Arc Second to Radian Converter
Angle · unit-converter
Convert Arc Second to Radian with a fixed input and output unit, step-by-step formula line, and reference tables. All calculations bridge through radians with fixed definitions (360° per turn, 400 grad per turn, 60′ per degree, 60″ per minute, plus practical units like MOA, urad, and NATO 6400 mils per turn).
About Arc Second
An arc second is 1/60 of an arc minute or 1/3600 of a degree. Common in astronomy and very fine angular resolution.
About Radian
The radian is the SI unit of plane angle. One radian is the angle subtended by an arc equal to the radius; 2π rad = one full circle.
How to convert arc seconds to radians
1 arc second equals 0.00000484813681109536 radian in this tool (via radian):
1 arcsec = (0.00000484813681109536 rad ÷ 1 rad) rad = 0.00000484813681109536 rad
Each arc second carries 0.00000484813681109536 rad and each radian 1 rad, so one arcsec equals 0.00000484813681109536 ÷ 1 rad.
Let θ(arcsec) be the angle in Arc Second (arcsec), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(arcsec) × (0.00000484813681109536 / 1)
Equivalently, divide by how many arcsec fit into one rad (rad per rad divided by rad per arcsec):
θ(rad) = θ(arcsec) ÷ 206264.80624709636
Examples
Example #1: Convert 1 arcsec to radian
1 arcsec = 1 arcsec × (0.00000484813681109536/1) rad = 0.0000048481 rad
1 arcsec = 1 arcsec ÷ 206264.80624709636 = 0.0000048481 rad
1 arcsec × (0.00000484813681109536/1) = 0.000005 rad
Example #2: Convert 10 arcsec to radian
10 arcsec = 10 arcsec × (0.00000484813681109536/1) rad = 0.0000484814 rad
10 arcsec = 10 arcsec ÷ 206264.80624709636 = 0.0000484814 rad
10 arcsec × (0.00000484813681109536/1) = 0.000048 rad
Summary
To convert Arc Second to Radian, multiply the value in arcsec by (0.00000484813681109536 rad per arcsec) / (1 rad per rad). Equivalently: value_rad = value_arcsec × (0.00000484813681109536 / 1). Numerically, 1 arcsec equals 0.00000484813681109536 rad.
Relationship context
Both Arc Second and Radian are converted by fixed multiples of the radian. Multiplying by (rad per arcsec) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Second (arcsec) | Radian (rad) |
|---|---|
| 0.1 | 0.0000004848 |
| 1 | 0.0000048481 |
| 2 | 0.0000096963 |
| 3 | 0.0000145444 |
| 4 | 0.0000193925 |
| 5 | 0.0000242407 |
| 6 | 0.0000290888 |
| 7 | 0.000033937 |
| 8 | 0.0000387851 |
| 9 | 0.0000436332 |
| Arc Second (arcsec) | Radian (rad) |
|---|---|
| 10 | 0.0000484814 |
| 20 | 0.0000969627 |
| 30 | 0.0001454441 |
| 40 | 0.0001939255 |
| 50 | 0.0002424068 |
| 60 | 0.0002908882 |
| 70 | 0.0003393696 |
| 80 | 0.0003878509 |
| 90 | 0.0004363323 |
| 100 | 0.0004848137 |