Microradian to Arc Second Converter
Angle · unit-converter
Convert Microradian to Arc Second 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 Microradian
A microradian is 1/1,000,000 radian. It is used for very small angular deviations in optics and precision metrology.
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.
How to convert microradians to arc seconds
1 microradian equals 0.20626480624709634 arc second in this tool (via radian):
1 urad = (0.000001 rad ÷ 0.00000484813681109536 rad) arcsec = 0.20626480624709634 arcsec
Each microradian carries 0.000001 rad and each arc second 0.00000484813681109536 rad, so one urad equals 0.000001 ÷ 0.00000484813681109536 arcsec.
Let θ(urad) be the angle in Microradian (urad), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(urad) × (0.000001 / 0.00000484813681109536)
Equivalently, divide by how many urad fit into one arcsec (rad per arcsec divided by rad per urad):
θ(arcsec) = θ(urad) ÷ 4.84813681109536
Examples
Example #1: Convert 1 urad to arc second
1 urad = 1 urad × (0.000001/0.00000484813681109536) arcsec = 0.2062648062 arcsec
1 urad = 1 urad ÷ 4.84813681109536 = 0.2062648062 arcsec
1 urad × (0.000001/0.00000484813681109536) = 0.206265 arcsec
Example #2: Convert 10 urad to arc second
10 urad = 10 urad × (0.000001/0.00000484813681109536) arcsec = 2.0626480625 arcsec
10 urad = 10 urad ÷ 4.84813681109536 = 2.0626480625 arcsec
10 urad × (0.000001/0.00000484813681109536) = 2.062648 arcsec
Summary
To convert Microradian to Arc Second, multiply the value in urad by (0.000001 rad per urad) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_urad × (0.000001 / 0.00000484813681109536). Numerically, 1 urad equals 0.20626480624709634 arcsec.
Relationship context
Both Microradian and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per urad) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Microradian (urad) | Arc Second (arcsec) |
|---|---|
| 0.1 | 0.0206264806 |
| 1 | 0.2062648062 |
| 2 | 0.4125296125 |
| 3 | 0.6187944187 |
| 4 | 0.825059225 |
| 5 | 1.0313240312 |
| 6 | 1.2375888375 |
| 7 | 1.4438536437 |
| 8 | 1.65011845 |
| 9 | 1.8563832562 |
| Microradian (urad) | Arc Second (arcsec) |
|---|---|
| 10 | 2.0626480625 |
| 20 | 4.1252961249 |
| 30 | 6.1879441874 |
| 40 | 8.2505922499 |
| 50 | 10.3132403124 |
| 60 | 12.3758883748 |
| 70 | 14.4385364373 |
| 80 | 16.5011844998 |
| 90 | 18.5638325622 |
| 100 | 20.6264806247 |