Minute of Angle (MOA) to Milliradian Converter
Angle · unit-converter
Convert Minute of Angle (MOA) to Milliradian 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
How to convert minutes of angle (moa) to milliradians
1 minute of angle (moa) equals 0.29088820866572157 milliradian in this tool (via radian):
1 moa = (0.0002908882086657216 rad ÷ 0.001 rad) mrad = 0.29088820866572157 mrad
Each minute of angle (moa) carries 0.0002908882086657216 rad and each milliradian 0.001 rad, so one moa equals 0.0002908882086657216 ÷ 0.001 mrad.
Let θ(moa) be the angle in Minute of Angle (MOA) (moa), and θ(mrad) in Milliradian (mrad). Then:
θ(mrad) = θ(moa) × (0.0002908882086657216 / 0.001)
Equivalently, divide by how many moa fit into one mrad (rad per mrad divided by rad per moa):
θ(mrad) = θ(moa) ÷ 3.4377467707849396
Examples
Example #1: Convert 1 moa to milliradian
1 moa = 1 moa × (0.0002908882086657216/0.001) mrad = 0.2908882087 mrad
1 moa = 1 moa ÷ 3.4377467707849396 = 0.2908882087 mrad
1 moa × (0.0002908882086657216/0.001) = 0.290888 mrad
Example #2: Convert 10 moa to milliradian
10 moa = 10 moa × (0.0002908882086657216/0.001) mrad = 2.9088820867 mrad
10 moa = 10 moa ÷ 3.4377467707849396 = 2.9088820867 mrad
10 moa × (0.0002908882086657216/0.001) = 2.908882 mrad
Summary
To convert Minute of Angle (MOA) to Milliradian, multiply the value in moa by (0.0002908882086657216 rad per moa) / (0.001 rad per mrad). Equivalently: value_mrad = value_moa × (0.0002908882086657216 / 0.001). Numerically, 1 moa equals 0.29088820866572157 mrad.
Relationship context
Both Minute of Angle (MOA) and Milliradian are converted by fixed multiples of the radian. Multiplying by (rad per moa) ÷ (rad per mrad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Minute of Angle (MOA) (moa) | Milliradian (mrad) |
|---|---|
| 0.1 | 0.0290888209 |
| 1 | 0.2908882087 |
| 2 | 0.5817764173 |
| 3 | 0.872664626 |
| 4 | 1.1635528347 |
| 5 | 1.4544410433 |
| 6 | 1.745329252 |
| 7 | 2.0362174607 |
| 8 | 2.3271056693 |
| 9 | 2.617993878 |
| Minute of Angle (MOA) (moa) | Milliradian (mrad) |
|---|---|
| 10 | 2.9088820867 |
| 20 | 5.8177641733 |
| 30 | 8.72664626 |
| 40 | 11.6355283466 |
| 50 | 14.5444104333 |
| 60 | 17.4532925199 |
| 70 | 20.3621746066 |
| 80 | 23.2710566933 |
| 90 | 26.1799387799 |
| 100 | 29.0888208666 |