Radian to Quadrant Converter
Angle · unit-converter
Convert Radian 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 Radian
The radian is the SI unit of plane angle. One radian is the angle subtended by an arc equal to the radius; 2π rad = one full circle.
About Quadrant
A quadrant is one quarter-turn: 90° or π/2 radians. It is useful in geometric and directional notation.
How to convert radians to quadrants
1 radian equals 0.6366197723675814 quadrant in this tool (via radian):
1 rad = (1 rad ÷ 1.5707963267948966 rad) quadrant = 0.6366197723675814 quadrant
Each radian carries 1 rad and each quadrant 1.5707963267948966 rad, so one rad equals 1 ÷ 1.5707963267948966 quadrant.
Let θ(rad) be the angle in Radian (rad), and θ(quadrant) in Quadrant (quadrant). Then:
θ(quadrant) = θ(rad) × (1 / 1.5707963267948966)
Equivalently, divide by how many rad fit into one quadrant (rad per quadrant divided by rad per rad):
θ(quadrant) = θ(rad) ÷ 1.5707963267948966
Examples
Example #1: Convert 1 rad to quadrant
1 rad = 1 rad × (1/1.5707963267948966) quadrant = 0.6366197724 quadrant
1 rad = 1 rad ÷ 1.5707963267948966 = 0.6366197724 quadrant
1 rad × (1/1.5707963267948966) = 0.636620 quadrant
Example #2: Convert 10 rad to quadrant
10 rad = 10 rad × (1/1.5707963267948966) quadrant = 6.3661977237 quadrant
10 rad = 10 rad ÷ 1.5707963267948966 = 6.3661977237 quadrant
10 rad × (1/1.5707963267948966) = 6.366198 quadrant
Summary
To convert Radian to Quadrant, multiply the value in rad by (1 rad per rad) / (1.5707963267948966 rad per quadrant). Equivalently: value_quadrant = value_rad × (1 / 1.5707963267948966). Numerically, 1 rad equals 0.6366197723675814 quadrant.
Relationship context
Both Radian and Quadrant are converted by fixed multiples of the radian. Multiplying by (rad per rad) ÷ (rad per quadrant) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Radian (rad) | Quadrant (quadrant) |
|---|---|
| 0.1 | 0.0636619772 |
| 1 | 0.6366197724 |
| 2 | 1.2732395447 |
| 3 | 1.9098593171 |
| 4 | 2.5464790895 |
| 5 | 3.1830988618 |
| 6 | 3.8197186342 |
| 7 | 4.4563384066 |
| 8 | 5.0929581789 |
| 9 | 5.7295779513 |
| Radian (rad) | Quadrant (quadrant) |
|---|---|
| 10 | 6.3661977237 |
| 20 | 12.7323954474 |
| 30 | 19.098593171 |
| 40 | 25.4647908947 |
| 50 | 31.8309886184 |
| 60 | 38.1971863421 |
| 70 | 44.5633840657 |
| 80 | 50.9295817894 |
| 90 | 57.2957795131 |
| 100 | 63.6619772368 |