Minute of Angle (MOA) to Radian Converter
Angle · unit-converter
Convert Minute of Angle (MOA) to Radian 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 Radian
The radian is the SI unit of plane angle. One radian is the angle subtended by an arc equal to the radius; 2π rad = one full circle.
How to convert minutes of angle (moa) to radians
1 minute of angle (moa) equals 0.0002908882086657216 radian in this tool (via radian):
1 moa = (0.0002908882086657216 rad ÷ 1 rad) rad = 0.0002908882086657216 rad
Each minute of angle (moa) carries 0.0002908882086657216 rad and each radian 1 rad, so one moa equals 0.0002908882086657216 ÷ 1 rad.
Let θ(moa) be the angle in Minute of Angle (MOA) (moa), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(moa) × (0.0002908882086657216 / 1)
Equivalently, divide by how many moa fit into one rad (rad per rad divided by rad per moa):
θ(rad) = θ(moa) ÷ 3437.7467707849396
Examples
Example #1: Convert 1 moa to radian
1 moa = 1 moa × (0.0002908882086657216/1) rad = 0.0002908882 rad
1 moa = 1 moa ÷ 3437.7467707849396 = 0.0002908882 rad
1 moa × (0.0002908882086657216/1) = 0.000291 rad
Example #2: Convert 10 moa to radian
10 moa = 10 moa × (0.0002908882086657216/1) rad = 0.0029088821 rad
10 moa = 10 moa ÷ 3437.7467707849396 = 0.0029088821 rad
10 moa × (0.0002908882086657216/1) = 0.002909 rad
Summary
To convert Minute of Angle (MOA) to Radian, multiply the value in moa by (0.0002908882086657216 rad per moa) / (1 rad per rad). Equivalently: value_rad = value_moa × (0.0002908882086657216 / 1). Numerically, 1 moa equals 0.0002908882086657216 rad.
Relationship context
Both Minute of Angle (MOA) and Radian are converted by fixed multiples of the radian. Multiplying by (rad per moa) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Minute of Angle (MOA) (moa) | Radian (rad) |
|---|---|
| 0.1 | 0.0000290888 |
| 1 | 0.0002908882 |
| 2 | 0.0005817764 |
| 3 | 0.0008726646 |
| 4 | 0.0011635528 |
| 5 | 0.001454441 |
| 6 | 0.0017453293 |
| 7 | 0.0020362175 |
| 8 | 0.0023271057 |
| 9 | 0.0026179939 |
| Minute of Angle (MOA) (moa) | Radian (rad) |
|---|---|
| 10 | 0.0029088821 |
| 20 | 0.0058177642 |
| 30 | 0.0087266463 |
| 40 | 0.0116355283 |
| 50 | 0.0145444104 |
| 60 | 0.0174532925 |
| 70 | 0.0203621746 |
| 80 | 0.0232710567 |
| 90 | 0.0261799388 |
| 100 | 0.0290888209 |