second

Non-SI unit accepted for use with SI

Name

Symbol

Quantity

Value in SI units

second

″

plane angle,
phase angle

^π⁄_648 000 rad

Definition

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

One arc second is ¹⁄_{1 296 000} of a turn, or ^π⁄_648 000 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.