Convert Arcseconds to Radians
Convert Arcseconds to Radians instantly. 1 Arcsecond (″) equals 0.000004848 Radians (rad).
Arcseconds to Radians conversion table
| Arcseconds (″) | Radians (rad) |
|---|---|
| 1 ″ | 0.000004848 rad |
| 2 ″ | 0.000009696 rad |
| 3 ″ | 0.00001454 rad |
| 5 ″ | 0.00002424 rad |
| 10 ″ | 0.00004848 rad |
| 20 ″ | 0.00009696 rad |
| 50 ″ | 0.0002424 rad |
| 100 ″ | 0.0004848 rad |
| 500 ″ | 0.002424 rad |
| 1,000 ″ | 0.004848 rad |
1 Arcsecond = 0.000004848 Radians · multiply Arcseconds by 0.000004848
About converting Arcseconds to Radians
Arcseconds (″) and Radians (rad) are both units of angle, so converting between them is a single multiplication: multiply your Arcseconds figure by 0.000004848. Ten Arcseconds comes to 0.00004848 Radians, and a hundred works out at 0.0004848 Radians.
Rule of thumb: going from Arcseconds to Radians divides, so the figure always shrinks — it takes about 206,264.81 Arcseconds to make a single Radian. If your answer came out bigger, you have the conversion the wrong way round.
What is an Arcsecond?
The arcsecond is a sixtieth of an arcminute, and it is where angle measurement becomes astronomy. The apparent width of a planet, the separation of a double star and the resolving power of a telescope are all quoted in arcseconds, and Earth’s atmosphere smears ground-based images to roughly an arcsecond of "seeing" — which is precisely why observatories go up mountains and telescopes go into orbit. It is a startlingly small angle: about what a coin subtends from several kilometers away. Precision optics, satellite pointing and surveying instruments all work in arcseconds or finer.
What is a Radian?
The radian is the SI unit of angle and the natural one for mathematics, because it is defined by the circle itself rather than by decree: it is the angle you have swept when the arc travelled around the rim is exactly as long as the radius. A full circle is exactly 2π radians, with no arbitrary count involved. That matters well beyond neatness — the calculus of sine and cosine only comes out clean in radians, and introducing degrees scatters stray constants through every derivative. It is why every programming language’s math library expects radians, and why feeding degrees to sin() is a classic bug in graphics and physics code.
To put both in perspective: atmospheric blur limits most ground telescopes to about one arcsecond, while a full circle is 2π radians.
The converter above updates as you type, and the table lists common values for quick reference. Need the opposite direction? Use the Radians to Arcseconds converter, or browse all Angle converters.
Frequently asked questions
How many Radians are in one Arcsecond?
There are 0.000004848 Radians in one Arcsecond.
How do I convert Arcseconds to Radians?
Multiply the number of Arcseconds by 0.000004848. For example, 10 Arcseconds = 0.00004848 Radians.
What is 100 Arcseconds in Radians?
100 Arcseconds is equal to 0.0004848 Radians.
How do I convert Radians to Arcseconds?
Multiply the Radians value by 206,264.81 (or divide by 0.000004848).
Is this Arcseconds to Radians conversion exact?
The definition is exact — Arcseconds and Radians are both fixed against the same base by international agreement — but the decimal shown here is rounded for readability, because the true ratio does not terminate. For engineering or scientific work, carry more decimal places than this page displays.
What is an Arcsecond?
The arcsecond is a sixtieth of an arcminute, and it is where angle measurement becomes astronomy. The apparent width of a planet, the separation of a double star and the resolving power of a telescope are all quoted in arcseconds, and Earth’s atmosphere smears ground-based images to roughly an arcsecond of "seeing" — which is precisely why observatories go up mountains and telescopes go into orbit. It is a startlingly small angle: about what a coin subtends from several kilometers away. Precision optics, satellite pointing and surveying instruments all work in arcseconds or finer.
What is a Radian?
The radian is the SI unit of angle and the natural one for mathematics, because it is defined by the circle itself rather than by decree: it is the angle you have swept when the arc travelled around the rim is exactly as long as the radius. A full circle is exactly 2π radians, with no arbitrary count involved. That matters well beyond neatness — the calculus of sine and cosine only comes out clean in radians, and introducing degrees scatters stray constants through every derivative. It is why every programming language’s math library expects radians, and why feeding degrees to sin() is a classic bug in graphics and physics code.