Arc Second to Minute of Angle (MOA) Converter
Angle · unit-converter
Convert Arc Second to Minute of Angle (MOA) 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 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.
How to convert arc seconds to minutes of angle (moa)
1 arc second equals 0.016666666666666666 minute of angle (moa) in this tool (via radian):
1 arcsec = (0.00000484813681109536 rad ÷ 0.0002908882086657216 rad) moa = 0.016666666666666666 moa
Each arc second carries 0.00000484813681109536 rad and each minute of angle (moa) 0.0002908882086657216 rad, so one arcsec equals 0.00000484813681109536 ÷ 0.0002908882086657216 moa.
Let θ(arcsec) be the angle in Arc Second (arcsec), and θ(moa) in Minute of Angle (MOA) (moa). Then:
θ(moa) = θ(arcsec) × (0.00000484813681109536 / 0.0002908882086657216)
Equivalently, divide by how many arcsec fit into one moa (rad per moa divided by rad per arcsec):
θ(moa) = θ(arcsec) ÷ 60
Examples
Example #1: Convert 1 arcsec to minute of angle (moa)
1 arcsec = 1 arcsec × (0.00000484813681109536/0.0002908882086657216) moa = 0.0166666667 moa
1 arcsec = 1 arcsec ÷ 60 = 0.0166666667 moa
1 arcsec × (0.00000484813681109536/0.0002908882086657216) = 0.016667 moa
Example #2: Convert 10 arcsec to minute of angle (moa)
10 arcsec = 10 arcsec × (0.00000484813681109536/0.0002908882086657216) moa = 0.1666666667 moa
10 arcsec = 10 arcsec ÷ 60 = 0.1666666667 moa
10 arcsec × (0.00000484813681109536/0.0002908882086657216) = 0.166667 moa
Summary
To convert Arc Second to Minute of Angle (MOA), multiply the value in arcsec by (0.00000484813681109536 rad per arcsec) / (0.0002908882086657216 rad per moa). Equivalently: value_moa = value_arcsec × (0.00000484813681109536 / 0.0002908882086657216). Numerically, 1 arcsec equals 0.016666666666666666 moa.
Relationship context
Both Arc Second and Minute of Angle (MOA) are converted by fixed multiples of the radian. Multiplying by (rad per arcsec) ÷ (rad per moa) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Second (arcsec) | Minute of Angle (MOA) (moa) |
|---|---|
| 0.1 | 0.0016666667 |
| 1 | 0.0166666667 |
| 2 | 0.0333333333 |
| 3 | 0.05 |
| 4 | 0.0666666667 |
| 5 | 0.0833333333 |
| 6 | 0.1 |
| 7 | 0.1166666667 |
| 8 | 0.1333333333 |
| 9 | 0.15 |
| Arc Second (arcsec) | Minute of Angle (MOA) (moa) |
|---|---|
| 10 | 0.1666666667 |
| 20 | 0.3333333333 |
| 30 | 0.5 |
| 40 | 0.6666666667 |
| 50 | 0.8333333333 |
| 60 | 1 |
| 70 | 1.1666666667 |
| 80 | 1.3333333333 |
| 90 | 1.5 |
| 100 | 1.6666666667 |