Quadrant to Microradian Converter
Angle · unit-converter
Convert Quadrant to Microradian 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 Microradian
A microradian is 1/1,000,000 radian. It is used for very small angular deviations in optics and precision metrology.
How to convert quadrants to microradians
1 quadrant equals 1570796.3267948967 microradian in this tool (via radian):
1 quadrant = (1.5707963267948966 rad ÷ 0.000001 rad) urad = 1570796.3267948967 urad
Each quadrant carries 1.5707963267948966 rad and each microradian 0.000001 rad, so one quadrant equals 1.5707963267948966 ÷ 0.000001 urad.
Let θ(quadrant) be the angle in Quadrant (quadrant), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(quadrant) × (1.5707963267948966 / 0.000001)
Equivalently, divide by how many quadrant fit into one urad (rad per urad divided by rad per quadrant):
θ(urad) = θ(quadrant) ÷ 6.366197723675813e-7
Examples
Example #1: Convert 1 quadrant to microradian
1 quadrant = 1 quadrant × (1.5707963267948966/0.000001) urad = 1570796.3267900001 urad
1 quadrant = 1 quadrant ÷ 6.366197723675813e-7 = 1570796.3267900001 urad
1 quadrant × (1.5707963267948966/0.000001) = 1,570,796.326795 urad
Example #2: Convert 10 quadrant to microradian
10 quadrant = 10 quadrant × (1.5707963267948966/0.000001) urad = 15707963.2678999994 urad
10 quadrant = 10 quadrant ÷ 6.366197723675813e-7 = 15707963.2678999994 urad
10 quadrant × (1.5707963267948966/0.000001) = 15,707,963.267949 urad
Summary
To convert Quadrant to Microradian, multiply the value in quadrant by (1.5707963267948966 rad per quadrant) / (0.000001 rad per urad). Equivalently: value_urad = value_quadrant × (1.5707963267948966 / 0.000001). Numerically, 1 quadrant equals 1570796.3267948967 urad.
Relationship context
Both Quadrant and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per quadrant) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Quadrant (quadrant) | Microradian (urad) |
|---|---|
| 0.1 | 157,079.632679 |
| 1 | 1,570,796.3267900001 |
| 2 | 3,141,592.6535899998 |
| 3 | 4,712,388.9803799996 |
| 4 | 6,283,185.3071799995 |
| 5 | 7,853,981.6339699998 |
| 6 | 9,424,777.9607699998 |
| 7 | 10,995,574.2875999995 |
| 8 | 12,566,370.6143999994 |
| 9 | 14,137,166.9411999993 |
| Quadrant (quadrant) | Microradian (urad) |
|---|---|
| 10 | 15,707,963.2678999994 |
| 20 | 31,415,926.5359000005 |
| 30 | 47,123,889.8038000017 |
| 40 | 62,831,853.071800001 |
| 50 | 78,539,816.3396999985 |
| 60 | 94,247,779.6077000052 |
| 70 | 109,955,742.876000002 |
| 80 | 125,663,706.1439999938 |
| 90 | 141,371,669.4120000005 |
| 100 | 157,079,632.6789999902 |