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Angle
Radians to Arcseconds
Convert radians (rad) to arcseconds (arcsec). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 rad = 206264.81 arcsec
Radians to Arcseconds Conversion Table
Common values, ready to copy:
| radians | arcseconds |
|---|---|
| 1 rad | 206264.81 arcsec |
| 2 rad | 412529.61 arcsec |
| 5 rad | 1.0313e+6 arcsec |
| 10 rad | 2.0626e+6 arcsec |
| 25 rad | 5.1566e+6 arcsec |
| 50 rad | 1.0313e+7 arcsec |
| 100 rad | 2.0626e+7 arcsec |
| 1,000 rad | 2.0626e+8 arcsec |
Formula
arcseconds = radians × 2.06264806e+5
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 Radians and Arcseconds
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.
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.
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 arcseconds = radians × 2.06264806e+5, 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 radians and arcseconds 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.