Radians to Arcseconds Converter
Convert angle measurements from radians (rad) to arcseconds ("). One radian equals approximately 206,265 arcseconds.
radians (rad)
Result
0"
Common Radians to Arcseconds Conversions
| Radians (rad) | Arcseconds (") |
|---|---|
| 0.000001 rad | 0.206" |
| 0.00001 rad | 2.063" |
| 0.0001 rad | 20.63" |
| 0.001 rad | 206.3" |
| 0.01 rad | 2,063" |
| 0.1 rad | 20,626" |
| 1 rad | 206,265" |
| π/2 (1.5708) rad | 324,000" (90°) |
How to Convert Radians to Arcseconds
An arcsecond is 1/3600 of a degree or 1/60 of an arcminute. To convert radians to arcseconds, multiply by 648000/π.
The Conversion Formula
arcseconds = radians × (648000 / π)
This can also be written as: arcseconds = radians × 206264.806
Understanding the Conversion
The conversion factor comes from: 1 radian = 180/π degrees, 1 degree = 3600 arcseconds. Therefore: 1 radian = (180/π) × 3600 = 648000/π arcseconds ≈ 206,265 arcseconds.
Example: Converting 0.01 Radians to Arcseconds
arcseconds = 0.01 rad × (648000 / π) = 0.01 × 206264.806 = 2062.65"
The Importance of Arcseconds
Arcseconds are critical in fields requiring extreme precision:
- Astronomy: Stellar parallax measured in arcseconds determines star distances
- Astrometry: Precise star positions and proper motions
- Telescope Resolution: The Hubble Space Telescope has ~0.05" resolution
- Geodesy: GPS positioning requires arcsecond-level accuracy
Parsec Connection
The parsec (pc), a unit of astronomical distance, is defined as the distance at which 1 AU subtends an angle of 1 arcsecond. 1 parsec ≈ 3.26 light-years.