Arc Second to Microradian Converter
Angle · unit-converter
Convert Arc Second 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 Second
An arc second is 1/60 of an arc minute or 1/3600 of a degree. Common in astronomy and very fine angular resolution.
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 seconds to microradians
1 arc second equals 4.84813681109536 microradian in this tool (via radian):
1 arcsec = (0.00000484813681109536 rad ÷ 0.000001 rad) urad = 4.84813681109536 urad
Each arc second carries 0.00000484813681109536 rad and each microradian 0.000001 rad, so one arcsec equals 0.00000484813681109536 ÷ 0.000001 urad.
Let θ(arcsec) be the angle in Arc Second (arcsec), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(arcsec) × (0.00000484813681109536 / 0.000001)
Equivalently, divide by how many arcsec fit into one urad (rad per urad divided by rad per arcsec):
θ(urad) = θ(arcsec) ÷ 0.20626480624709634
Examples
Example #1: Convert 1 arcsec to microradian
1 arcsec = 1 arcsec × (0.00000484813681109536/0.000001) urad = 4.8481368111 urad
1 arcsec = 1 arcsec ÷ 0.20626480624709634 = 4.8481368111 urad
1 arcsec × (0.00000484813681109536/0.000001) = 4.848137 urad
Example #2: Convert 10 arcsec to microradian
10 arcsec = 10 arcsec × (0.00000484813681109536/0.000001) urad = 48.481368111 urad
10 arcsec = 10 arcsec ÷ 0.20626480624709634 = 48.481368111 urad
10 arcsec × (0.00000484813681109536/0.000001) = 48.481368 urad
Summary
To convert Arc Second to Microradian, multiply the value in arcsec by (0.00000484813681109536 rad per arcsec) / (0.000001 rad per urad). Equivalently: value_urad = value_arcsec × (0.00000484813681109536 / 0.000001). Numerically, 1 arcsec equals 4.84813681109536 urad.
Relationship context
Both Arc Second and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per arcsec) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Second (arcsec) | Microradian (urad) |
|---|---|
| 0.1 | 0.4848136811 |
| 1 | 4.8481368111 |
| 2 | 9.6962736222 |
| 3 | 14.5444104333 |
| 4 | 19.3925472444 |
| 5 | 24.2406840555 |
| 6 | 29.0888208666 |
| 7 | 33.9369576777 |
| 8 | 38.7850944888 |
| 9 | 43.6332312999 |
| Arc Second (arcsec) | Microradian (urad) |
|---|---|
| 10 | 48.481368111 |
| 20 | 96.9627362219 |
| 30 | 145.444104333 |
| 40 | 193.925472444 |
| 50 | 242.406840555 |
| 60 | 290.888208666 |
| 70 | 339.369576777 |
| 80 | 387.850944888 |
| 90 | 436.332312999 |
| 100 | 484.81368111 |