How to convert radians to arcseconds
″ = rad × 206,264.8062Multiply the value in radians by 206,264.8062. To go the other way, multiply by 0.000004848136811 (or divide by 206,264.8062).
A radian is larger than an arcsecond: one radian contains 206,264.8062 arcseconds.
Worked examples
- 1 radian1 rad × 206,264.8062 = 206,264.8062 ″
- 5 radians5 rad × 206,264.8062 = 1,031,324.031 ″
- 10 radians10 rad × 206,264.8062 = 2,062,648.062 ″
- 20 radians20 rad × 206,264.8062 = 4,125,296.125 ″
- 100 radians100 rad × 206,264.8062 = 20,626,480.62 ″
Radians to arcseconds conversion table
Values are calculated by the conversion engine and rounded to 8 significant figures.
| Radians (rad) | Arcseconds (″) |
|---|---|
| 0.1 rad | 20,626.481 ″ |
| 0.25 rad | 51,566.202 ″ |
| 0.5 rad | 103,132.4 ″ |
| 1 rad | 206,264.81 ″ |
| 2 rad | 412,529.61 ″ |
| 3 rad | 618,794.42 ″ |
| 4 rad | 825,059.22 ″ |
| 5 rad | 1,031,324 ″ |
| 6 rad | 1,237,588.8 ″ |
| 7 rad | 1,443,853.6 ″ |
| 8 rad | 1,650,118.4 ″ |
| 9 rad | 1,856,383.3 ″ |
| 10 rad | 2,062,648.1 ″ |
| Radians (rad) | Arcseconds (″) |
|---|---|
| 12 rad | 2,475,177.7 ″ |
| 15 rad | 3,093,972.1 ″ |
| 20 rad | 4,125,296.1 ″ |
| 25 rad | 5,156,620.2 ″ |
| 30 rad | 6,187,944.2 ″ |
| 40 rad | 8,250,592.2 ″ |
| 50 rad | 10,313,240 ″ |
| 75 rad | 15,469,860 ″ |
| 100 rad | 20,626,481 ″ |
| 250 rad | 51,566,202 ″ |
| 500 rad | 103,132,400 ″ |
| 1,000 rad | 206,264,810 ″ |
About the units
Radian (rad)
The angle subtended by an arc equal in length to the radius; 2π rad make a full turn, so 1 rad ≈ 57.2958°.
Arcsecond (″)
The arcsecond (″) is a unit of angle. One arcsecond equals 0.000004848136811 radians (rad).
Frequently asked questions
How many arcseconds are in one radian?
There are 206,264.8062 arcseconds in one radian, and this value is exact by definition.
How do I convert radians to arcseconds?
Multiply the number of radians by 206,264.8062. For example, 10 rad × 206,264.8062 = 2,062,648.062 ″.
How many radians are in one arcsecond?
One arcsecond equals 0.000004848136811 radians. That is the reverse factor, 1 ÷ 206,264.8062.
What is 10 radians in arcseconds?
10 rad = 2,062,648.062 ″.
Is this rad to ″ converter accurate?
Yes. Both units are defined exactly in terms of SI units, so the conversion factor is exact; results are shown to 12 significant figures by default and you can change precision in the converter. Calculations run in your browser using the same tested engine that generated this page.