The second of arc is a unit of plane angle equal to one sixtieth of a minute of arc, or one three-thousand-six-hundredth of a degree. Its symbol is arcsec, or a double prime after the number, and it is also called the arcsecond. A full circle contains 1,296,000 of them.
It is the working unit of positional astronomy. Star positions, proper motions and the apparent diameters of planets are all quoted in arcseconds, and the best ground-based telescopes are limited by atmospheric turbulence to a resolution of about half an arcsecond on a good night. Space telescopes escape that limit; the Hubble Space Telescope resolves detail around one twentieth of an arcsecond.
The parsec, the standard unit of astronomical distance, is defined directly from it. A star one parsec away shows an annual parallax of exactly one arcsecond as the Earth moves from one side of its orbit to the other, and the name is a contraction of parallax and second. No star is that close, so every measured stellar parallax is smaller than one arcsecond, and the Gaia spacecraft measures some to a few millionths of one.
On Earth, an arcsecond of latitude is about 31 metres, which is why coordinates written in degrees, minutes and seconds need decimal fractions of a second to locate a building. Surveying instruments and telescope mounts are specified by how many arcseconds of error they carry, and precision optical work uses the unit for angular tolerances.
The atmosphere sets the practical limit for a telescope on the ground. Turbulence in the air smears a star into a blur typically one arcsecond across, a quantity astronomers call the seeing, and the finest mountain sites reach a few tenths of that on a good night. Beating it requires either going above the air or correcting for it in real time with a deformable mirror. Space telescopes and modern astrometry work far below the arcsecond: the Gaia spacecraft measures stellar positions to tens of microarcseconds, which is the angle a coin would subtend on the Moon, and radio interferometers spanning continents do better still.
One second of arc equals one sixtieth of a minute of arc, one three-thousand-six-hundredth of a degree, or about 4.84814 millionths of a radian.
| Unit | Symbol | 1 Second of arc equals | 1 of these equals | Converter |
|---|---|---|---|---|
| Minute of arc | arcmin | 0.0166666666667 arcmin | 60 arcsec | Seconds of arc to Minutes of arc |
| Degree | deg | 0.000277777777778 deg | 3600 arcsec | Seconds of arc to Degrees |
| Radian | rad | 0.0000048481368111 rad | 206264.806247 arcsec | Seconds of arc to Radians |