Quadrant to Radian Converter
Angle · unit-converter
Convert Quadrant to Radian 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 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.
How to convert quadrants to radians
1 quadrant equals 1.5707963267948966 radian in this tool (via radian):
1 quadrant = (1.5707963267948966 rad ÷ 1 rad) rad = 1.5707963267948966 rad
Each quadrant carries 1.5707963267948966 rad and each radian 1 rad, so one quadrant equals 1.5707963267948966 ÷ 1 rad.
Let θ(quadrant) be the angle in Quadrant (quadrant), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(quadrant) × (1.5707963267948966 / 1)
Equivalently, divide by how many quadrant fit into one rad (rad per rad divided by rad per quadrant):
θ(rad) = θ(quadrant) ÷ 0.6366197723675814
Examples
Example #1: Convert 1 quadrant to radian
1 quadrant = 1 quadrant × (1.5707963267948966/1) rad = 1.5707963268 rad
1 quadrant = 1 quadrant ÷ 0.6366197723675814 = 1.5707963268 rad
1 quadrant × (1.5707963267948966/1) = 1.570796 rad
Example #2: Convert 10 quadrant to radian
10 quadrant = 10 quadrant × (1.5707963267948966/1) rad = 15.7079632679 rad
10 quadrant = 10 quadrant ÷ 0.6366197723675814 = 15.7079632679 rad
10 quadrant × (1.5707963267948966/1) = 15.707963 rad
Summary
To convert Quadrant to Radian, multiply the value in quadrant by (1.5707963267948966 rad per quadrant) / (1 rad per rad). Equivalently: value_rad = value_quadrant × (1.5707963267948966 / 1). Numerically, 1 quadrant equals 1.5707963267948966 rad.
Relationship context
Both Quadrant and Radian are converted by fixed multiples of the radian. Multiplying by (rad per quadrant) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Quadrant (quadrant) | Radian (rad) |
|---|---|
| 0.1 | 0.1570796327 |
| 1 | 1.5707963268 |
| 2 | 3.1415926536 |
| 3 | 4.7123889804 |
| 4 | 6.2831853072 |
| 5 | 7.853981634 |
| 6 | 9.4247779608 |
| 7 | 10.9955742876 |
| 8 | 12.5663706144 |
| 9 | 14.1371669412 |
| Quadrant (quadrant) | Radian (rad) |
|---|---|
| 10 | 15.7079632679 |
| 20 | 31.4159265359 |
| 30 | 47.1238898038 |
| 40 | 62.8318530718 |
| 50 | 78.5398163397 |
| 60 | 94.2477796077 |
| 70 | 109.955742876 |
| 80 | 125.663706144 |
| 90 | 141.371669412 |
| 100 | 157.079632679 |