z > 14) sit at ≈ 4-10 Gpc in light-travel distance — 13-14 billion years of voyage.
To make it exact in SI units. Until 2015, the parsec was implicitly tied to the AU, itself tied to solar mass (before 2012): a chain of fuzzy definitions. The IAU fixed the AU at exactly 149,597,870,700 m in 2012, then, for consistency, fixed the parsec at (648,000/π) AU in 2015 (Resolution B2). The parsec thus becomes a pure numerical constant, ≈ 3.0856775815 × 10¹⁶ m. This semantic surgery changed nothing in real measurements but aligned the astronomical unit family with the modern SI.