Convert Arcseconds to Radians (″ to rad)
1 second of arc (″) = 0.000004848136811 radians (rad). 1 rad = 206264.8062 ″. Example: 15 ″ = 15 × 0.000004848136811 = 0.00007272205217 rad.
Also searched as seconds of arc to rad, seconds of arc in rad, seconds of arc into radians, ″ to rad, ″ in radians, ″ into radian, second of arc to radian, ″ to radians converter and how many radians in a second of arc.
1 ″ = 0.000004848136811 rad
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk second of arc to radian converter to paste a column from Excel.
How to Convert Arcsecond to Radian
- 1 ″ = 0.000004848136811 rad
- 1 rad = 206264.8062 ″
- Example: convert 15 ″ to rad: 15 ″ = 15 × 0.000004848136811 rad = 0.00007272205217 rad
Formula
rad = ″ × 0.000004848136811095
or rad = ″ ÷ 206264.8062471
Derivation from SI units:
- 1″ = (1/3600)° = π/648 000 rad.
- 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).
Both units are defined exactly, so the factor is exact. Arcsecond definition: second of arc; Radian definition: radian.
Worked examples
- A reading of 15 ″ converts to 0.00007272205217 rad.
15 ″ × 0.000004848136811 = 0.00007272205217 rad - A value of 60 ″ is 0.0002908882087 rad.
60 ″ × 0.000004848136811 = 0.0002908882087 rad
Arcsecond to Radian conversion table
| Arcseconds (″) | Radians (rad) |
|---|---|
| 1 ″ | 0.000004848136811 rad |
| 5 ″ | 0.00002424068406 rad |
| 10 ″ | 0.00004848136811 rad |
| 15 ″ | 0.00007272205217 rad |
| 30 ″ | 0.0001454441043 rad |
| 36 ″ | 0.0001745329252 rad |
| 60 ″ | 0.0002908882087 rad |
| 100 ″ | 0.0004848136811 rad |
| 1000 ″ | 0.004848136811 rad |
| 3600 ″ | 0.01745329252 rad |
Where it's used
Arcseconds are used for astronomy (parallax, star positions), while radians appear in trigonometry and calculus (derivatives of sin and cos assume radians). Both measure plane angle, so the conversion is a fixed factor.
Arcsecond to other angle units
| Conversion | 1 ″ equals |
|---|---|
| second of arc to radian | 0.000004848136811 rad |
| second of arc to degree | 0.0002777777778 ° |
| second of arc to gradian | 0.0003086419753 gon |
| second of arc to revolution | 7.716049383 × 10⁻⁷ rev |
| second of arc to minute of arc | 0.01666666667 ′ |
Frequently asked questions
How many radians are in 1 second of arc?
1 ″ = 0.000004848136811 rad.
How do I convert seconds of arc to radians?
Multiply the value in ″ by 0.000004848136811, or divide it by 206264.8062. For example, 15 ″ × 0.000004848136811 = 0.00007272205217 rad.
Is the ″ to rad 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 Arcseconds to Radians (″ to rad). Retrieved October 25, 2026, from https://scientificconverters.com/angle/arcseconds-to-radians/
IEEE
Scientific Converters, "Convert Arcseconds to Radians (″ to rad)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/arcseconds-to-radians/