Arc Minute to Microradian Converter
Angle · unit-converter
Convert Arc Minute 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 Arc Minute
An arc minute is 1/60 of a degree (π/10,800 rad). Used in astronomy, navigation, and precision optics (MOA).
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 arc minutes to microradians
1 arc minute equals 290.8882086657216 microradian in this tool (via radian):
1 arcmin = (0.0002908882086657216 rad ÷ 0.000001 rad) urad = 290.8882086657216 urad
Each arc minute carries 0.0002908882086657216 rad and each microradian 0.000001 rad, so one arcmin equals 0.0002908882086657216 ÷ 0.000001 urad.
Let θ(arcmin) be the angle in Arc Minute (arcmin), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(arcmin) × (0.0002908882086657216 / 0.000001)
Equivalently, divide by how many arcmin fit into one urad (rad per urad divided by rad per arcmin):
θ(urad) = θ(arcmin) ÷ 0.003437746770784939
Examples
Example #1: Convert 1 arcmin to microradian
1 arcmin = 1 arcmin × (0.0002908882086657216/0.000001) urad = 290.888208666 urad
1 arcmin = 1 arcmin ÷ 0.003437746770784939 = 290.888208666 urad
1 arcmin × (0.0002908882086657216/0.000001) = 290.888209 urad
Example #2: Convert 10 arcmin to microradian
10 arcmin = 10 arcmin × (0.0002908882086657216/0.000001) urad = 2908.88208666 urad
10 arcmin = 10 arcmin ÷ 0.003437746770784939 = 2908.88208666 urad
10 arcmin × (0.0002908882086657216/0.000001) = 2,908.882087 urad
Summary
To convert Arc Minute to Microradian, multiply the value in arcmin by (0.0002908882086657216 rad per arcmin) / (0.000001 rad per urad). Equivalently: value_urad = value_arcmin × (0.0002908882086657216 / 0.000001). Numerically, 1 arcmin equals 290.8882086657216 urad.
Relationship context
Both Arc Minute and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per arcmin) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Minute (arcmin) | 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 |
| Arc Minute (arcmin) | 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 |