Convert Radians to Arcseconds (rad to ″)
1 radian (rad) = 206264.8062 seconds of arc (″). 1 ″ = 0.000004848136811 rad. Example: 15 rad = 15 × 206264.8062 = 3093972.094 ″.
Also searched as radians to ″, radians in ″, radians into seconds of arc, rad to ″, rad in seconds of arc, rad into second of arc, radian to second of arc, rad to seconds of arc converter and how many seconds of arc in a radian.
1 rad = 206264.8062 ″
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk radian to second of arc converter to paste a column from Excel.
How to Convert Radian to Arcsecond
- 1 rad = 206264.8062 ″
- 1 ″ = 0.000004848136811 rad
- Example: convert 15 rad to ″: 15 rad = 15 × 206264.8062 ″ = 3093972.094 ″
Formula
″ = rad × 206264.8062471
Derivation from SI units:
- The SI unit of plane angle: the angle subtended at the centre of a circle by an arc equal in length to the radius (1 rad = 1 m/m).
- 1″ = (1/3600)° = π/648 000 rad.
Both units are defined exactly, so the factor is exact. Radian definition: radian; Arcsecond definition: second of arc.
Worked examples
- A reading of 2 rad converts to 412529.6125 ″.
2 rad × 206264.8062 = 412529.6125 ″ - A value of 4 rad is 825059.225 ″.
4 rad × 206264.8062 = 825059.225 ″
Radian to Arcsecond conversion table
| Radians (rad) | Arcseconds (″) |
|---|---|
| 0.5 rad | 103132.4031 ″ |
| 1 rad | 206264.8062 ″ |
| 1.5 rad | 309397.2094 ″ |
| 2 rad | 412529.6125 ″ |
| 3 rad | 618794.4187 ″ |
| 3.14159 rad | 647999.4527 ″ |
| 4 rad | 825059.225 ″ |
| 5 rad | 1031324.031 ″ |
| 6 rad | 1237588.837 ″ |
| 6.28318 rad | 1295998.905 ″ |
Where it's used
Radians are used for trigonometry and calculus (derivatives of sin and cos assume radians), while seconds of arc appear in astronomy (parallax, star positions). Both measure plane angle, so the conversion is a fixed factor.
Radian to other angle units
| Conversion | 1 rad equals |
|---|---|
| radian to second of arc | 206264.8062 ″ |
| radian to degree | 57.29577951 ° |
| radian to gradian | 63.66197724 gon |
| radian to revolution | 0.1591549431 rev |
| radian to minute of arc | 3437.746771 ′ |
Frequently asked questions
How many seconds of arc are in 1 radian?
1 rad = 206264.8062 ″.
How do I convert radians to seconds of arc?
Multiply the value in rad by 206264.8062. For example, 15 rad × 206264.8062 = 3093972.094 ″.
Is the rad to ″ conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 4 (radian) and Table 8 (non-SI units accepted for use with the SI).
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Convert Radians to Arcseconds (rad to ″). Retrieved October 25, 2026, from https://scientificconverters.com/angle/radians-to-arcseconds/
IEEE
Scientific Converters, "Convert Radians to Arcseconds (rad to ″)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/radians-to-arcseconds/