Quadrant to Arc Minute Converter
Angle · unit-converter
Convert Quadrant to Arc Minute 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 Minute
An arc minute is 1/60 of a degree (π/10,800 rad). Used in astronomy, navigation, and precision optics (MOA).
How to convert quadrants to arc minutes
1 quadrant equals 5400 arc minute in this tool (via radian):
1 quadrant = (1.5707963267948966 rad ÷ 0.0002908882086657216 rad) arcmin = 5400 arcmin
Each quadrant carries 1.5707963267948966 rad and each arc minute 0.0002908882086657216 rad, so one quadrant equals 1.5707963267948966 ÷ 0.0002908882086657216 arcmin.
Let θ(quadrant) be the angle in Quadrant (quadrant), and θ(arcmin) in Arc Minute (arcmin). Then:
θ(arcmin) = θ(quadrant) × (1.5707963267948966 / 0.0002908882086657216)
Equivalently, divide by how many quadrant fit into one arcmin (rad per arcmin divided by rad per quadrant):
θ(arcmin) = θ(quadrant) ÷ 0.00018518518518518518
Examples
Example #1: Convert 1 quadrant to arc minute
1 quadrant = 1 quadrant × (1.5707963267948966/0.0002908882086657216) arcmin = 5400 arcmin
1 quadrant = 1 quadrant ÷ 0.00018518518518518518 = 5400 arcmin
1 quadrant × (1.5707963267948966/0.0002908882086657216) = 5,400.000000 arcmin
Example #2: Convert 10 quadrant to arc minute
10 quadrant = 10 quadrant × (1.5707963267948966/0.0002908882086657216) arcmin = 54000 arcmin
10 quadrant = 10 quadrant ÷ 0.00018518518518518518 = 54000 arcmin
10 quadrant × (1.5707963267948966/0.0002908882086657216) = 54,000.000000 arcmin
Summary
To convert Quadrant to Arc Minute, multiply the value in quadrant by (1.5707963267948966 rad per quadrant) / (0.0002908882086657216 rad per arcmin). Equivalently: value_arcmin = value_quadrant × (1.5707963267948966 / 0.0002908882086657216). Numerically, 1 quadrant equals 5400 arcmin.
Relationship context
Both Quadrant and Arc Minute are converted by fixed multiples of the radian. Multiplying by (rad per quadrant) ÷ (rad per arcmin) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Quadrant (quadrant) | Arc Minute (arcmin) |
|---|---|
| 0.1 | 540 |
| 1 | 5,400 |
| 2 | 10,800 |
| 3 | 16,200 |
| 4 | 21,600 |
| 5 | 27,000 |
| 6 | 32,400 |
| 7 | 37,800 |
| 8 | 43,200 |
| 9 | 48,600 |
| Quadrant (quadrant) | Arc Minute (arcmin) |
|---|---|
| 10 | 54,000 |
| 20 | 108,000 |
| 30 | 162,000 |
| 40 | 216,000 |
| 50 | 270,000 |
| 60 | 324,000 |
| 70 | 378,000 |
| 80 | 432,000 |
| 90 | 486,000 |
| 100 | 540,000 |