Milliradian to Arc Second Converter
Angle · unit-converter
Convert Milliradian 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
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 milliradians to arc seconds
1 milliradian equals 206.26480624709637 arc second in this tool (via radian):
1 mrad = (0.001 rad ÷ 0.00000484813681109536 rad) arcsec = 206.26480624709637 arcsec
Each milliradian carries 0.001 rad and each arc second 0.00000484813681109536 rad, so one mrad equals 0.001 ÷ 0.00000484813681109536 arcsec.
Let θ(mrad) be the angle in Milliradian (mrad), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(mrad) × (0.001 / 0.00000484813681109536)
Equivalently, divide by how many mrad fit into one arcsec (rad per arcsec divided by rad per mrad):
θ(arcsec) = θ(mrad) ÷ 0.0048481368110953596
Examples
Example #1: Convert 1 mrad to arc second
1 mrad = 1 mrad × (0.001/0.00000484813681109536) arcsec = 206.264806247 arcsec
1 mrad = 1 mrad ÷ 0.0048481368110953596 = 206.264806247 arcsec
1 mrad × (0.001/0.00000484813681109536) = 206.264806 arcsec
Example #2: Convert 10 mrad to arc second
10 mrad = 10 mrad × (0.001/0.00000484813681109536) arcsec = 2062.64806247 arcsec
10 mrad = 10 mrad ÷ 0.0048481368110953596 = 2062.64806247 arcsec
10 mrad × (0.001/0.00000484813681109536) = 2,062.648062 arcsec
Summary
To convert Milliradian to Arc Second, multiply the value in mrad by (0.001 rad per mrad) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_mrad × (0.001 / 0.00000484813681109536). Numerically, 1 mrad equals 206.26480624709637 arcsec.
Relationship context
Both Milliradian and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per mrad) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Milliradian (mrad) | Arc Second (arcsec) |
|---|---|
| 0.1 | 20.6264806247 |
| 1 | 206.264806247 |
| 2 | 412.529612494 |
| 3 | 618.794418741 |
| 4 | 825.059224988 |
| 5 | 1,031.32403124 |
| 6 | 1,237.58883748 |
| 7 | 1,443.85364373 |
| 8 | 1,650.11844998 |
| 9 | 1,856.38325622 |
| Milliradian (mrad) | Arc Second (arcsec) |
|---|---|
| 10 | 2,062.64806247 |
| 20 | 4,125.29612494 |
| 30 | 6,187.94418741 |
| 40 | 8,250.59224988 |
| 50 | 10,313.2403124 |
| 60 | 12,375.8883748 |
| 70 | 14,438.5364373 |
| 80 | 16,501.1844998 |
| 90 | 18,563.8325622 |
| 100 | 20,626.4806247 |