Arcseconds to Radians (″ to rad)

1 arcsecond equals 0.000004848136811 radians (rounded).

How to convert arcseconds to radians

To convert arcseconds to radians, multiply the number of arcseconds by 0.000004848136811. The factor is rounded to 10 significant digits. To go the other way, multiply radians by 206,264.8062 (rounded).

radians = arcseconds × 0.000004848136811

Example: 10 arcseconds = 0.00004848136811 radians.

About these units

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)

Radian (rad)

Metric (SI)Current unit

The SI unit of angle: the angle at the center of a circle subtended by an arc equal in length to the radius. A full turn is 2π radians (about 6.2832).

The radian builds its unit out of the circle itself. Lay a length of string equal to the radius along the circumference, and the angle that arc makes at the center is one radian. The SI Brochure calls it the coherent unit of plane angle, and it also serves as the coherent unit of phase angle, which grows by 2π radians over one period of a repeating wave. The same document notes that you could write rad as m/m, but warns that this is not intrinsic and can mislead, since angle is not the same kind of quantity as an ordinary ratio of lengths. It also records an alternative definition: a right angle equals π/2 radian.

A circle's circumference is 2π times its radius, so a full turn is 2π radians, about 6.2832, which makes one radian roughly 57.3 degrees, or about 0.159 of a turn. The SI Brochure's table of derived units expresses angular velocity in radians per second.

1 radian = 0.1591549431 turns (approximately).

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

Related conversions

See all angle units.