Radian to Minute of Angle (MOA) Converter
Angle · unit-converter
Convert Radian 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 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.
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 radians to minutes of angle (moa)
1 radian equals 3437.7467707849396 minute of angle (moa) in this tool (via radian):
1 rad = (1 rad ÷ 0.0002908882086657216 rad) moa = 3437.7467707849396 moa
Each radian carries 1 rad and each minute of angle (moa) 0.0002908882086657216 rad, so one rad equals 1 ÷ 0.0002908882086657216 moa.
Let θ(rad) be the angle in Radian (rad), and θ(moa) in Minute of Angle (MOA) (moa). Then:
θ(moa) = θ(rad) × (1 / 0.0002908882086657216)
Equivalently, divide by how many rad fit into one moa (rad per moa divided by rad per rad):
θ(moa) = θ(rad) ÷ 0.0002908882086657216
Examples
Example #1: Convert 1 rad to minute of angle (moa)
1 rad = 1 rad × (1/0.0002908882086657216) moa = 3437.74677078 moa
1 rad = 1 rad ÷ 0.0002908882086657216 = 3437.74677078 moa
1 rad × (1/0.0002908882086657216) = 3,437.746771 moa
Example #2: Convert 10 rad to minute of angle (moa)
10 rad = 10 rad × (1/0.0002908882086657216) moa = 34377.4677078 moa
10 rad = 10 rad ÷ 0.0002908882086657216 = 34377.4677078 moa
10 rad × (1/0.0002908882086657216) = 34,377.467708 moa
Summary
To convert Radian to Minute of Angle (MOA), multiply the value in rad by (1 rad per rad) / (0.0002908882086657216 rad per moa). Equivalently: value_moa = value_rad × (1 / 0.0002908882086657216). Numerically, 1 rad equals 3437.7467707849396 moa.
Relationship context
Both Radian and Minute of Angle (MOA) are converted by fixed multiples of the radian. Multiplying by (rad per rad) ÷ (rad per moa) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Radian (rad) | Minute of Angle (MOA) (moa) |
|---|---|
| 0.1 | 343.774677078 |
| 1 | 3,437.74677078 |
| 2 | 6,875.49354157 |
| 3 | 10,313.2403124 |
| 4 | 13,750.9870831 |
| 5 | 17,188.7338539 |
| 6 | 20,626.4806247 |
| 7 | 24,064.2273955 |
| 8 | 27,501.9741663 |
| 9 | 30,939.7209371 |
| Radian (rad) | Minute of Angle (MOA) (moa) |
|---|---|
| 10 | 34,377.4677078 |
| 20 | 68,754.9354157 |
| 30 | 103,132.403124 |
| 40 | 137,509.870831 |
| 50 | 171,887.338539 |
| 60 | 206,264.806247 |
| 70 | 240,642.273955 |
| 80 | 275,019.741663 |
| 90 | 309,397.209371 |
| 100 | 343,774.677078 |