Radians to Arcseconds
An instant radians-to-arcseconds converter, with the formula and a reference table below.
| Radians | Arcseconds |
|---|---|
| 1 rad | 206264.806247 ″ |
| 2 rad | 412529.612494 ″ |
| 3 rad | 618794.418741 ″ |
| 5 rad | 1031324.031235 ″ |
| 10 rad | 2062648.062471 ″ |
| 25 rad | 5156620.156177 ″ |
| 50 rad | 10313240.312355 ″ |
| 100 rad | 20626480.62471 ″ |
How to use
- Enter a value in the Radians field.
- The Arcseconds figure appears immediately — no button to press.
- Typing in the Arcseconds field converts back to Radians the same way.
- Use the reference table for the values that come up most often.
Radians to Arcseconds formula
To convert radians to arcseconds, multiply by 206264.806.
″ = rad × 206264.806
Why this factor: the radian and the arcsecond are both defined against the degree, so dividing one definition by the other gives 206264.806 directly. Both definitions are set out in full below.
To go the other way, divide by 206264.806 — or use the Arcseconds to Radians converter, which is the same calculation reversed.
Worked example
Take 45 rad and multiply by the factor 206264.806: the result is 9281916.281119 ″.
45 rad × 206264.806 = 9281916.281119 ″
The converter above does this for any value you type, in either direction.
What is a radian?
A radian is the angle that subtends an arc equal in length to the circle's radius — the natural unit of angle.
Definition: A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.
Where it is used: Calculus and trigonometry, physics, and every standard programming library's sin, cos and tan.
Worth knowing: Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
What is an arcsecond?
An arcsecond is one 3,600th of a degree — the precision unit of astronomy.
Definition: Exactly 1/3600 degree, or 1/60 arcminute. Symbol is the double prime (″).
Where it is used: Telescope resolution and seeing, stellar parallax (the basis of the parsec), and precision surveying.
Radians vs Arcseconds
The radian is an SI unit while the arcsecond is a specialized unit. That is why the factor between them is not a round number: the two systems were defined independently and only later tied together by exact agreement.
Frequently asked questions
How many arcseconds are in a radian?
One radian equals 206264.806 arcseconds.
What is the formula to convert radians to arcseconds?
Multiply the number of radians by 206264.806. To reverse it, divide by 206264.806 instead.
How do I convert arcseconds back to radians?
Divide by 206264.806, which is the same as multiplying by 4.84813681e-06.
How many arcseconds are in 10 radians?
10 rad works out to 2062648.062471 ″.
Is there anything to watch out for with radians?
Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
How is the radian defined?
A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.