Arc Second to Milliradian Converter
Angle · unit-converter
Convert Arc Second to Milliradian 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
How to convert arc seconds to milliradians
1 arc second equals 0.0048481368110953596 milliradian in this tool (via radian):
1 arcsec = (0.00000484813681109536 rad ÷ 0.001 rad) mrad = 0.0048481368110953596 mrad
Each arc second carries 0.00000484813681109536 rad and each milliradian 0.001 rad, so one arcsec equals 0.00000484813681109536 ÷ 0.001 mrad.
Let θ(arcsec) be the angle in Arc Second (arcsec), and θ(mrad) in Milliradian (mrad). Then:
θ(mrad) = θ(arcsec) × (0.00000484813681109536 / 0.001)
Equivalently, divide by how many arcsec fit into one mrad (rad per mrad divided by rad per arcsec):
θ(mrad) = θ(arcsec) ÷ 206.26480624709637
Examples
Example #1: Convert 1 arcsec to milliradian
1 arcsec = 1 arcsec × (0.00000484813681109536/0.001) mrad = 0.0048481368 mrad
1 arcsec = 1 arcsec ÷ 206.26480624709637 = 0.0048481368 mrad
1 arcsec × (0.00000484813681109536/0.001) = 0.004848 mrad
Example #2: Convert 10 arcsec to milliradian
10 arcsec = 10 arcsec × (0.00000484813681109536/0.001) mrad = 0.0484813681 mrad
10 arcsec = 10 arcsec ÷ 206.26480624709637 = 0.0484813681 mrad
10 arcsec × (0.00000484813681109536/0.001) = 0.048481 mrad
Summary
To convert Arc Second to Milliradian, multiply the value in arcsec by (0.00000484813681109536 rad per arcsec) / (0.001 rad per mrad). Equivalently: value_mrad = value_arcsec × (0.00000484813681109536 / 0.001). Numerically, 1 arcsec equals 0.0048481368110953596 mrad.
Relationship context
Both Arc Second and Milliradian are converted by fixed multiples of the radian. Multiplying by (rad per arcsec) ÷ (rad per mrad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Second (arcsec) | Milliradian (mrad) |
|---|---|
| 0.1 | 0.0004848137 |
| 1 | 0.0048481368 |
| 2 | 0.0096962736 |
| 3 | 0.0145444104 |
| 4 | 0.0193925472 |
| 5 | 0.0242406841 |
| 6 | 0.0290888209 |
| 7 | 0.0339369577 |
| 8 | 0.0387850945 |
| 9 | 0.0436332313 |
| Arc Second (arcsec) | Milliradian (mrad) |
|---|---|
| 10 | 0.0484813681 |
| 20 | 0.0969627362 |
| 30 | 0.1454441043 |
| 40 | 0.1939254724 |
| 50 | 0.2424068406 |
| 60 | 0.2908882087 |
| 70 | 0.3393695768 |
| 80 | 0.3878509449 |
| 90 | 0.436332313 |
| 100 | 0.4848136811 |