Degrees to Arcseconds (° to ″)

1 degree equals 3,600 arcseconds exactly.

How to convert degrees to arcseconds

To convert degrees to arcseconds, multiply the number of degrees by 3,600. This factor is exact. To go the other way, multiply arcseconds by 0.0002777777778 (rounded).

arcseconds = degrees × 3,600

Example: 10 degrees = 36,000 arcseconds.

About these units

Degree (°)

General & non-SICurrent unit

One 360th of a full turn. The everyday unit of angle, inherited from the ancient Babylonians' base-60 counting.

Dividing the circle into 360 parts traces back to the astronomers of ancient Babylon, who counted in base 60. Why 360 in particular is still debated. One explanation points to Persian and Babylonian calendars, which used a year of about 360 days, so the Sun seemed to advance roughly one degree each day. Another says the Babylonians started from the angle of an equilateral triangle and split it into 60 pieces, and a third credits early chord-based trigonometry, where a chord equal to the radius made a natural base. Greek astronomers such as Aristarchus and Hipparchus were among the first to use Babylonian astronomical knowledge systematically.

The number also divides well. 360 has 24 divisors and splits evenly by every whole number from 1 to 10 except 7, which suits a world cut into 24 time zones of 15 degrees of longitude each. Each degree breaks into 60 arcminutes, and each of those into 60 arcseconds. The SI Brochure lists the degree among the widely used non-SI units, equal to π/180 radian, about 0.01745. For scale, the Moon and the Sun each look about half a degree wide, and a little finger held at arm's length covers roughly one degree of sky.

1 degree = 0.002777777778 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Degree (angle); Wikipedia: Angular diameter

Arcsecond (″)

General & non-SICurrent unit

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

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-.

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

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

Related conversions

See all angle units.