One arcsecond is 1/3600 degree.
Arcseconds to Radians Converter — arcsec to rad
Convert Arcsecond (arcsec) to Radian (rad) using the exact conversion factor (1 arcsecond = 0.0000048481 radian). See the formula, worked examples, conversion table, history, and common uses.
Arcseconds to Radians converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
The radian is the SI angle unit.
Result = input x 4.84813681e-6 / 1.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Arcseconds to Radians
Arcsecond and Radian are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Specifically: One arcsecond is 1/3600 degree, and the radian is the SI angle unit.
Formula
radians = arcseconds × 0.0000048481368111
This factor comes from each unit's defined relationship to the category's base unit: 1 arcsecond equals 0.0000048481368111 base units, and 1 radian equals 1 base unit, so dividing one by the other gives the direct arcsecond-to-radian factor of 0.0000048481368111.
Simple example
1 arcsec × 0.000004848136811 = 0.0000048481 rad
1 arcsecond = 0.0000048481 radians.
Real-world example
90 arcsec × 0.000004848136811 = 0.0004363323 rad
90 arcseconds = 0.0004363323 radians.
Conversion table
| Arcsecond (arcsec) | Radian (rad) |
|---|---|
| 0 arcsec | 0 rad |
| 30 arcsec | 0.0001454441 rad |
| 45 arcsec | 0.0002181662 rad |
| 90 arcsec | 0.0004363323 rad |
| 180 arcsec | 0.0008726646 rad |
| 360 arcsec | 0.0017453293 rad |
Reverse conversion: Radian to Arcsecond
0.0000048481 rad × 206264.8062 = 0.9999924072 arcsec
0.0000048481 radians = 0.9999924072 arcseconds.
arcseconds = radians × 206264.806247
For a page dedicated to this direction, see Radian to Arcsecond.
Understanding the Arcsecond (arcsec)
One arcsecond is 1/3600 degree.
Understanding the Radian
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Where it's used: Standard angle unit in mathematics, physics, and engineering worldwide.
Uses of the Radian today
- Calculus and trigonometry (derivatives of trig functions are simplest in radians)
- Physics and engineering (angular velocity, rotational mechanics)
- Computer graphics and robotics
History of the Radian
The radian was developed in the 1870s, with the term itself coined by James Thomson (brother of Lord Kelvin) around 1873, formalizing a ratio-based angle measure that mathematicians had used implicitly for calculus since Newton and Leibniz.
It was adopted as the SI derived unit of angle because it makes many physics and calculus formulas simpler than using degrees.
Historical origin. Radian was not the invention of a single named person; it developed through the process described above.
Radian — sources
- BIPM SI Brochure — Coherent derived units — Defines the radian as the SI unit of plane angle.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many radians are in 1 arcsecond?
1 arcsecond equals 0.0000048481 radians, using the exact defined conversion factor rather than an estimate.
How do I convert arcsecond to radian?
Multiply the arcsecond value by 0.000004848136811. The converter above does this instantly to whatever precision you set.
How do I convert radian back to arcsecond?
Use the reverse factor: 1 radian equals 206,264.8062 arcseconds. You can also use the swap control in the converter above to flip the direction instantly.
What is a arcsecond?
Arcsecond (arcsec) is a unit of angle.
What is a radian?
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Is the arcsecond to radian conversion exact?
Yes. Both arcsecond and radian are defined by fixed standards rather than physical artifacts, so the factor of 0.000004848136811 used above is exact to as many digits as you choose to display.