Arc Second to Quadrant Converter
Angle · unit-converter
Convert Arc Second to Quadrant 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 Quadrant
A quadrant is one quarter-turn: 90° or π/2 radians. It is useful in geometric and directional notation.
How to convert arc seconds to quadrants
1 arc second equals 0.00000308641975308642 quadrant in this tool (via radian):
1 arcsec = (0.00000484813681109536 rad ÷ 1.5707963267948966 rad) quadrant = 0.00000308641975308642 quadrant
Each arc second carries 0.00000484813681109536 rad and each quadrant 1.5707963267948966 rad, so one arcsec equals 0.00000484813681109536 ÷ 1.5707963267948966 quadrant.
Let θ(arcsec) be the angle in Arc Second (arcsec), and θ(quadrant) in Quadrant (quadrant). Then:
θ(quadrant) = θ(arcsec) × (0.00000484813681109536 / 1.5707963267948966)
Equivalently, divide by how many arcsec fit into one quadrant (rad per quadrant divided by rad per arcsec):
θ(quadrant) = θ(arcsec) ÷ 324000
Examples
Example #1: Convert 1 arcsec to quadrant
1 arcsec = 1 arcsec × (0.00000484813681109536/1.5707963267948966) quadrant = 0.0000030864 quadrant
1 arcsec = 1 arcsec ÷ 324000 = 0.0000030864 quadrant
1 arcsec × (0.00000484813681109536/1.5707963267948966) = 0.000003 quadrant
Example #2: Convert 10 arcsec to quadrant
10 arcsec = 10 arcsec × (0.00000484813681109536/1.5707963267948966) quadrant = 0.0000308642 quadrant
10 arcsec = 10 arcsec ÷ 324000 = 0.0000308642 quadrant
10 arcsec × (0.00000484813681109536/1.5707963267948966) = 0.000031 quadrant
Summary
To convert Arc Second to Quadrant, multiply the value in arcsec by (0.00000484813681109536 rad per arcsec) / (1.5707963267948966 rad per quadrant). Equivalently: value_quadrant = value_arcsec × (0.00000484813681109536 / 1.5707963267948966). Numerically, 1 arcsec equals 0.00000308641975308642 quadrant.
Relationship context
Both Arc Second and Quadrant are converted by fixed multiples of the radian. Multiplying by (rad per arcsec) ÷ (rad per quadrant) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Second (arcsec) | Quadrant (quadrant) |
|---|---|
| 0.1 | 0.0000003086 |
| 1 | 0.0000030864 |
| 2 | 0.0000061728 |
| 3 | 0.0000092593 |
| 4 | 0.0000123457 |
| 5 | 0.0000154321 |
| 6 | 0.0000185185 |
| 7 | 0.0000216049 |
| 8 | 0.0000246914 |
| 9 | 0.0000277778 |
| Arc Second (arcsec) | Quadrant (quadrant) |
|---|---|
| 10 | 0.0000308642 |
| 20 | 0.0000617284 |
| 30 | 0.0000925926 |
| 40 | 0.0001234568 |
| 50 | 0.000154321 |
| 60 | 0.0001851852 |
| 70 | 0.0002160494 |
| 80 | 0.0002469136 |
| 90 | 0.0002777778 |
| 100 | 0.000308642 |