Quadrant to Degree Converter
Angle · unit-converter
Convert Quadrant to Degree 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 Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
How to convert quadrants to degrees
1 quadrant equals 90 degree in this tool (via radian):
1 quadrant = (1.5707963267948966 rad ÷ 0.017453292519943295 rad) deg = 90 deg
Each quadrant carries 1.5707963267948966 rad and each degree 0.017453292519943295 rad, so one quadrant equals 1.5707963267948966 ÷ 0.017453292519943295 deg.
Let θ(quadrant) be the angle in Quadrant (quadrant), and θ(deg) in Degree (deg). Then:
θ(deg) = θ(quadrant) × (1.5707963267948966 / 0.017453292519943295)
Equivalently, divide by how many quadrant fit into one deg (rad per deg divided by rad per quadrant):
θ(deg) = θ(quadrant) ÷ 0.011111111111111112
Examples
Example #1: Convert 1 quadrant to degree
1 quadrant = 1 quadrant × (1.5707963267948966/0.017453292519943295) deg = 90 deg
1 quadrant = 1 quadrant ÷ 0.011111111111111112 = 90 deg
1 quadrant × (1.5707963267948966/0.017453292519943295) = 90.000000 deg
Example #2: Convert 10 quadrant to degree
10 quadrant = 10 quadrant × (1.5707963267948966/0.017453292519943295) deg = 900 deg
10 quadrant = 10 quadrant ÷ 0.011111111111111112 = 900 deg
10 quadrant × (1.5707963267948966/0.017453292519943295) = 900.000000 deg
Summary
To convert Quadrant to Degree, multiply the value in quadrant by (1.5707963267948966 rad per quadrant) / (0.017453292519943295 rad per deg). Equivalently: value_deg = value_quadrant × (1.5707963267948966 / 0.017453292519943295). Numerically, 1 quadrant equals 90 deg.
Relationship context
Both Quadrant and Degree are converted by fixed multiples of the radian. Multiplying by (rad per quadrant) ÷ (rad per deg) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Quadrant (quadrant) | Degree (deg) |
|---|---|
| 0.1 | 9 |
| 1 | 90 |
| 2 | 180 |
| 3 | 270 |
| 4 | 360 |
| 5 | 450 |
| 6 | 540 |
| 7 | 630 |
| 8 | 720 |
| 9 | 810 |
| Quadrant (quadrant) | Degree (deg) |
|---|---|
| 10 | 900 |
| 20 | 1,800 |
| 30 | 2,700 |
| 40 | 3,600 |
| 50 | 4,500 |
| 60 | 5,400 |
| 70 | 6,300 |
| 80 | 7,200 |
| 90 | 8,100 |
| 100 | 9,000 |