Minute of Angle (MOA) to Arc Second Converter
Angle · unit-converter
Convert Minute of Angle (MOA) 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 Minute of Angle (MOA)
Minute of angle (MOA) equals one arc minute (1/60 degree). It is widely used in firearms optics and precision aiming.
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 minutes of angle (moa) to arc seconds
1 minute of angle (moa) equals 60 arc second in this tool (via radian):
1 moa = (0.0002908882086657216 rad ÷ 0.00000484813681109536 rad) arcsec = 60 arcsec
Each minute of angle (moa) carries 0.0002908882086657216 rad and each arc second 0.00000484813681109536 rad, so one moa equals 0.0002908882086657216 ÷ 0.00000484813681109536 arcsec.
Let θ(moa) be the angle in Minute of Angle (MOA) (moa), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(moa) × (0.0002908882086657216 / 0.00000484813681109536)
Equivalently, divide by how many moa fit into one arcsec (rad per arcsec divided by rad per moa):
θ(arcsec) = θ(moa) ÷ 0.016666666666666666
Examples
Example #1: Convert 1 moa to arc second
1 moa = 1 moa × (0.0002908882086657216/0.00000484813681109536) arcsec = 60 arcsec
1 moa = 1 moa ÷ 0.016666666666666666 = 60 arcsec
1 moa × (0.0002908882086657216/0.00000484813681109536) = 60.000000 arcsec
Example #2: Convert 10 moa to arc second
10 moa = 10 moa × (0.0002908882086657216/0.00000484813681109536) arcsec = 600 arcsec
10 moa = 10 moa ÷ 0.016666666666666666 = 600 arcsec
10 moa × (0.0002908882086657216/0.00000484813681109536) = 600.000000 arcsec
Summary
To convert Minute of Angle (MOA) to Arc Second, multiply the value in moa by (0.0002908882086657216 rad per moa) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_moa × (0.0002908882086657216 / 0.00000484813681109536). Numerically, 1 moa equals 60 arcsec.
Relationship context
Both Minute of Angle (MOA) and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per moa) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Minute of Angle (MOA) (moa) | Arc Second (arcsec) |
|---|---|
| 0.1 | 6 |
| 1 | 60 |
| 2 | 120 |
| 3 | 180 |
| 4 | 240 |
| 5 | 300 |
| 6 | 360 |
| 7 | 420 |
| 8 | 480 |
| 9 | 540 |
| Minute of Angle (MOA) (moa) | Arc Second (arcsec) |
|---|---|
| 10 | 600 |
| 20 | 1,200 |
| 30 | 1,800 |
| 40 | 2,400 |
| 50 | 3,000 |
| 60 | 3,600 |
| 70 | 4,200 |
| 80 | 4,800 |
| 90 | 5,400 |
| 100 | 6,000 |