Radian to Arc Second Converter
Angle · unit-converter
Convert Radian to Arc Second 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 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.
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.
How to convert radians to arc seconds
1 radian equals 206264.80624709636 arc second in this tool (via radian):
1 rad = (1 rad ÷ 0.00000484813681109536 rad) arcsec = 206264.80624709636 arcsec
Each radian carries 1 rad and each arc second 0.00000484813681109536 rad, so one rad equals 1 ÷ 0.00000484813681109536 arcsec.
Let θ(rad) be the angle in Radian (rad), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(rad) × (1 / 0.00000484813681109536)
Equivalently, divide by how many rad fit into one arcsec (rad per arcsec divided by rad per rad):
θ(arcsec) = θ(rad) ÷ 0.00000484813681109536
Examples
Example #1: Convert 1 rad to arc second
1 rad = 1 rad × (1/0.00000484813681109536) arcsec = 206264.806247 arcsec
1 rad = 1 rad ÷ 0.00000484813681109536 = 206264.806247 arcsec
1 rad × (1/0.00000484813681109536) = 206,264.806247 arcsec
Example #2: Convert 10 rad to arc second
10 rad = 10 rad × (1/0.00000484813681109536) arcsec = 2062648.06247 arcsec
10 rad = 10 rad ÷ 0.00000484813681109536 = 2062648.06247 arcsec
10 rad × (1/0.00000484813681109536) = 2,062,648.062471 arcsec
Summary
To convert Radian to Arc Second, multiply the value in rad by (1 rad per rad) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_rad × (1 / 0.00000484813681109536). Numerically, 1 rad equals 206264.80624709636 arcsec.
Relationship context
Both Radian and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per rad) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Radian (rad) | Arc Second (arcsec) |
|---|---|
| 0.1 | 20,626.4806247 |
| 1 | 206,264.806247 |
| 2 | 412,529.612494 |
| 3 | 618,794.418741 |
| 4 | 825,059.224988 |
| 5 | 1,031,324.03124 |
| 6 | 1,237,588.83748 |
| 7 | 1,443,853.6437299999 |
| 8 | 1,650,118.44998 |
| 9 | 1,856,383.2562200001 |
| Radian (rad) | Arc Second (arcsec) |
|---|---|
| 10 | 2,062,648.06247 |
| 20 | 4,125,296.12494 |
| 30 | 6,187,944.1874099998 |
| 40 | 8,250,592.24988 |
| 50 | 10,313,240.3124000002 |
| 60 | 12,375,888.3748000003 |
| 70 | 14,438,536.4373000003 |
| 80 | 16,501,184.4998000003 |
| 90 | 18,563,832.5621999986 |
| 100 | 20,626,480.6246999986 |