Mil to Arc Second Converter
Angle · unit-converter
Convert Mil 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 Mil
NATO mils split a full circle into 6,400 parts for artillery and tactical optics; 1 mil = 2π/6400 rad.
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 mils (nato, 6400) to arc seconds
1 mil equals 202.5 arc second in this tool (via radian):
1 mil = (0.0009817477042468104 rad ÷ 0.00000484813681109536 rad) arcsec = 202.5 arcsec
Each mil carries 0.0009817477042468104 rad and each arc second 0.00000484813681109536 rad, so one mil equals 0.0009817477042468104 ÷ 0.00000484813681109536 arcsec.
Let θ(mil) be the angle in Mil (mil), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(mil) × (0.0009817477042468104 / 0.00000484813681109536)
Equivalently, divide by how many mil fit into one arcsec (rad per arcsec divided by rad per mil):
θ(arcsec) = θ(mil) ÷ 0.0049382716049382715
Examples
Example #1: Convert 1 mil to arc second
1 mil = 1 mil × (0.0009817477042468104/0.00000484813681109536) arcsec = 202.5 arcsec
1 mil = 1 mil ÷ 0.0049382716049382715 = 202.5 arcsec
1 mil × (0.0009817477042468104/0.00000484813681109536) = 202.500000 arcsec
Example #2: Convert 10 mil to arc second
10 mil = 10 mil × (0.0009817477042468104/0.00000484813681109536) arcsec = 2025 arcsec
10 mil = 10 mil ÷ 0.0049382716049382715 = 2025 arcsec
10 mil × (0.0009817477042468104/0.00000484813681109536) = 2,025.000000 arcsec
Summary
To convert Mil to Arc Second, multiply the value in mil by (0.0009817477042468104 rad per mil) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_mil × (0.0009817477042468104 / 0.00000484813681109536). Numerically, 1 mil equals 202.5 arcsec.
Relationship context
Both Mil and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per mil) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Mil (mil) | Arc Second (arcsec) |
|---|---|
| 0.1 | 20.25 |
| 1 | 202.5 |
| 2 | 405 |
| 3 | 607.5 |
| 4 | 810 |
| 5 | 1,012.5 |
| 6 | 1,215 |
| 7 | 1,417.5 |
| 8 | 1,620 |
| 9 | 1,822.5 |
| Mil (mil) | Arc Second (arcsec) |
|---|---|
| 10 | 2,025 |
| 20 | 4,050 |
| 30 | 6,075 |
| 40 | 8,100 |
| 50 | 10,125 |
| 60 | 12,150 |
| 70 | 14,175 |
| 80 | 16,200 |
| 90 | 18,225 |
| 100 | 20,250 |