Arc Minute to Milliradian Converter
Angle · unit-converter
Convert Arc Minute 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 Arc Minute
An arc minute is 1/60 of a degree (π/10,800 rad). Used in astronomy, navigation, and precision optics (MOA).
About Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
How to convert arc minutes to milliradians
1 arc minute equals 0.29088820866572157 milliradian in this tool (via radian):
1 arcmin = (0.0002908882086657216 rad ÷ 0.001 rad) mrad = 0.29088820866572157 mrad
Each arc minute carries 0.0002908882086657216 rad and each milliradian 0.001 rad, so one arcmin equals 0.0002908882086657216 ÷ 0.001 mrad.
Let θ(arcmin) be the angle in Arc Minute (arcmin), and θ(mrad) in Milliradian (mrad). Then:
θ(mrad) = θ(arcmin) × (0.0002908882086657216 / 0.001)
Equivalently, divide by how many arcmin fit into one mrad (rad per mrad divided by rad per arcmin):
θ(mrad) = θ(arcmin) ÷ 3.4377467707849396
Examples
Example #1: Convert 1 arcmin to milliradian
1 arcmin = 1 arcmin × (0.0002908882086657216/0.001) mrad = 0.2908882087 mrad
1 arcmin = 1 arcmin ÷ 3.4377467707849396 = 0.2908882087 mrad
1 arcmin × (0.0002908882086657216/0.001) = 0.290888 mrad
Example #2: Convert 10 arcmin to milliradian
10 arcmin = 10 arcmin × (0.0002908882086657216/0.001) mrad = 2.9088820867 mrad
10 arcmin = 10 arcmin ÷ 3.4377467707849396 = 2.9088820867 mrad
10 arcmin × (0.0002908882086657216/0.001) = 2.908882 mrad
Summary
To convert Arc Minute to Milliradian, multiply the value in arcmin by (0.0002908882086657216 rad per arcmin) / (0.001 rad per mrad). Equivalently: value_mrad = value_arcmin × (0.0002908882086657216 / 0.001). Numerically, 1 arcmin equals 0.29088820866572157 mrad.
Relationship context
Both Arc Minute and Milliradian are converted by fixed multiples of the radian. Multiplying by (rad per arcmin) ÷ (rad per mrad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Minute (arcmin) | 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 |
| Arc Minute (arcmin) | 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 |