Arcseconds (″) to Radians (rad) Conversion
Arcseconds
The arcsecond (″, Unicode U+2033) is a unit of angle equal to exactly 1/3,600 of a degree, or 1/60 of an arcminute (approximately 4.848 × 10⁻⁶ radians). It is the standard unit of angular resolution in astronomy: the Hubble Space Telescope achieves a resolution of approximately 0.05 arcseconds; the nearest star, Proxima Centauri, has a parallax of 0.769 arcseconds — the basis for measuring its distance. In geodesy, GPS coordinates are routinely recorded to sub-arcsecond precision, corresponding to positional accuracy of approximately 30 metres on Earth's surface.
Radians
The radian (rad) is the SI derived unit of plane angle, defined as the angle subtended at the centre of a circle by an arc whose length equals the radius. One full rotation equals exactly 2π radians (≈ 6.2832 rad), and one radian equals approximately 57.2958°. The radian is preferred in mathematics and physics because it makes the derivatives of trigonometric functions algebraically clean — d/dx(sin x) = cos x only when x is in radians. Rotational speed (rad/s) and angular frequency in oscillatory systems are always expressed in radians.
| Arcseconds (″) | Radians (rad) |
|---|---|
| 0.1 ″ | 0.000000485 rad |
| 1 ″ | 0.00000485 rad |
| 2 ″ | 0.0000097 rad |
| 3 ″ | 0.0000145 rad |
| 5 ″ | 0.0000242 rad |
| 10 ″ | 0.0000485 rad |
| 20 ″ | 0.000097 rad |
| 30 ″ | 0.000145 rad |
| 50 ″ | 0.000242 rad |
| 100 ″ | 0.000485 rad |
| 1000 ″ | 0.00485 rad |
Frequently Asked Questions (FAQ)
How many radians are in 1 arcseconds?
1 arcseconds (″) is exactly 0.00000485 radians (rad).
How do I convert arcseconds to radians?
Multiply the value in arcseconds by 0.00000485 to get the result in radians. Or use the converter above — type any number and see the result instantly.