Minute of Angle (MOA) to Microradian Converter
Angle · unit-converter
Convert Minute of Angle (MOA) 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 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 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 minutes of angle (moa) to microradians
1 minute of angle (moa) equals 290.8882086657216 microradian in this tool (via radian):
1 moa = (0.0002908882086657216 rad ÷ 0.000001 rad) urad = 290.8882086657216 urad
Each minute of angle (moa) carries 0.0002908882086657216 rad and each microradian 0.000001 rad, so one moa equals 0.0002908882086657216 ÷ 0.000001 urad.
Let θ(moa) be the angle in Minute of Angle (MOA) (moa), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(moa) × (0.0002908882086657216 / 0.000001)
Equivalently, divide by how many moa fit into one urad (rad per urad divided by rad per moa):
θ(urad) = θ(moa) ÷ 0.003437746770784939
Examples
Example #1: Convert 1 moa to microradian
1 moa = 1 moa × (0.0002908882086657216/0.000001) urad = 290.888208666 urad
1 moa = 1 moa ÷ 0.003437746770784939 = 290.888208666 urad
1 moa × (0.0002908882086657216/0.000001) = 290.888209 urad
Example #2: Convert 10 moa to microradian
10 moa = 10 moa × (0.0002908882086657216/0.000001) urad = 2908.88208666 urad
10 moa = 10 moa ÷ 0.003437746770784939 = 2908.88208666 urad
10 moa × (0.0002908882086657216/0.000001) = 2,908.882087 urad
Summary
To convert Minute of Angle (MOA) to Microradian, multiply the value in moa by (0.0002908882086657216 rad per moa) / (0.000001 rad per urad). Equivalently: value_urad = value_moa × (0.0002908882086657216 / 0.000001). Numerically, 1 moa equals 290.8882086657216 urad.
Relationship context
Both Minute of Angle (MOA) and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per moa) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Minute of Angle (MOA) (moa) | Microradian (urad) |
|---|---|
| 0.1 | 29.0888208666 |
| 1 | 290.888208666 |
| 2 | 581.776417331 |
| 3 | 872.664625997 |
| 4 | 1,163.55283466 |
| 5 | 1,454.44104333 |
| 6 | 1,745.32925199 |
| 7 | 2,036.21746066 |
| 8 | 2,327.10566933 |
| 9 | 2,617.99387799 |
| Minute of Angle (MOA) (moa) | Microradian (urad) |
|---|---|
| 10 | 2,908.88208666 |
| 20 | 5,817.76417331 |
| 30 | 8,726.64625997 |
| 40 | 11,635.5283466 |
| 50 | 14,544.4104333 |
| 60 | 17,453.2925199 |
| 70 | 20,362.1746066 |
| 80 | 23,271.0566933 |
| 90 | 26,179.9387799 |
| 100 | 29,088.8208666 |