Arcseconds to Radians
Type a value in either box to convert between arcseconds and radians. The factor is 4.84814e-06.
| Arcseconds | Radians |
|---|---|
| 1 ″ | 4.84814e-06 rad |
| 2 ″ | 9.69627e-06 rad |
| 3 ″ | 1.45444e-05 rad |
| 5 ″ | 2.42407e-05 rad |
| 10 ″ | 4.84814e-05 rad |
| 25 ″ | 0.000121 rad |
| 50 ″ | 0.000242 rad |
| 100 ″ | 0.000485 rad |
How to use
- Enter a value in the Arcseconds field.
- The Radians figure appears immediately — no button to press.
- Typing in the Radians field converts back to Arcseconds the same way.
- Use the reference table for the values that come up most often.
Arcseconds to Radians formula
To convert arcseconds to radians, multiply by 4.84813681e-06.
rad = ″ × 4.84813681e-06
Why this factor: the arcsecond and the radian are both defined against the degree, so dividing one definition by the other gives 4.84813681e-06 directly. Both definitions are set out in full below.
To go the other way, divide by 4.84813681e-06 — or use the Radians to Arcseconds converter, which is the same calculation reversed.
Worked example
Take 45 ″ and multiply by the factor 4.84813681e-06: the result is 0.000218 rad.
45 ″ × 4.84813681e-06 = 0.000218 rad
The converter above does this for any value you type, in either direction.
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.
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.
Arcseconds vs Radians
The arcsecond is a specialized unit while the radian is an SI 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 radians are in an arcsecond?
One arcsecond equals 4.84813681e-06 radians.
What is the formula to convert arcseconds to radians?
Multiply the number of arcseconds by 4.84813681e-06. To reverse it, divide by 4.84813681e-06 instead.
How do I convert radians back to arcseconds?
Divide by 4.84813681e-06, which is the same as multiplying by 206264.806.
How many radians are in 10 arcseconds?
10 ″ works out to 4.84814e-05 rad.
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 arcsecond defined?
Exactly 1/3600 degree, or 1/60 arcminute. Symbol is the double prime (″).