Degree to Quadrant Converter
Angle · unit-converter
Convert Degree 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 Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
About Quadrant
A quadrant is one quarter-turn: 90° or π/2 radians. It is useful in geometric and directional notation.
How to convert degrees to quadrants
1 degree equals 0.011111111111111112 quadrant in this tool (via radian):
1 deg = (0.017453292519943295 rad ÷ 1.5707963267948966 rad) quadrant = 0.011111111111111112 quadrant
Each degree carries 0.017453292519943295 rad and each quadrant 1.5707963267948966 rad, so one deg equals 0.017453292519943295 ÷ 1.5707963267948966 quadrant.
Let θ(deg) be the angle in Degree (deg), and θ(quadrant) in Quadrant (quadrant). Then:
θ(quadrant) = θ(deg) × (0.017453292519943295 / 1.5707963267948966)
Equivalently, divide by how many deg fit into one quadrant (rad per quadrant divided by rad per deg):
θ(quadrant) = θ(deg) ÷ 90
Examples
Example #1: Convert 1 deg to quadrant
1 deg = 1 deg × (0.017453292519943295/1.5707963267948966) quadrant = 0.0111111111 quadrant
1 deg = 1 deg ÷ 90 = 0.0111111111 quadrant
1 deg × (0.017453292519943295/1.5707963267948966) = 0.011111 quadrant
Example #2: Convert 10 deg to quadrant
10 deg = 10 deg × (0.017453292519943295/1.5707963267948966) quadrant = 0.1111111111 quadrant
10 deg = 10 deg ÷ 90 = 0.1111111111 quadrant
10 deg × (0.017453292519943295/1.5707963267948966) = 0.111111 quadrant
Summary
To convert Degree to Quadrant, multiply the value in deg by (0.017453292519943295 rad per deg) / (1.5707963267948966 rad per quadrant). Equivalently: value_quadrant = value_deg × (0.017453292519943295 / 1.5707963267948966). Numerically, 1 deg equals 0.011111111111111112 quadrant.
Relationship context
Both Degree and Quadrant are converted by fixed multiples of the radian. Multiplying by (rad per deg) ÷ (rad per quadrant) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Degree (deg) | Quadrant (quadrant) |
|---|---|
| 0.1 | 0.0011111111 |
| 1 | 0.0111111111 |
| 2 | 0.0222222222 |
| 3 | 0.0333333333 |
| 4 | 0.0444444444 |
| 5 | 0.0555555556 |
| 6 | 0.0666666667 |
| 7 | 0.0777777778 |
| 8 | 0.0888888889 |
| 9 | 0.1 |
| Degree (deg) | Quadrant (quadrant) |
|---|---|
| 10 | 0.1111111111 |
| 20 | 0.2222222222 |
| 30 | 0.3333333333 |
| 40 | 0.4444444444 |
| 50 | 0.5555555556 |
| 60 | 0.6666666667 |
| 70 | 0.7777777778 |
| 80 | 0.8888888889 |
| 90 | 1 |
| 100 | 1.1111111111 |