An arcsecond, often called a second of arc and written with the double-prime symbol (″) or two ASCII single quotes, is a unit for measuring angles. It belongs to the sexagesimal system of degrees, minutes and seconds and is commonly used where small angular separations must be expressed precisely, for example in mathematics and astronomy. One arcsecond equals one sixtieth of an arcminute and one three‑thousand‑six‑hundredth of a degree.

Definition and common conversions

The arcsecond is defined relative to the degree. Key relations are:

  • 1 degree = 60 arcminutes (′); 1 arcminute = 60 arcseconds (″).
  • 1 arcsecond = 1/3,600 degree; a full circle contains 360 × 3,600 = 1,296,000 arcseconds (full circle).
  • In radians the exact relation is 1 arcsecond = π / 648000 radians, approximately 4.848136811×10−6 rad.

Notation, names and subdivisions

Notation uses a prime (′) for arcminutes and a double prime (″) for arcseconds; the words "minute" and "second" derive from Latin terms describing fractional parts (minuta and secunda). For high precision, astronomers and geodesists use milliarcseconds (mas, 10−3″) and microarcseconds (μas, 10−6″).

Uses and examples

Arcseconds appear where very small angles matter. Human visual acuity is roughly 1 arcminute (≈60″); the Moon and Sun each subtend about 0.5° ≈ 1,800″. High-resolution telescopes can resolve fractions of an arcsecond: for example, space telescopes achieve resolutions on the order of 0.05″ in visible light. In practical surveying, 1″ at a distance of 1 kilometer corresponds to about 4.85 millimetres, while at the distance of 1 astronomical unit (Earth–Sun distance) 1″ subtends roughly 725 kilometres.

Astronomical importance and the parsec

One of the most significant uses of the arcsecond is in stellar parallax. By definition, a star with a parallax of 1 arcsecond lies at a distance of 1 parsec. This geometrical definition links angular measurement to distance: 1 parsec ≈ 206,265 astronomical units, or about 3.26 light‑years. Astrometry, the precise measurement of positions and motions of celestial objects, routinely reports angles in milliarcseconds and microarcseconds to map stellar motions and detect exoplanets.

History and context

The division of the circle into degrees, minutes and seconds has origins in ancient sexagesimal counting (notably Babylonian) and medieval Latin terminology. Over time the system was adopted in navigation, cartography and astronomy, and it remains convenient for expressing angular sizes that lie between whole degrees and the tiny fractions needed for modern observational work. For related concepts see degree and applications in precision measurement.