Quadrant to Arc Second Converter
Angle · unit-converter
Convert Quadrant 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 Quadrant
A quadrant is one quarter-turn: 90° or π/2 radians. It is useful in geometric and directional notation.
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 quadrants to arc seconds
1 quadrant equals 324000 arc second in this tool (via radian):
1 quadrant = (1.5707963267948966 rad ÷ 0.00000484813681109536 rad) arcsec = 324000 arcsec
Each quadrant carries 1.5707963267948966 rad and each arc second 0.00000484813681109536 rad, so one quadrant equals 1.5707963267948966 ÷ 0.00000484813681109536 arcsec.
Let θ(quadrant) be the angle in Quadrant (quadrant), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(quadrant) × (1.5707963267948966 / 0.00000484813681109536)
Equivalently, divide by how many quadrant fit into one arcsec (rad per arcsec divided by rad per quadrant):
θ(arcsec) = θ(quadrant) ÷ 0.00000308641975308642
Examples
Example #1: Convert 1 quadrant to arc second
1 quadrant = 1 quadrant × (1.5707963267948966/0.00000484813681109536) arcsec = 324000 arcsec
1 quadrant = 1 quadrant ÷ 0.00000308641975308642 = 324000 arcsec
1 quadrant × (1.5707963267948966/0.00000484813681109536) = 324,000.000000 arcsec
Example #2: Convert 10 quadrant to arc second
10 quadrant = 10 quadrant × (1.5707963267948966/0.00000484813681109536) arcsec = 3240000 arcsec
10 quadrant = 10 quadrant ÷ 0.00000308641975308642 = 3240000 arcsec
10 quadrant × (1.5707963267948966/0.00000484813681109536) = 3,240,000.000000 arcsec
Summary
To convert Quadrant to Arc Second, multiply the value in quadrant by (1.5707963267948966 rad per quadrant) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_quadrant × (1.5707963267948966 / 0.00000484813681109536). Numerically, 1 quadrant equals 324000 arcsec.
Relationship context
Both Quadrant and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per quadrant) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Quadrant (quadrant) | Arc Second (arcsec) |
|---|---|
| 0.1 | 32,400 |
| 1 | 324,000 |
| 2 | 648,000 |
| 3 | 972,000 |
| 4 | 1,296,000 |
| 5 | 1,620,000 |
| 6 | 1,944,000 |
| 7 | 2,268,000 |
| 8 | 2,592,000 |
| 9 | 2,916,000 |
| Quadrant (quadrant) | Arc Second (arcsec) |
|---|---|
| 10 | 3,240,000 |
| 20 | 6,480,000 |
| 30 | 9,720,000 |
| 40 | 12,960,000 |
| 50 | 16,200,000 |
| 60 | 19,440,000 |
| 70 | 22,680,000 |
| 80 | 25,920,000 |
| 90 | 29,160,000 |
| 100 | 32,400,000 |