Convert Radians to Arcseconds
Convert Radians to Arcseconds instantly. 1 Radian (rad) equals 206,264.81 Arcseconds (″).
Radians to Arcseconds conversion table
| Radians (rad) | Arcseconds (″) |
|---|---|
| 1 rad | 206,264.81 ″ |
| 2 rad | 412,529.61 ″ |
| 3 rad | 618,794.42 ″ |
| 5 rad | 1,031,324.03 ″ |
| 10 rad | 2,062,648.06 ″ |
| 20 rad | 4,125,296.12 ″ |
| 50 rad | 10,313,240.3 ″ |
| 100 rad | 20,626,480.61 ″ |
| 500 rad | 103,132,403.04 ″ |
| 1,000 rad | 206,264,806.08 ″ |
1 Radian = 206,264.81 Arcseconds · multiply Radians by 206,264.81
About converting Radians to Arcseconds
Radians (rad) and Arcseconds (″) are both units of angle, so converting between them is a single multiplication: multiply your Radians figure by 206,264.81. Ten Radians comes to 2,062,648.06 Arcseconds, and a hundred works out at 20,626,480.61 Arcseconds.
Rule of thumb: going from Radians to Arcseconds multiplies, so the figure always grows — one Radian is already 206,264.81 Arcseconds. If your answer came out smaller, you have the conversion the wrong way round.
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.
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.
To put both in perspective: a full circle is 2π radians, while atmospheric blur limits most ground telescopes to about one arcsecond.
The converter above updates as you type, and the table lists common values for quick reference. Need the opposite direction? Use the Arcseconds to Radians converter, or browse all Angle converters.
Frequently asked questions
How many Arcseconds are in one Radian?
There are 206,264.81 Arcseconds in one Radian.
How do I convert Radians to Arcseconds?
Multiply the number of Radians by 206,264.81. For example, 10 Radians = 2,062,648.06 Arcseconds.
What is 100 Radians in Arcseconds?
100 Radians is equal to 20,626,480.61 Arcseconds.
How do I convert Arcseconds to Radians?
Multiply the Arcseconds value by 0.000004848 (or divide by 206,264.81).
Is this Radians to Arcseconds conversion exact?
The definition is exact — Radians and Arcseconds 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 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.
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.