Quadrant to Milliradian Converter
Angle · unit-converter
Convert Quadrant to Milliradian 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
How to convert quadrants to milliradians
1 quadrant equals 1570.7963267948965 milliradian in this tool (via radian):
1 quadrant = (1.5707963267948966 rad ÷ 0.001 rad) mrad = 1570.7963267948965 mrad
Each quadrant carries 1.5707963267948966 rad and each milliradian 0.001 rad, so one quadrant equals 1.5707963267948966 ÷ 0.001 mrad.
Let θ(quadrant) be the angle in Quadrant (quadrant), and θ(mrad) in Milliradian (mrad). Then:
θ(mrad) = θ(quadrant) × (1.5707963267948966 / 0.001)
Equivalently, divide by how many quadrant fit into one mrad (rad per mrad divided by rad per quadrant):
θ(mrad) = θ(quadrant) ÷ 0.0006366197723675814
Examples
Example #1: Convert 1 quadrant to milliradian
1 quadrant = 1 quadrant × (1.5707963267948966/0.001) mrad = 1570.79632679 mrad
1 quadrant = 1 quadrant ÷ 0.0006366197723675814 = 1570.79632679 mrad
1 quadrant × (1.5707963267948966/0.001) = 1,570.796327 mrad
Example #2: Convert 10 quadrant to milliradian
10 quadrant = 10 quadrant × (1.5707963267948966/0.001) mrad = 15707.9632679 mrad
10 quadrant = 10 quadrant ÷ 0.0006366197723675814 = 15707.9632679 mrad
10 quadrant × (1.5707963267948966/0.001) = 15,707.963268 mrad
Summary
To convert Quadrant to Milliradian, multiply the value in quadrant by (1.5707963267948966 rad per quadrant) / (0.001 rad per mrad). Equivalently: value_mrad = value_quadrant × (1.5707963267948966 / 0.001). Numerically, 1 quadrant equals 1570.7963267948965 mrad.
Relationship context
Both Quadrant and Milliradian are converted by fixed multiples of the radian. Multiplying by (rad per quadrant) ÷ (rad per mrad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Quadrant (quadrant) | Milliradian (mrad) |
|---|---|
| 0.1 | 157.079632679 |
| 1 | 1,570.79632679 |
| 2 | 3,141.59265359 |
| 3 | 4,712.38898038 |
| 4 | 6,283.18530718 |
| 5 | 7,853.98163397 |
| 6 | 9,424.77796077 |
| 7 | 10,995.5742876 |
| 8 | 12,566.3706144 |
| 9 | 14,137.1669412 |
| Quadrant (quadrant) | Milliradian (mrad) |
|---|---|
| 10 | 15,707.9632679 |
| 20 | 31,415.9265359 |
| 30 | 47,123.8898038 |
| 40 | 62,831.8530718 |
| 50 | 78,539.8163397 |
| 60 | 94,247.7796077 |
| 70 | 109,955.742876 |
| 80 | 125,663.706144 |
| 90 | 141,371.669412 |
| 100 | 157,079.632679 |