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Angle
Arcseconds to Radians
Convert arcseconds (arcsec) to radians (rad). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 arcsec = 4.8481e-6 rad
Arcseconds to Radians Conversion Table
Common values, ready to copy:
| arcseconds | radians |
|---|---|
| 1 arcsec | 4.8481e-6 rad |
| 2 arcsec | 9.6963e-6 rad |
| 5 arcsec | 2.4241e-5 rad |
| 10 arcsec | 4.8481e-5 rad |
| 25 arcsec | 0.000121 rad |
| 50 arcsec | 0.000242 rad |
| 100 arcsec | 0.000485 rad |
| 1,000 arcsec | 0.004848 rad |
Formula
radians = arcseconds × 4.84813681e-6
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
About Arcseconds and Radians
Arcseconds (arcsec): 1/60 of an arcminute, or 1/3600 of a degree; the unit for very small angles in astronomy. Common uses: Astronomical resolution (a telescope's resolving power in arcseconds), positional precision of stars, and very fine engineering angle specifications.
Radians (rad): The natural SI unit for angle; one radian is the angle subtended by an arc equal in length to the radius (so a full circle is 2π radians ≈ 6.283). Common uses: Mathematics (calculus, trigonometry derivatives), physics, computer graphics, and any context where the formula simplifies in radians.
How the conversion works
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
The exact relationship is radians = arcseconds × 4.84813681e-6, which the calculator at the top of this page applies in both directions. Type into either field and the other updates immediately.
When this conversion matters
Converting between arcseconds and radians comes up wherever angle measurements move between systems — from one country's conventions to another's, from a scientific reference to a practical specification, or from one industry's working unit to another's. The calculator and reference table above cover the everyday range; for unusual values you can type any number into either field.