Arcsecond (″)

One sixtieth of an arcminute (1/3,600 degree). Used for tiny angles in astronomy.

1 arcsecond = 7.716049383×10⁻⁷ turns (approximately).

About the arcsecond

An arcsecond is 1/3,600 of a degree, or 1/1,296,000 of a turn. In radians it is π/648,000, about 4.85 millionths, so it covers roughly 4.8 millimeters at a distance of 1 kilometer. The SI Brochure treats it as an alternative name for the second of plane angle, with the symbol as or ″, and counts it among the widely used non-SI units.

Astronomy is where it matters most. The parsec is the distance at which a star shows a parallax of one arcsecond, about 3.26 light-years, so a star's distance in parsecs is the reciprocal of its parallax in arcseconds. The unit also appears in planetary angular diameters, binary star separations, and star motions. For comparison, the Sun's disk is roughly 1,900 arcseconds across. Smaller angles use the prefixes milli- and micro-.

Sources: BIPM SI Brochure, 9th edition (2019); ESA Gaia: Cosmic distances; NIST Guide to the SI, Appendix B.8 (angle conversion factors)

Arcsecond conversion chart

1 arcsecond expressed in every other angle unit:

Unit	1 arcsecond
Degrees	0.0002777777778
Radians	0.000004848136811
Gradians	0.0003086419753
Turns	7.716049383×10⁻⁷
Arcminutes	0.01666666667
Milliarcseconds	1,000
Milliradians	0.004848136811
Right Angles	0.000003086419753
Octants	0.000006172839506
Sextants	0.00000462962963
Hour Angles	0.00001851851852
Mils (NATO)	0.004938271605
Zodiac Signs	0.000009259259259
Compass Points	0.00002469135802
Mils (Soviet)	0.00462962963
Streck	0.004861111111
Binary Degrees	0.0001975308642

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