| Seconds of arc (arcsec) | Degrees (deg) |
|---|---|
| 1 Second of arc | 0.000277777777778 deg |
| 2 Seconds of arc | 0.000555555555556 deg |
| 3 Seconds of arc | 0.000833333333333 deg |
| 4 Seconds of arc | 0.00111111111111 deg |
| 5 Seconds of arc | 0.00138888888889 deg |
| 10 Seconds of arc | 0.00277777777778 deg |
| 20 Seconds of arc | 0.00555555555556 deg |
| 25 Seconds of arc | 0.00694444444444 deg |
| 50 Seconds of arc | 0.0138888888889 deg |
| 100 Seconds of arc | 0.0277777777778 deg |
| Reference | Seconds of arc (arcsec) | Degrees (deg) |
|---|---|---|
| A right angle | 324000 arcsec | 90 deg |
| A half turn | 648000 arcsec | 180 deg |
| A full turn | 1296000 arcsec | 360 deg |
| Earth's axial tilt | 84384 arcsec | 23.44 deg |
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.
The degree is a unit of plane angle equal to one three-hundred-and-sixtieth of a full turn. Its symbol is a small raised circle, and the abbreviation deg is used where that character is unavailable. It is not an SI unit but is accepted for use with the SI, and it remains the ordinary way of stating an angle outside pure mathematics.
The choice of 360 is Babylonian. Their sexagesimal arithmetic worked in sixties, and 360 is close to the number of days in a year, so the sun appears to advance roughly one degree along the ecliptic each day. The number is also unusually convenient: it divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120 and 180, so most common fractions of a circle land on whole degrees.
Subdivision follows the same base. A degree splits into 60 minutes of arc and each minute into 60 seconds of arc, which is why latitude and longitude are written in degrees, minutes and seconds. Decimal degrees have largely replaced that notation in software, since a single number is easier to compute with, but navigation charts and astronomical catalogues keep the older form.
Everything from surveying and construction to camera lenses, screw threads and compass bearings is specified in degrees. A right angle is 90, a straight line 180, a full rotation 360, and those three facts carry most everyday geometry without any conversion at all.
The metric system tried to replace it and failed. Revolutionary France introduced the gradian, one hundredth of a right angle, so that a quarter turn was 100 units and a full turn 400. It survives in a few surveying instruments in continental Europe and in the gradian key still found on pocket calculators, but nothing else adopted it. Modern practice has instead moved away from minutes and seconds while keeping the degree itself: satellite navigation, mapping software and geographic databases store latitude and longitude as decimal degrees, so 51 degrees 30 minutes becomes 51.5. The two notations describe the same angle, and confusing one for the other misplaces a position by tens of kilometres.
One degree equals about 0.0174533 radians, 60 minutes of arc, or 3600 seconds of arc.