# second

##### Non-SI unit accepted for use with SI
Name Symbol Quantity Value in SI units
second plane angle,
phase angle
π648 000 rad ### Definition

The arc second, symbol ″, is a non-SI unit of plane angle accepted for use with the SI.

One arc second is 11 296 000 of a turn, or π648 000 of a radian.

The arc second is a non-SI unit accepted for use with the SI.

The conversion between radians and arc seconds follows from the relations: 1 turn = 360°, 1° = 60′ and 1′ = 60″. $360^\circ = 2 \pi \mspace{6mu} \text{rad}\\ \\ \\ 1^\circ \mspace{17mu} = \dfrac{\pi}{180} \mspace{6mu} \text{rad}\\ \\ \\ 1^\prime \mspace{19mu} = \dfrac{\pi}{10 \ 800} \mspace{6mu} \text{rad}\\ \\ \\ 1^{\prime \prime} \mspace{15mu} = \dfrac{\pi}{648 \ 000} \mspace{6mu} \text{rad}$

For some applications such as in astronomy, small angles are measured in arcseconds (i.e. seconds of plane angle), denoted as ″, or milliarcseconds, microarcseconds and picoarcseconds, denoted mas, μas and pas, respectively, where arcsecond is an alternative name for second of plane angle.