# Radians to Seconds of Arc Converter

Enter the angle in radians below to get the value converted to seconds of arc. The calculator supports values containing decimals, fractions, and π: (π/2, 1/2π, etc)

**Results in Seconds of Arc:**

Do you want to convert seconds of arc to radians?

## How to Convert Radians to Seconds of Arc

To convert a measurement in radians to a measurement in seconds of arc, multiply the angle by the following conversion ratio: 206,264.806247 seconds of arc/radian.

Since one radian is equal to 206,264.806247 seconds of arc, you can use this simple formula to convert:

seconds of arc = radians × 206,264.806247

The angle in seconds of arc is equal to the angle in radians multiplied by 206,264.806247.

**For example,**here's how to convert 5 radians to seconds of arc using the formula above.

### How Many Seconds of Arc Are in a Radian?

There are **206,264.806247** seconds of arc in a radian, which is why we use this value in the formula above.

1 rad = 206,264.806247"

Radians and seconds of arc are both units used to measure angle. Keep reading to learn more about each unit of measure.

## What Is a Radian?

A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc.^{[1]} 1 radian is equal to 180/π degrees, or about 57.29578°. There are about 6.28318 radians in a circle.

The radian is the SI derived unit for angle in the metric system. Radians can be abbreviated as *rad*, and are also sometimes abbreviated as * ^{c}*,

*r*, or

*. For example, 1 radian can be written as 1 rad, 1*

^{R}^{c}, 1 r, or 1

^{R}.

Radians are often expressed using their definition.
The formula to find an angle in radians is θ = s/r, where the angle in radians *θ* is equal to the arc length *s* divided by the radius *r*.
Thus, radians may also be expressed as the formula of arc length over the radius.

Radians are also considered to be a "unitless" unit. That is, when multiplying or dividing by radians, the result does not include radians as part of the final units.

For example, when determining the length of an arc for a given angle, we use the formula above, rearranged to be s = θr. If θ is in radians and r is in meters, then the units of s will be meters, not radian-meters. If θ were in degrees, however, then s would have units of degree-meters.

Learn more about radians.

## What Is a Second of Arc?

The second of arc is a unit of angle equal to 1/60th of one minute of arc or 1/3,600 of one degree.

A second of arc is sometimes also referred to as an arc second or arcsecond. Seconds of arc can be abbreviated as *arcsec*, and are also sometimes abbreviated as *asec*. For example, 1 second of arc can be written as 1 arcsec or 1 asec.

The second of arc is most commonly expressed using a double prime (″), though a double quote is often used as well. For example, 1 second of arc is most often written as 1″.

Learn more about seconds of arc.

## Radian to Second of Arc Conversion Table

Radians | Seconds Of Arc |
---|---|

0.00001 rad | 2.0626" |

0.00002 rad | 4.1253" |

0.00003 rad | 6.1879" |

0.00004 rad | 8.2506" |

0.00005 rad | 10.31" |

0.00006 rad | 12.38" |

0.00007 rad | 14.44" |

0.00008 rad | 16.5" |

0.00009 rad | 18.56" |

0.000001 rad | 0.206265" |

0.00001 rad | 2.0626" |

0.0001 rad | 20.63" |

0.001 rad | 206.26" |

0.01 rad | 2,063" |

0.1 rad | 20,626" |

1 rad | 206,265" |

## References

- International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf

## More Radian & Second of Arc Conversions

- radians to milliradians
- radians to degrees
- radians to minutes of arc
- radians to gradians
- radians to revolutions
- radians to circles
- radians to mils
- milliradians to seconds of arc
- degrees to seconds of arc
- minutes of arc to seconds of arc
- gradians to seconds of arc
- revolutions to seconds of arc
- circles to seconds of arc
- mils to seconds of arc