Minute of Angle (MOA) to Quadrant Converter
Angle · unit-converter
Convert Minute of Angle (MOA) 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 Minute of Angle (MOA)
Minute of angle (MOA) equals one arc minute (1/60 degree). It is widely used in firearms optics and precision aiming.
About Quadrant
A quadrant is one quarter-turn: 90° or π/2 radians. It is useful in geometric and directional notation.
How to convert minutes of angle (moa) to quadrants
1 minute of angle (moa) equals 0.00018518518518518518 quadrant in this tool (via radian):
1 moa = (0.0002908882086657216 rad ÷ 1.5707963267948966 rad) quadrant = 0.00018518518518518518 quadrant
Each minute of angle (moa) carries 0.0002908882086657216 rad and each quadrant 1.5707963267948966 rad, so one moa equals 0.0002908882086657216 ÷ 1.5707963267948966 quadrant.
Let θ(moa) be the angle in Minute of Angle (MOA) (moa), and θ(quadrant) in Quadrant (quadrant). Then:
θ(quadrant) = θ(moa) × (0.0002908882086657216 / 1.5707963267948966)
Equivalently, divide by how many moa fit into one quadrant (rad per quadrant divided by rad per moa):
θ(quadrant) = θ(moa) ÷ 5400
Examples
Example #1: Convert 1 moa to quadrant
1 moa = 1 moa × (0.0002908882086657216/1.5707963267948966) quadrant = 0.0001851852 quadrant
1 moa = 1 moa ÷ 5400 = 0.0001851852 quadrant
1 moa × (0.0002908882086657216/1.5707963267948966) = 0.000185 quadrant
Example #2: Convert 10 moa to quadrant
10 moa = 10 moa × (0.0002908882086657216/1.5707963267948966) quadrant = 0.0018518519 quadrant
10 moa = 10 moa ÷ 5400 = 0.0018518519 quadrant
10 moa × (0.0002908882086657216/1.5707963267948966) = 0.001852 quadrant
Summary
To convert Minute of Angle (MOA) to Quadrant, multiply the value in moa by (0.0002908882086657216 rad per moa) / (1.5707963267948966 rad per quadrant). Equivalently: value_quadrant = value_moa × (0.0002908882086657216 / 1.5707963267948966). Numerically, 1 moa equals 0.00018518518518518518 quadrant.
Relationship context
Both Minute of Angle (MOA) and Quadrant are converted by fixed multiples of the radian. Multiplying by (rad per moa) ÷ (rad per quadrant) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Minute of Angle (MOA) (moa) | Quadrant (quadrant) |
|---|---|
| 0.1 | 0.0000185185 |
| 1 | 0.0001851852 |
| 2 | 0.0003703704 |
| 3 | 0.0005555556 |
| 4 | 0.0007407407 |
| 5 | 0.0009259259 |
| 6 | 0.0011111111 |
| 7 | 0.0012962963 |
| 8 | 0.0014814815 |
| 9 | 0.0016666667 |
| Minute of Angle (MOA) (moa) | Quadrant (quadrant) |
|---|---|
| 10 | 0.0018518519 |
| 20 | 0.0037037037 |
| 30 | 0.0055555556 |
| 40 | 0.0074074074 |
| 50 | 0.0092592593 |
| 60 | 0.0111111111 |
| 70 | 0.012962963 |
| 80 | 0.0148148148 |
| 90 | 0.0166666667 |
| 100 | 0.0185185185 |